{"paper_id":"4238ae1f-e7f8-4cdd-b762-bce50d5e9e3c","body_text":"Investigation into the prediction of arm joint rotation acceleration utilizing signal fusion and time-series network methodologies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Investigation into the prediction of arm joint rotation acceleration utilizing signal fusion and time-series network methodologies Yu Bai, XiaoRong Guan, Long He, Shi Cheng, Rui Zhang, Huibin Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5384176/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the present investigation, to enhance the precision of human movement intention detection, a dual-modality approach was proposed, integrating both surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing the nerve potential activity and the vibrational characteristics of muscle contractions, respectively, were utilized to train a predictive model for estimating arm joint rotational acceleration. Participants with intact shoulder joints were enrolled in this study, during which both MMG and sEMG signal were acquired using wireless sensor technology. In this research, The BiTCN-BiGRU-Attention algorithm, an integration of Bidirectional Temporal Convolutional Networks (BiTCN), Bidirectional GRU (BiGRU) architecture and Muti-Attention layer, was proposed for acceleration prediction. What’s more, the BiTCN-BiGRU-Attention algorithm was developed by combining the Black-winged Kite Algorithm (BKA) for the optimization of hyperparameters. The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm was employed to remove random noise of both MMG and sEMG signal from the acquired data. Various methodologies were employed to substantiate the superior performance of the CEEMDAN and BKA-BiTCN-BiGRU-Attention algorithm. Utilizing comparative analyses with conventional algorithms, including backpropagation neural networks (BP), random forests (RF), and support vector machines (SVM), the BKA-BiTCN-BiGRU-Attention model demonstrated superior predictive performance, yielding a prediction accuracy with mean squared error (MSE) of 0.00153, root mean squared error (RMSE) of 0.0128, mean absolute error (MAE) of 0.0098, and a R 2 of 0.990.The comparative analysis with conventional signal decomposition techniques, including Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Concurrent Ensemble Empirical Mode Decomposition (CEEMD), has revealed that the MMG and sEMG signal processed via the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm exhibit the minimum envelope entropy. This finding indicates that the resultant sub-signals derived from CEEMDAN decomposition are characterized by the lowest levels of random noise. The amalgamation of the sub-signals residing within the respective frequency band was executed, resulting in the formation of MMG and sEMG signal. Biological sciences/Biological techniques Physical sciences/Engineering Mechanomyography surface electromyography signal fusion Bidirectional Temporal Convolutional Networks Bidirectional GRU Attention mechanism Black-winged Kite algorithm Complete Ensemble Empirical Mode Decomposition with Adaptive Noise algorithm Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Note In the present study, we introduced an innovative approach for the extraction of multi-channel MMG and sEMG signal, alongside a predictive model for estimating shoulder joint acceleration. Human participants were engaged in the experimental procedures conducted within this study. Ethical clearance and authorization for all experimental procedures and protocols were obtained from the Medical Ethics Committee of Nanjing Medical University, with the approval number designated as 2021-SR109. 2. Introduction In recent years, there has been a marked surge in scholarly investigation into the domain of wearable exoskeletons and robotic appendages. Wearable exoskeletons have been utilized to a restricted degree within industrial and service sectors, primarily aimed at mitigating physical exertion and augmenting operational efficiency. Moreover, certain wearable exoskeleton devices are employed within the domain of medical rehabilitation to facilitate the restoration of mobility in patients suffering from limb injuries [1]. Wearable robotic appendages are distinguished from wearable exoskeletons by their purpose of endowing the user with an auxiliary limb, effectively serving as a 'third hand' or 'third leg'. This facilitates the execution of tasks that are unattainable through the user's unaided physical capabilities [2]. Wearable exoskeletons and wearable robotic limbs, albeit exhibiting distinct characteristics, converge in a fundamental prerequisite; they necessitate seamless operational synchronization with human operators. To facilitate effective collaboration between human limbs and wearable exoskeletons, it is imperative that the kinematic synchronization between the exoskeletal movements and the human body's motion is achieved. Moreover, the wearable robotic limbs must be capable of precisely interpreting the user's movement intentions to ensure accurate and harmonious coordination. To fulfill the stated objectives, it is imperative to conduct comprehensive research into the recognition of human movement intention, encompassing the classification of movements, the identification and forecasting of joint kinematics, as well as the recognition and prediction of the trajectory of limb endpoint movements [3]. The forecasting of human articulation and extremity motion has attracted considerable scholarly attention. Advanced deep learning methodologies have experienced swift progression lately. These methodologies diverge from conventional machine learning by focusing on discerning the underlying patterns and feature levels within data samples. Knowledge gleaned from such learning is instrumental in comprehending written content, images, and audio inputs. Gottlieb's work from 1998 delved into the activation sequences of muscles during deliberate single-joint actions, particularly swift elbow bending [4]. Jarić and colleagues, in 2006, examined the correlations between muscular kinetic indices and motion variables in intricate activities [5]. Mountjoy's team, in 2010, introduced a technique employing the swift orthogonal search technique to ascertain ideal joint angles for upper limb muscle simulations [6]. Crouch's group, in 2016, crafted a musculoskeletal simulation to anticipate hand and wrist actions from surface electromyography signals [7]. Ding and associates, also in 2016, tackled the difficulty of precisely inferring ongoing multi-joint actions from multi-channel surface EMG readings [8]. Sloot and co-authors, in 2018, scrutinized the analysis of joint forces and powers in walking, emphasizing irregular kinetic behaviors [9]. Xie and team, in 2020, applied a regression neural network fine-tuned by the golden ratio method to forecast lower limb joint angles utilizing diverse signal sources [10]. Qiu and colleagues, in 2021, suggested an algorithm for real-time learning and inferring human ambulatory intent for controlling lower limb exoskeletons [11]. Ren's group, in 2022, employed a Long Short-Term Memory (LSTM) algorithm to anticipate the paths of lower limb exoskeleton movement [12]. Zhong and others, in 2022, proposed a muscle synergy-guided adaptive network-based fuzzy inference system to predict uninterrupted knee joint actions, surpassing the efficacy of conventional numerical traits from individual sEMG channels [13]. Collectively, these investigations have propelled the field of human joint and limb movement prediction through a variety of innovative approaches and technological advancements. Surface electromyography (sEMG) is a non-invasive technique used to measure the electrical activity of muscles through electrodes placed on the skin. This method has gained significant attention in various fields, including rehabilitation, sports science, and human-computer interaction. The reliability and accuracy of sEMG signal acquisition are crucial for its effective application, and numerous studies have explored different aspects of this technology. The sEMG signals are generated by the electrical potential produced during muscle contractions. The voltage detected by the electrodes can be related to the activity of specific muscles, provided that proper electrode placement protocols are followed. The signal typically ranges from zero to several hundred microvolts as muscle activation occurs, making it essential to ensure signal reliability and minimize errors and artifacts during acquisition [14]. Additionally, advanced algorithms, including machine learning techniques, have been applied to classify gestures based on sEMG signals. Studies have shown that using deep learning models can significantly improve gesture recognition accuracy, making sEMG a powerful tool for applications in human-computer interaction [15-16]. Mechanomyography (MMG) is an emerging technique for assessing muscle function by measuring the mechanical signals produced by muscle contractions. This article explores the methodologies, advancements, and applications of MMG signal acquisition, highlighting its significance in various fields, particularly in prosthetics and rehabilitation. Mechanomyography involves the detection of mechanical vibrations generated by muscle activity. Unlike electromyography (EMG), which measures electrical signals, MMG captures the mechanical response of muscles, providing a complementary perspective on muscle function. The acquisition of MMG signals is crucial for applications in human-computer interaction, rehabilitation, and sports science. In the present investigation, to enhance the precision of human movement intention detection, a dual-modality approach was proposed, integrating both surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing the nerve potential activity and the vibrational characteristics of muscle contractions, respectively, were utilized to train a predictive model for estimating arm joint rotational acceleration. Research [17] combined the rigid-tendon Hill model with the fused TD features of sEMG and MMG to build the Unscented Particle Filter (UPF)-optimized SS model, outperforming the BPNN, SVR, and GRNN and significantly reducing the demand for training data volume. Critical for distilling significant traits from raw sEMG and MMG signals is adept signal processing. Standard preprocessing involves noise and baseline drift elimination through filtering, succeeded by feature extraction methods customized to the dataset's nuances [18]. Metrics such as the mean absolute value and root mean square from the time domain, paired with frequency domain attributes like power spectral density, are routinely utilized [19]. Advanced methodologies, including ensemble empirical mode decomposition (EEMD) and its adaptive noise counterpart, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), are utilized to meticulously enhance sEMG signals by breaking them down into intrinsic mode functions for targeted feature extraction [20, 21]. It is vital to choose suitable performance indicators to gauge the efficacy of diverse predictive algorithms. Indicators like root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²) offer quantitative measures of the congruence between forecasted joint angles or limb movements and actual data points [22, 23]. By analyzing the disparities and relative merits of Bidirectional Temporal Convolutional Networks (BiTCN) [24], Bidirectional Gated Recurrent Units (BiGRU) [25], and Transformer models [26], this study developed an innovative time series prediction algorithm, resulting in enhanced accuracy for forecasting shoulder joint acceleration. Utilizing the advanced hyperparameter optimization technique, specifically the Black-winged Kite Algorithm (BKA) [27], we have developed the BKA-BiTCN-BiGRU-Attention model for the prediction of shoulder joint acceleration. To mitigate the effects of random noise present in both MMG and sEMG signals, this study introduced the utilization of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm. The linear envelope extraction and full-wave rectification techniques were employed as critical preprocessing steps for the signal data. The experimental findings indicate that the proposed methodology not only reduces prediction errors but also enhances model performance relative to conventional approaches. These outcomes underscore the proposed method's extensive applicability and potential value across a wider spectrum of applications. 3. Experiments and Methods This chapter primarily introduced the experimental details, MMG and sEMG extracting and pre-processing methods and shoulder joint acceleration forecasting method. Figure 1 briefly illustrated the specific process of this study. 3.1. Experimental Procedures Twelve participants, equally divided between six males and six females, were enrolled in the experimental protocol. The participants exhibited no symptoms of arm sprain and reported an absence of painful muscle discomfort. The participant age distribution encompassed a range of 22 to 26 years, with an average age of 25.2 years, ± 3.24 standard deviation. Their average stature was measured at 174.8 cm, ± 8.29 cm standard deviation, and their mean body weight was recorded as 69.7 kg, ± 10.69 kg standard deviation. All participants were fully informed regarding the study's objectives and procedures, and they provided written informed consent prior to their enrollment in the trial. The study protocol mandated that participants execute forward arm raises in a sequence of 10 sets, with each set comprising 10 consecutive repetitions. Simultaneous acquisition of surface electromyography (sEMG) and mechanomyography (MMG) signals from the participants, in conjunction with shoulder joint kinematic data, was performed throughout the experimental protocol. To mitigate the impact of data variability associated with muscle fatigue, participants were instructed to undergo a 3-minute rest period subsequent to each exercise set. 3.2. Data collection 3.2.1 sEMG and MMG collection In this study, the Cometa wireless myoelectricity device was employed to concurrently capture acceleration and sEMG signals, as depicted in Figs. 2 a and 2 b. This advanced technology allows for a non-invasive approach to monitor muscle activity through high-resolution data acquisition, making it an ideal choice for investigating dynamic movements such as arm front raises. Subsequently, MMG signal was derived from the acceleration data [ 28 ], providing additional insights into muscle mechanical properties during contraction. The sampling rate of both signals is 2000HZ The primary focus of the investigation was the prediction of shoulder joint acceleration during the execution of arm front raises. To achieve this, the research hinged on the anatomical distribution of the human shoulder muscles, with specific emphasis on the anterior, middle, and posterior deltoid muscle bundles. These muscle groups were selected as the target sites for signal collection due to their pivotal role in shoulder movement and stability. Figure 3 delineates the strategic positions for sensor deployment, ensuring comprehensive coverage of the targeted muscle areas. Before initiating the experimental procedure, it was crucial to prepare the designated sites adequately. The skin overlying the anterior, middle, and posterior deltoids was meticulously sanitized using medical-grade alcohol. This step is essential for reducing impedance and enhancing the quality of the acquired sEMG signals. Proper securement of the sensors to the musculature is equally important to mitigate the potential deflection of the sEMG signal collection apparatus during physical activity, thereby ensuring accurate data collection. For each subject, the total duration of the experiment was approximately 45 minutes. This included preparation time, calibration of the equipment, a brief familiarization period, and multiple trials of arm front raises. However, the exact duration varied slightly among subjects due to individual differences in preparation time and the number of trials required to obtain reliable data. Despite these minor variations, all subjects underwent the same experimental protocol to ensure consistency across the study. To maintain consistent movement speed among participants, a metronome set at a fixed tempo was used. Subjects were instructed to synchronize their arm movements with the auditory cues provided by the metronome, which helped standardize the pace of the arm front raises. Additionally, verbal feedback was provided to participants if deviations from the prescribed speed were observed. This method ensured that any variability in the data could be attributed primarily to physiological factors rather than differences in movement speed. Furthermore, maintaining consistent inter-sensor spacing at approximately 30 millimeters was critical. This practice minimizes crosstalk between adjacent electrodes, which could otherwise distort the recorded signals and compromise the integrity of the data [ 29 ]. By adhering to these meticulous preparation and placement protocols, along with standardized movement speeds, the researchers ensured that the collected data accurately reflected the physiological processes under investigation, thus contributing to more reliable predictions of shoulder joint acceleration during arm front raises. 3.2.2 removing random noise of MMG and sEMG signals The study introduced the utilization of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm for the purpose of removing random noise of MMG and sEMG signals. The CEEMDAN algorithm represents a sophisticated advancement in the domain of signal processing, significantly refining the Empirical Mode Decomposition (EMD) and its extension, the Ensemble Empirical Mode Decomposition (EEMD) techniques. The Comprehensive Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) facilitates the precise reconstruction of the original signal from its decomposed elements by incorporating adaptive noise into each ensemble member. This method enhances the spectral separation of the Intrinsic Mode Functions (IMFs), thereby optimizing the decomposition process. Subsequent to the isolation of MMG and sEMG signal, a comparative assessment of the envelope entropy across various extraction methodologies was conducted to ascertain the efficacy of the novel approach presented. 3.2.3 Joint Acceleration data collection In the conduct of this study, the STT-IWS inertial sensor units—fabricated by Motio STT systems, in San Sebastián, Spain—were employed to gather acceleration metrics pertaining to the shoulder joint's movement during an anterior arm elevation. The IMU was shown in Fig. 4. These compact, wireless IMUs house a triaxial accelerometer, a triaxial gyroscope, and a triaxial magnetometer, amalgamating to offer an all-encompassing motion tracing functionality. Securing the IMU to the humerus bone facilitated the acquisition of exact three-dimensional linear acceleration data, subsequent to which this linear acceleration data was transformed into the angular acceleration values corresponding to the shoulder joint's motion. 3.3. Data Pre-Processing Method The MMG and sEMG signal exhibited characteristics of non-stationary time series data, which required rigorous pre-processing procedures prior to the implementation of deep learning methodologies [ 29 ]. Because MMG and EMG are both high-frequency vibration signals, human joint acceleration is a low-frequency signal, and the upper envelope signals of EMG and MMG are highly correlated with human joint acceleration, this study uses the upper envelope signal to realize the prediction of joint acceleration, so the MMG and EMG signals need to be preprocessed first and then used to train the acceleration prediction model. The pre-processing phase encompassed the following successive steps: (1) DC offset removal involves the elimination of the direct current (DC) component present in both MMG and sEMG signal. (2) Full-wave rectification involves the transformation of the entire signal spectrum such that all values are converted to their positive counterparts, a process applied to both MMG and sEMG signal. (3) Linear envelope extraction involves the isolation of the signal envelope from MMG and sEMG signal. (4) Normalization involves adjusting the MMG and sEMG signal to conform to a standardized scale. 3.4. Time Series Forecasting based on BKA-BiTCN-BiGRU-Attention model 3.4.1 Hyperparameter Optimization Algorithm: Black-winged Kite Algorithm (BKA) The current study introduces an enhanced optimization methodology that is founded on the principles of the Black-winged Kite Algorithm (BKA). The algorithmic framework employs a simulation of the black-winged kite's predatory attack strategies and migratory patterns to ascertain the optimal solution. The computational model is structured into three distinct stages: initialization, the simulation of attack behaviors, and the emigration dynamics. 1. During the initialization phase, the algorithm generates a population of candidate solutions at random. Subsequently, the solution with the highest fitness value is identified and designated as the leading individual within the population. 2. Black-winged kites exhibit an attack behavior wherein each individual modifies its positional orientation in response to its own specific location and fitness metric, optimizing the search outcomes. 3. In instances where the fitness metric of the present group is found to be inferior to that of a randomly selected group, the leading individual abdicates its leadership role and integrates into the migrating cohort. Conversely, if the fitness metric remains favorable, the leader maintains its role, directing the group's progression. The strategic selection process of competent leadership is instrumental in facilitating successful migratory patterns and systemic optimization. 3.4.2 Bidirectional and Multi-scale Feature Extraction: Bidirectional Temporal Convolutional Networks (BiTCN) Bidirectional Temporal Convolutional Networks (BiTCN) are comprised of a pair of temporal convolutional networks (TCNs), configured to process data in a bidirectional manner, the structure of BiTCN was shown in Fig. 5 . The initial neural network is tasked with encoding the prospective covariates of the time series data, whereas the subsequent network is responsible for encoding the historical observations and associated covariates. This methodology maintains the integrity of temporal information inherent to sequential data, while necessitating a reduced number of sequential processing steps compared to the prevalent Bidirectional Long Short-Term Memory (BiLSTM) architectures. Consequently, it manifests as an improvement in computational efficiency 3.4.3 Contextual Information Bidirectional Processing: Bidirectional GRU (BiGRU) A Gated Recurrent Unit (GRU) constitutes a variant of the recurrent neural network (RNN) architecture, enabling the preservation of information from preceding input sequences to facilitate enhanced predictive accuracy for subsequent input data. This functionality is especially pertinent in sequence processing applications, wherein the integrity of input sequence order is of paramount importance. The gated recurrent unit (GRU) architecture comprises two principal components, namely the reset gate and the update gate, which are integral to its functionality. The reset gate governs the selective discarding of information from the preceding input, whereas the update gate regulates the retention of specific elements from the current input within the memory store. Through the manipulation of these gating mechanisms throughout the training process, GRUs are capable of discerning patterns and enhancing the precision of their predictive capabilities. Bidirectional Gated Recurrent Units (BiGRUs) are designed to sequentially process input data in both a forward and reverse direction. The model incorporates a dual-Gated Recurrent Unit (GRU) architecture, wherein one GRU processes the input sequence in its conventional order, while the other processes the input in an inverted sequence. BiGRU architecture proficiently encapsulates contextual data from both antecedent and subsequent input sequences. 3.4.4 BiTCN-BiGRU-Attention The BiTCN-BiGRU-Attention model comprises the BiTCN (Bidirectional Temporal Convolutional Network), BiGRU (Bidirectional Gated Recurrent Unit), and the Multi-head attention mechanism integrated into a cohesive architecture. Multi-head attention expands upon the self-attention mechanism by concurrently executing several self-attention processes, each utilizing distinct sets of learned weight vectors. Each individual self-attention mechanism within the parallel architecture is designated as a head. Subsequently, the outputs derived from these heads are aggregated through concatenation, followed by a linear transformation to yield the ultimate output. Advantages of Multi-Head Attention: Multi-head attention facilitates an enhanced representation by concurrently analyzing disparate segments of the sequence, thereby enabling the capture of a broader and more varied array of features. efficiency is further enhanced by the ability to distribute tasks across various processing units, thereby expediting the completion of complex calculations. Parallel processing facilitates the simultaneous execution of multiple operations, significantly reducing the time required for computations. Enhanced Generalization Capabilities: The model's proficiency in concurrently attending to diverse facets of the input data facilitates improved generalization across a spectrum of tasks and varied datasets. In the present study, the model incorporates a multi-head self-attention mechanism subsequent to the BiTCN-BiGRU layer integration. The self-attention mechanism is indispensable for facilitating the model's ability to selectively concentrate on the most salient elements within a sequence, thereby maintaining the integrity of critical information during the processing of extensive sequences. The precise methodology for establishing connections is delineated within the network structure diagram. The implementation of the attention mechanism facilitates an enhancement in the model's interpretative capacity and performance metrics by dynamically allocating weighted emphasis to the most pertinent features. The allocation of weight distribution enhances the intra-model feature interactions, facilitating the acquisition of more intricate and sophisticated feature representations by the model. The structure of BiTCN-BiGRU-Attention was shown in Fig. 6. 4. Results 4.1. Results of Data Acquisition 4.1.1 Result of MMG extraction The analysis exhibited in Figs. 7 and 8 demonstrates that the CEEMDAN algorithm efficiently decomposes the original signal into a series of sub-signals, each with its unique center frequency characteristics. The IMF6, IMF7, and IMF8 signals, characterized by frequencies falling within the MMG signal bandwidth (10–100 Hz), are classified as MMG, distinguishing them from the residual signals, which are categorized as noise. In Fig. 9 , the efficacy of the proposed method is juxtaposed with six alternative algorithms: Ensemble Synchro-squeezing Mode Decomposition (ESMD), Fast Ensemble Empirical Mode Decomposition (FEMD), Variational Mode Decomposition (VMD), Complete Ensemble Empirical Mode Decomposition (CEEMD), Ensemble Empirical Mode Decomposition (EEMD), and Empirical Mode Decomposition (EMD), to ascertain comparative performance. The empirical mode decomposition technique, specifically the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), yielded sub-signals characterized by minimal envelope entropy. This finding suggests that these derived sub-signals are associated with the lowest levels of random noise. The results indicate that the algorithm exhibits a pronounced advantage in its ability to reduce noise. Envelope Entropy is a key concept in signal processing and information theory, especially for analyzing time-varying signals. It integrates signal envelope characteristics with entropy, which measures unpredictability. The envelope reflects amplitude variations over time, while entropy gauges the randomness within this envelope. This method has proven valuable in analyzing EEG and EMG signals, facilitating the detection of abnormalities and monitoring physiological states. Highly sensitive to changes in amplitude, envelope entropy excels in capturing subtle variations in non-stationary signals. By providing a clear quantitative measure of signal complexity, it aids in interpretation and decision-making processes. Thus, envelope entropy offers an effective tool for assessing signal variability and complexity in biomedical applications. 4.1.2 Results of sEMG Acquisition The analysis depicted in Figs. 10 and 11 demonstrates that the CEEMDAN algorithm efficiently decomposes the original signal into a series of sub-signals, each with its unique central frequency. The IMF2-8 signals, characterized by frequencies falling within the sEMG signal band range of 10–500 Hz, are discerned as sEMG signals. Conversely, all other signals are classified as extraneous noise. In Fig. 12 , additional six algorithms were implemented for comparative analysis against the proposed method. The CEEMDAN decomposition yields sub-signals characterized by minimal envelope entropy, suggesting a lower presence of random noise within these sub-signals. The findings corroborate the algorithm's enhanced proficiency in reducing noise interference. 4.2. Results of Data Processing In Fig. 13 and Fig. 14 , it is demonstrated that the preparation of MMG and sEMG data was accomplished through a series of four distinct procedural steps. The envelope order constitutes a critical determinant within the linear envelope model, markedly influencing its configurative morphology and, by extension, the predictive precision of the algorithmic computations. The subsequent section will delineate the influence of envelope order on the precision of predictive accuracy. 4.3. Results of Time Series Forecasting This study employs a six-fold cross-validation to rigorously assess various processing aspects, including signal extraction, hyperparameter optimization, and the comparative analysis of different classification algorithms. In each fold, five segments were used for training and one for testing. Performance metrics such as MSE, RMSE, MAE, MAPE, and R² were recorded. The process was iterated six times to ensure all participants' data contributed equally to training and testing. Final metrics were averaged across all folds to provide a robust evaluation, minimizing bias and variance. This method ensured comprehensive model assessment while maintaining result reliability. 4.3.1 Forecasting test result of single person and multi-person The optimal parameters for this model are detailed in Table 1 . Table 2 delineates the performance outcomes of the BiTCN-BiGRU-Attention model when applied to single-person datasets, whereas Table 3 exhibits the corresponding results for multi-person datasets. The graphical representations indicate that the BiTCN-BiGRU-Attention model exhibits a high degree of prediction accuracy across both individual and collective participant datasets. For individual datasets, the highest accuracy was achieved in the case of subject S06, characterized by the metrics: mean squared error (MSE) of 0.000692, root mean squared error (RMSE) of 0.00832, mean absolute error (MAE) of 0.00664, and a R 2 of 0.998. For multi-person datasets, the optimal accuracy metrics achieved were characterized by a Mean Squared Error (MSE) of 0.00153, a Root Mean Square Error (RMSE) of 0.0128, a Mean Absolute Error (MAE) of 0.0098, and a R 2 value of 0.990. Table 3 provides empirical evidence that the Black-winged Kite Algorithm (BKA) successfully optimizes the hyperparameters, thereby markedly improving the predictive accuracy of the algorithm. To evaluate whether there is a statistically significant difference in the R 2 between BKA-BiTCN-BiGRU-Attention and BiTCN-BiGRU-Attention, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table 3 , the P-value were significantly lower than the commonly accepted level (α = 0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between BKA-BiTCN-BiGRU-Attention and BiTCN-BiGRU-Attention. Table 1 best parameters parameters Arm side raises Arm front raises Learning rate 0.0097 0.0096 number of neurons in BiGRU 50 50 key value of attention mechanism 2 2 regularization parameters 0.000010093 0.000010139 delay step 3 3 forecast span step 1 1 Number of filters in BiTCN 64 64 Filter size 5 5 Table 2 Forecasting test result of different subjects Subject number MSE RMSE MAE MAPE R 2 1 0.00448 \\(\\:\\pm\\:\\) 0.00013 0.0212 \\(\\:\\pm\\:\\) 0.0011 0.0157 \\(\\:\\pm\\:\\) 0.0012 0.0159 \\(\\:\\pm\\:\\) 0.0013 0.986 \\(\\:\\pm\\:\\) 0.0041 2 0.00129 \\(\\:\\pm\\:\\) 0.0005 0.01136 \\(\\:\\pm\\:\\) 0.00083 0.00831 \\(\\:\\pm\\:\\) 0.00091 0.0149 \\(\\:\\pm\\:\\) 0.00094 0.993 \\(\\:\\pm\\:\\) 0.0052 3 0.00168 \\(\\:\\pm\\:\\) 0.0004 0.0112 \\(\\:\\pm\\:\\) 0.00073 0.00836 \\(\\:\\pm\\:\\) 0.0093 0.0149 \\(\\:\\pm\\:\\) 0.00099 0.994 \\(\\:\\pm\\:\\) 0.0051 4 0.000939 \\(\\:\\pm\\:\\) 0.00007 0.00916 \\(\\:\\pm\\:\\) 0.00067 0.00706 \\(\\:\\pm\\:\\) 0.00081 0.0148 \\(\\:\\pm\\:\\) 0.0010 0.997 \\(\\:\\pm\\:\\) 0.0047 5 0.004483 \\(\\:\\pm\\:\\) 0.0001 0.0211 \\(\\:\\pm\\:\\) 0.0013 0.0185 \\(\\:\\pm\\:\\) 0.0014 0.0164 \\(\\:\\pm\\:\\) 0.0012 0.979 \\(\\:\\pm\\:\\) 0.0054 6 0.000692 \\(\\:\\pm\\:\\) 0.00008 0.00832 \\(\\:\\pm\\:\\) 0.00079 0.00664 \\(\\:\\pm\\:\\) 0.0059 0.014 \\(\\:\\pm\\:\\) 0.0011 0.998 \\(\\:\\pm\\:\\) 0.0042 7 0.000998 \\(\\:\\pm\\:\\) 0.00008 0.00915 \\(\\:\\pm\\:\\) 0.00081 0.00849 \\(\\:\\pm\\:\\) 0.0090 0.0148 \\(\\:\\pm\\:\\) 0.0013 0.994 \\(\\:\\pm\\:\\) 0.0043 8 0.00157 \\(\\:\\pm\\:\\) 0.0004 0.0125 \\(\\:\\pm\\:\\) 0.00071 0.0101 \\(\\:\\pm\\:\\) 0.0013 0.0154 \\(\\:\\pm\\:\\) 0.0014 0.991 \\(\\:\\pm\\:\\) 0.0051 9 0.00115 \\(\\:\\pm\\:\\) 0.0003 0.0108 \\(\\:\\pm\\:\\) 0.00069 0.0114 \\(\\:\\pm\\:\\) 0.0094 0.0156 \\(\\:\\pm\\:\\) 0.0016 0.990 \\(\\:\\pm\\:\\) 0.0049 10 0.00448 \\(\\:\\pm\\:\\) 0.00012 0.0231 \\(\\:\\pm\\:\\) 0.0014 0.0165 \\(\\:\\pm\\:\\) 0.0013 0.0197 \\(\\:\\pm\\:\\) 0.0018 0.979 \\(\\:\\pm\\:\\) 0.0037 11 0.00149 \\(\\:\\pm\\:\\) 0.0002 0.0184 \\(\\:\\pm\\:\\) 0.00019 0.0139 \\(\\:\\pm\\:\\) 0.0012 0.0176 \\(\\:\\pm\\:\\) 0.0016 0.987 \\(\\:\\pm\\:\\) 0.0039 12 0.000758 \\(\\:\\pm\\:\\) 0.000097 0.00859 \\(\\:\\pm\\:\\) 0.00093 0.00831 \\(\\:\\pm\\:\\) 0.0071 0.0148 \\(\\:\\pm\\:\\) 0.0012 0.996 \\(\\:\\pm\\:\\) 0.0009 Table 3 Forecasting train result of mix database method MSE RMSE MAE MAPE R 2 P-value BKA-BiTCN-BiGRU-Attention 0.00153 \\(\\:\\pm\\:\\) 0.0003 0.0128 \\(\\:\\pm\\:\\) 0.0012 0.0098 \\(\\:\\pm\\:\\) 0.0009 0.0142 \\(\\:\\pm\\:\\) 0.0017 0.990 \\(\\:\\pm\\:\\) 0.0041 / BiTCN-BiGRU-Attention 0.00415 \\(\\:\\pm\\:\\) 0.0008 0.0209 \\(\\:\\pm\\:\\) 0.0019 0.0235 \\(\\:\\pm\\:\\) 0.0018 0.0168 \\(\\:\\pm\\:\\) 0.0021 0.973 \\(\\:\\pm\\:\\) 0.0050 0.0007 4.3.2 Forecasting test result of different MMG extraction methods Table 4 Forecasting test result of different MMG extraction methods method MSE RMSE MAE MAPE R 2 P-value CEEMDAN 0.00153 \\(\\:\\pm\\:\\) 0.0003 0.0128 \\(\\:\\pm\\:\\) 0.0012 0.0098 \\(\\:\\pm\\:\\) 0.0009 0.0142 \\(\\:\\pm\\:\\) 0.0017 0.990 \\(\\:\\pm\\:\\) 0.0041 / ICEEMDAN 0.0019 \\(\\:\\pm\\:\\) 0.0005 0.019 \\(\\:\\pm\\:\\) 0.00014 0.018 \\(\\:\\pm\\:\\) 0.0014 0.016 \\(\\:\\pm\\:\\) 0.0019 0.965 \\(\\:\\pm\\:\\) 0.0036 0.009 FEMD 0.0051 \\(\\:\\pm\\:\\) 0.0007 0.072 \\(\\:\\pm\\:\\) 0.0036 0.069 \\(\\:\\pm\\:\\) 0.0036 0.021 \\(\\:\\pm\\:\\) 0.0021 0.932 \\(\\:\\pm\\:\\) 0.0031 0.00081 TVD_EMD 0.0074 \\(\\:\\pm\\:\\) 0.0009 0.081 \\(\\:\\pm\\:\\) 0.0041 0.079 \\(\\:\\pm\\:\\) 0.0049 0.024 \\(\\:\\pm\\:\\) 0.0023 0.926 \\(\\:\\pm\\:\\) 0.0036 0.00047 CEEMD 0.0095 \\(\\:\\pm\\:\\) 0.0009 0.095 \\(\\:\\pm\\:\\) 0.0043 0.081 \\(\\:\\pm\\:\\) 0.0048 0.026 \\(\\:\\pm\\:\\) 0.0024 0.913 \\(\\:\\pm\\:\\) 0.0040 0.00009 EEMD 0.0071 \\(\\:\\pm\\:\\) 0.0006 0.087 \\(\\:\\pm\\:\\) 0.0039 0.080 \\(\\:\\pm\\:\\) 0.0037 0.025 \\(\\:\\pm\\:\\) 0.0024 0.913 \\(\\:\\pm\\:\\) 0.0042 0.00009 EMD 0.0083 \\(\\:\\pm\\:\\) 0.0008 0.090 \\(\\:\\pm\\:\\) 0.0039 0.090 \\(\\:\\pm\\:\\) 0.0053 0.031 \\(\\:\\pm\\:\\) 0.0029 0.903 \\(\\:\\pm\\:\\) 0.0048 0.00004 Table 4 delineates the predictive outcomes derived from various signal extraction methodologies when applied to multi-person datasets. The analysis yielded that the CEEMDAN algorithm demonstrated the superior predictive performance, evidenced by the metrics: mean squared error (MSE) of 0.000153, root mean squared error (RMSE) of 0.0128, mean absolute error (MAE) of 0.0098, and a R 2 of 0.990. The analysis indicates that MMG and sEMG signals isolated utilizing CEEMDAN technique exhibit the highest degree of correlation with human joint acceleration. Moreover, CEEMDAN demonstrates superior noise reduction capabilities. To evaluate whether there is a statistically significant difference in the R 2 between CEEMDAN and other algorithms, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table 3 , the P-value were significantly lower than the commonly accepted level (α = 0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between CEEMDAN and other algorithms. 4.3.3 Forecasting test result of different forecast methods Table 5 Forecasting test result of different forecast methods method MSE RMSE MAE MAPE R 2 P-value BiTCN-BiGRU-Attention 0.00415 \\(\\:\\pm\\:\\) 0.0008 0.0209 \\(\\:\\pm\\:\\) 0.0019 0.0235 \\(\\:\\pm\\:\\) 0.0018 0.0168 \\(\\:\\pm\\:\\) 0.0021 0.973 \\(\\:\\pm\\:\\) 0.0050 / BP 0.00419 \\(\\:\\pm\\:\\) 0.0007 0.0615 \\(\\:\\pm\\:\\) 0.0043 0.0831 \\(\\:\\pm\\:\\) 0.0069 0.0261 \\(\\:\\pm\\:\\) 0.0029 0.943 \\(\\:\\pm\\:\\) 0.0039 0.00069 CNN 0.00468 \\(\\:\\pm\\:\\) 0.0008 0.0727 \\(\\:\\pm\\:\\) 0.0053 0.0757 \\(\\:\\pm\\:\\) 0.0056 0.0241 \\(\\:\\pm\\:\\) 0.0028 0.938 \\(\\:\\pm\\:\\) 0.0037 0.00031 SVM 0.00329 \\(\\:\\pm\\:\\) 0.0006 0.0536 \\(\\:\\pm\\:\\) 0.0039 0.0631 \\(\\:\\pm\\:\\) 0.0041 0.0216 \\(\\:\\pm\\:\\) 0.0022 0.953 \\(\\:\\pm\\:\\) 0.0041 0.0017 BiLSTM 0.00478 \\(\\:\\pm\\:\\) 0.0011 0.0709 \\(\\:\\pm\\:\\) 0.0042 0.0857 \\(\\:\\pm\\:\\) 0.0056 0.0294 \\(\\:\\pm\\:\\) 0.0026 0.939 \\(\\:\\pm\\:\\) 0.0042 0.00032 ELM 0.00513 \\(\\:\\pm\\:\\) 0.0012 0.0736 \\(\\:\\pm\\:\\) 0.0041 0.0803 \\(\\:\\pm\\:\\) 0.0051 0.0254 \\(\\:\\pm\\:\\) 0.0036 0.938 \\(\\:\\pm\\:\\) 0.0035 0.00036 RF 0.00651 \\(\\:\\pm\\:\\) 0.0016 0.0787 \\(\\:\\pm\\:\\) 0.0049 0.0801 \\(\\:\\pm\\:\\) 0.0052 0.0253 \\(\\:\\pm\\:\\) 0.0039 0.935 \\(\\:\\pm\\:\\) 0.0051 0.00026 RBF 0.00452 \\(\\:\\pm\\:\\) 0.0007 0.0693 \\(\\:\\pm\\:\\) 0.0037 0.0641 \\(\\:\\pm\\:\\) 0.0036 0.0209 \\(\\:\\pm\\:\\) 0.0018 0.941 \\(\\:\\pm\\:\\) 0.0060 0.00039 LSTM 0.00528 \\(\\:\\pm\\:\\) 0.0014 0.0772 \\(\\:\\pm\\:\\) 0.0051 0.0784 \\(\\:\\pm\\:\\) 0.0046 0.0219 \\(\\:\\pm\\:\\) 0.0017 0.940 \\(\\:\\pm\\:\\) 0.0056 0.00027 Table 5 presents the forecasting results of different methods using multi-person datasets. The BiTCN-BiGRU-Attention algorithm demonstrated the best performance, with the following metrics: MSE = 0.00415, RMSE = 0.0209, MAE = 0.0235, and R 2 = 0.973. 4.3.4 Forecasting test result of different input signals Table 6 Forecasting test result of different input signals signal MSE RMSE MAE MAPE R 2 P-value MMG 0.00247 \\(\\:\\pm\\:\\) 0.0007 0.0492 \\(\\:\\pm\\:\\) 0.0041 0.0372 \\(\\:\\pm\\:\\) 0.0046 0.0178 \\(\\:\\pm\\:\\) 0.0026 0.945 \\(\\:\\pm\\:\\) 0.0035 0.0008 sEMG 0.00238 \\(\\:\\pm\\:\\) 0.0008 0.0471 \\(\\:\\pm\\:\\) 0.0046 0.0384 \\(\\:\\pm\\:\\) 0.0041 0.0179 \\(\\:\\pm\\:\\) 0.0021 0.948 \\(\\:\\pm\\:\\) 0.0032 0.0006 MMG + sEMG 0.00153 \\(\\:\\pm\\:\\) 0.0003 0.0128 \\(\\:\\pm\\:\\) 0.0012 0.0098 \\(\\:\\pm\\:\\) 0.0009 0.0142 \\(\\:\\pm\\:\\) 0.0017 0.990 \\(\\:\\pm\\:\\) 0.0041 / Table 6 delineates the outcomes of single MMG signal, single sEMG signal, and the integrated signal of MMG and sEMG, utilizing multi-subject datasets. The findings suggest that the integration of MMG and sEMG signals confers optimal predictive accuracy, as evidenced by the following performance metrics: Mean Squared Error (MSE) equaled 0.00153, Root Mean Squared Error (RMSE) was 0.0128, Mean Absolute Error (MAE) was recorded at 0.0098, and a R 2 was 0.990. MMG and sEMG were utilized to capture distinct forms of data resultant from muscle contraction, with MMG focusing on the vibration signals and sEMG detecting the associated electrical activity. The two datasets exhibit a significant positive correlation with joint acceleration; however, the integrity of this correlation is compromised by the aliasing artifacts introduced by noise signals, resulting in a partial loss of correlation. Thus, the amalgamation of the two signals serves to mutually complement one another, thereby enhancing the precision of predictive outcomes. To evaluate whether there is a statistically significant difference in the R 2 between MMG + sEMG and other signal resources, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table 3 , the P-value were significantly lower than the commonly accepted level (α = 0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between MMG + sEMG and other signal resources. 5. Discussion In this research, an innovative dual-modality approach for enhancing the precision of human movement intention detection was proposed through the integration of surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing nerve potential activity and the vibrational characteristics of muscle contractions respectively, are utilized to train a predictive model for estimating arm joint rotational acceleration. Key Contributions of this research: Dual-Modality Approach: The study uniquely integrates sEMG and MMG signals for predicting shoulder joint acceleration. This combination leverages the strengths of both signal types to improve the accuracy of predictions. Advanced Algorithm Development: The BiTCN-BiGRU-Attention algorithm, which combines Bidirectional Temporal Convolutional Networks (BiTCN), Bidirectional GRU (BiGRU) architecture, and Multi-Attention layer, was developed. The optimization of this algorithm's hyperparameters was achieved through the Black-winged Kite Algorithm (BKA). Noise Reduction Techniques: To mitigate random noise in the acquired data, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm was employed, leading to improved signal quality and thus more accurate predictions. The application of the CEEMDAN algorithm for noise reduction led to significant improvements in signal quality, as evidenced by lower envelope entropy compared to other decomposition techniques like EMD, VMD, and CEEMD. This enhancement in signal fidelity directly contributed to more precise predictions of arm joint rotational acceleration. Moreover, the integration of the BKA-BiTCN-BiGRU-Attention model demonstrated superior predictive performance metrics (MSE = 0.00153, RMSE = 0.0128, MAE = 0.0098, R² = 0.990), highlighting its effectiveness over traditional models like BPNN, RF, and SVM. Limitations of this research: Restricted Application Scope: The current investigation is centered on the prediction of acceleration patterns in shoulder joint motion. Subsequent investigations may be directed towards exploring additional joints and varying types of movements to corroborate the generalizability of the model across a wider range of conditions. The kinematic attributes of shoulder joint articulation exhibit distinct characteristics when compared to other synovial joints, which underscores the need for additional investigation into the distinct signal features and specialized processing techniques applicable to this joint and its unique dynamics. Practical Application Validation: Subsequent to the model's validation within a controlled laboratory setting, additional assessments are imperative to ascertain its efficacy in operational scenarios. Specifically, the model's resilience and its capability to maintain real-time performance in intricate environmental conditions necessitate thorough evaluation. Diverse perturbations can arise in real-world applications, necessitating the verification of the model's efficacy across a spectrum of operational conditions. Hardware Implementation: The present model is predominantly executed within a computational simulation framework. Subsequent research endeavors should focus on the integration of the proposed methodologies within embedded systems, in order to satisfy the stringent constraints of real-time operation and energy efficiency. Constraints imposed by the hardware of embedded systems can compromise the efficacy of computational models, thereby mandating additional algorithmic optimization to ensure compatibility with the specific characteristics of the hardware substrates. 6. Conclusion This research underscores the potential of integrating advanced signal processing techniques with deep learning methodologies to enhance the accuracy of human movement prediction models. The findings suggest that the proposed approach not only reduces prediction errors but also significantly improves model performance compared to traditional methods. The methodology presented offers extensive applicability across various domains, particularly in wearable exoskeletons and robotic appendages, paving the way for more intuitive human-machine interactions. Future work could explore the scalability of these methods to other joints and movements, further broadening their impact on rehabilitation technologies and beyond. Several directions for future research emerge from this study: Scalability and Generalization: Expanding the scope to include various types of movements and joints will test the robustness and versatility of the proposed methodology. This would involve collecting diverse datasets and potentially adapting the model architecture to accommodate different kinematic patterns. Real-Time Applications: Developing more efficient implementations of the BKA-BiTCN-BiGRU-Attention model to enable real-time applications in wearable exoskeletons and robotic appendages. This could involve hardware optimization or software improvements to reduce latency and computational overhead. Individualized Models: Investigating personalized models tailored to individual users' physiological characteristics could improve prediction accuracy. Machine learning techniques capable of adapting to user-specific patterns over time may offer enhanced performance. Interdisciplinary Collaboration: Collaborating with experts in biomechanics, rehabilitation medicine, and human-computer interaction could provide valuable insights for refining the model and extending its applications. Such collaborations could also facilitate the translation of this technology into clinical practice. Longitudinal Studies: Conducting longitudinal studies to assess the long-term stability and adaptability of the model under varying conditions (e.g., fatigue, injury recovery) is crucial. Understanding how the model performs over extended periods can inform its reliability and utility in practical settings. Declarations Acknowledgments The authors are grateful to the editors and anonymous reviewers for their valuable comments and suggestions, the creators of the source code for generously providing it, and the researchers whose findings are cited in this paper for serving as a reference and inspiration, the experiment participant and Nanjing University of Science and Technology for their support of this study. Thanks to the experiment participants and Postgraduate Research Practice Innovation Program of Jiangsu Province for their support of this study. Conflict of Interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contributions: Yu Bai: Conceptualization, methodology, data curation, writing original draft. Xiaorong Guan: Funding acquisition, supervision, resources. Shi Cheng: Formal analysis, visualization. Rui Zhang: Data curation, investigation. Long He: Validation, resources. Hui Bin Li: Supervision, software. Funding: This project is funded by Postgraduate Research Practice Innovation Program of Jiangsu Province (Grant NO. KYCX23_0512). Availability of Data and Materials: The code and data used during the current study are available from: https://gitee.com/baiyu1928/b-b-b-a. Author confirm for Ethical review I confirm that all methods were performed in accordance with the relevant guidelines and regulations by including a statement in the methods section to this effect. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-5384176\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":437699776,\"identity\":\"5926cd1e-1ba3-40da-b278-58feeaa719e8\",\"order_by\":0,\"name\":\"Yu Bai\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Yu\",\"middleName\":\"\",\"lastName\":\"Bai\",\"suffix\":\"\"},{\"id\":437699777,\"identity\":\"51be24d0-5ef9-4bb9-a2ca-eb0f52dee766\",\"order_by\":1,\"name\":\"XiaoRong Guan\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYHACxgcMPBCWBLFamA1AWnhI0cIGVkm8FvmI3GfVBTKH7e0ZmA/e5mGwyyOoxfDMcbPbM3gOJ/YwsCVb8zAkFxPW0t7GdpuH53ACDwOPmTQPw4HEBoJamtnYioFa7HkY+L8Rp0WevY2NGaiFsYeBh404LQY8x5ileXjSE3sOsxlbzjFIJsKWGWmMn3l7rO3Z25sf3nhTYUeELQeABNBVwBgFcwmpB9kCNvQHESpHwSgYBaNg5AIAw2cu2QQdBWIAAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"XiaoRong\",\"middleName\":\"\",\"lastName\":\"Guan\",\"suffix\":\"\"},{\"id\":437699778,\"identity\":\"b0d54b5d-9fe3-4854-8806-25f8a22e68a8\",\"order_by\":2,\"name\":\"Long He\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Long\",\"middleName\":\"\",\"lastName\":\"He\",\"suffix\":\"\"},{\"id\":437699779,\"identity\":\"c973ba18-2de4-4c44-a0db-5d2b9abc69ed\",\"order_by\":3,\"name\":\"Shi Cheng\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Shi\",\"middleName\":\"\",\"lastName\":\"Cheng\",\"suffix\":\"\"},{\"id\":437699780,\"identity\":\"6989b629-034f-4e46-8610-49e792bf84eb\",\"order_by\":4,\"name\":\"Rui Zhang\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Rui\",\"middleName\":\"\",\"lastName\":\"Zhang\",\"suffix\":\"\"},{\"id\":437699781,\"identity\":\"a56958dc-75d8-47ab-a4f7-f7ae33926aef\",\"order_by\":5,\"name\":\"Huibin Li\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Nanjing University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Huibin\",\"middleName\":\"\",\"lastName\":\"Li\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-11-04 02:23:20\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-5384176/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-5384176/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":79904621,\"identity\":\"1c94eb84-ef80-4f32-9fb5-1e246cea67f3\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 10:48:55\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":88851,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eprocess of this study\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/d5f4a635f141ec2bc23f9507.png\"},{\"id\":79905567,\"identity\":\"d30a0b24-363b-4330-8d3a-16b4adcc9ed7\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 10:56:55\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":43876,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e(a) myoelectricity device with conductive gel. (b) myoelectricity device acceleration acquisition diagram\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/5dc7379dd5c715216867622e.png\"},{\"id\":79906210,\"identity\":\"6f766ba9-7dea-4293-8bbe-1ed6df565690\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 11:04:55\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":37341,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eSchematic diagram of sensor wearing position\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/b1dc714ce20f26c2cc1594e3.png\"},{\"id\":79904623,\"identity\":\"db600e99-7448-45ea-8ad5-b727a3cf15bb\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 10:48:55\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 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10:48:55\",\"extension\":\"png\",\"order_by\":11,\"title\":\"Figure 11\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":55970,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003espectrogram of IMFs\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"11.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/c29934690211e1c9cfcfab5c.png\"},{\"id\":79907687,\"identity\":\"df3c7d04-0f08-444a-9c69-2dce10cec22c\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 11:12:55\",\"extension\":\"png\",\"order_by\":12,\"title\":\"Figure 12\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":5604,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eEnvelope entropy of different extraction methods\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"12.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/849e6bf4367c3bb00c2b1100.png\"},{\"id\":79904638,\"identity\":\"c4f1364d-cfb7-4a74-b022-06410adba6c5\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 10:48:56\",\"extension\":\"png\",\"order_by\":13,\"title\":\"Figure 13\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":25515,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003esEMG data and prepared sEMG data\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"13.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/8479259515b5261d44146bd6.png\"},{\"id\":79904649,\"identity\":\"03ae5b8c-a610-4848-9c71-c8f0d7a5a5ac\",\"added_by\":\"auto\",\"created_at\":\"2025-04-04 10:48:56\",\"extension\":\"png\",\"order_by\":14,\"title\":\"Figure 14\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":25443,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eMMG data and prepared MMG data\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"14.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/64f5353c49e2a56b7bf6308f.png\"},{\"id\":83097929,\"identity\":\"5200bda7-970e-4ee5-aade-aaddb0a8b920\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 04:01:35\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1803345,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5384176/v1/9a002cdc-8c6a-43d6-a386-8306e7538c56.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Investigation into the prediction of arm joint rotation acceleration utilizing signal fusion and time-series network methodologies\",\"fulltext\":[{\"header\":\"1. Note\",\"content\":\"\\u003cp\\u003eIn the present study, we introduced an innovative approach for the extraction of multi-channel MMG and sEMG signal, alongside a predictive model for estimating shoulder joint acceleration. Human participants were engaged in the experimental procedures conducted within this study. Ethical clearance and authorization for all experimental procedures and protocols were obtained from the Medical Ethics Committee of Nanjing Medical University, with the approval number designated as 2021-SR109.\\u003c/p\\u003e\"},{\"header\":\"2. Introduction\",\"content\":\"\\u003cp\\u003eIn recent years, there has been a marked surge in scholarly investigation into the domain of wearable exoskeletons and robotic appendages. Wearable exoskeletons have been utilized to a restricted degree within industrial and service sectors, primarily aimed at mitigating physical exertion and augmenting operational efficiency. Moreover, certain wearable exoskeleton devices are employed within the domain of medical rehabilitation to facilitate the restoration of mobility in patients suffering from limb injuries [1]. Wearable robotic appendages are distinguished from wearable exoskeletons by their purpose of endowing the user with an auxiliary limb, effectively serving as a 'third hand' or 'third leg'. This facilitates the execution of tasks that are unattainable through the user's unaided physical capabilities [2]. Wearable exoskeletons and wearable robotic limbs, albeit exhibiting distinct characteristics, converge in a fundamental prerequisite; they necessitate seamless operational synchronization with human operators. To facilitate effective collaboration between human limbs and wearable exoskeletons, it is imperative that the kinematic synchronization between the exoskeletal movements and the human body's motion is achieved. Moreover, the wearable robotic limbs must be capable of precisely interpreting the user's movement intentions to ensure accurate and harmonious coordination. To fulfill the stated objectives, it is imperative to conduct comprehensive research into the recognition of human movement intention, encompassing the classification of movements, the identification and forecasting of joint kinematics, as well as the recognition and prediction of the trajectory of limb endpoint movements [3].\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThe forecasting of human articulation and extremity motion has attracted considerable scholarly attention. Advanced deep learning methodologies have experienced swift progression lately. These methodologies diverge from conventional machine learning by focusing on discerning the underlying patterns and feature levels within data samples. Knowledge gleaned from such learning is instrumental in comprehending written content, images, and audio inputs. Gottlieb's work from 1998 delved into the activation sequences of muscles during deliberate single-joint actions, particularly swift elbow bending [4]. Jarić and colleagues, in 2006, examined the correlations between muscular kinetic indices and motion variables in intricate activities [5]. Mountjoy's team, in 2010, introduced a technique employing the swift orthogonal search technique to ascertain ideal joint angles for upper limb muscle simulations [6]. Crouch's group, in 2016, crafted a musculoskeletal simulation to anticipate hand and wrist actions from surface electromyography signals [7]. Ding and associates, also in 2016, tackled the difficulty of precisely inferring ongoing multi-joint actions from multi-channel surface EMG readings [8]. Sloot and co-authors, in 2018, scrutinized the analysis of joint forces and powers in walking, emphasizing irregular kinetic behaviors [9]. Xie and team, in 2020, applied a regression neural network fine-tuned by the golden ratio method to forecast lower limb joint angles utilizing diverse signal sources [10]. Qiu and colleagues, in 2021, suggested an algorithm for real-time learning and inferring human ambulatory intent for controlling lower limb exoskeletons [11]. Ren's group, in 2022, employed a Long Short-Term Memory (LSTM) algorithm to anticipate the paths of lower limb exoskeleton movement [12]. Zhong and others, in 2022, proposed a muscle synergy-guided adaptive network-based fuzzy inference system to predict uninterrupted knee joint actions, surpassing the efficacy of conventional numerical traits from individual sEMG channels [13]. Collectively, these investigations have propelled the field of human joint and limb movement prediction through a variety of innovative approaches and technological advancements.\\u003c/p\\u003e\\n\\u003cp\\u003eSurface electromyography (sEMG) is a non-invasive technique used to measure the electrical activity of muscles through electrodes placed on the skin. This method has gained significant attention in various fields, including rehabilitation, sports science, and human-computer interaction. The reliability and accuracy of sEMG signal acquisition are crucial for its effective application, and numerous studies have explored different aspects of this technology. The sEMG signals are generated by the electrical potential produced during muscle contractions. The voltage detected by the electrodes can be related to the activity of specific muscles, provided that proper electrode placement protocols are followed. The signal typically ranges from zero to several hundred microvolts as muscle activation occurs, making it essential to ensure signal reliability and minimize errors and artifacts during acquisition [14]. Additionally, advanced algorithms, including machine learning techniques, have been applied to classify gestures based on sEMG signals. Studies have shown that using deep learning models can significantly improve gesture recognition accuracy, making sEMG a powerful tool for applications in human-computer interaction [15-16]. Mechanomyography (MMG) is an emerging technique for assessing muscle function by measuring the mechanical signals produced by muscle contractions. This article explores the methodologies, advancements, and applications of MMG signal acquisition, highlighting its significance in various fields, particularly in prosthetics and rehabilitation. Mechanomyography involves the detection of mechanical vibrations generated by muscle activity. Unlike electromyography (EMG), which measures electrical signals, MMG captures the mechanical response of muscles, providing a complementary perspective on muscle function. The acquisition of MMG signals is crucial for applications in human-computer interaction, rehabilitation, and sports science. In the present investigation, to enhance the precision of human movement intention detection, a dual-modality approach was proposed, integrating both surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing the nerve potential activity and the vibrational characteristics of muscle contractions, respectively, were utilized to train a predictive model for estimating arm joint rotational acceleration. Research [17] combined the rigid-tendon Hill model with the fused TD features of sEMG and MMG to build the Unscented Particle Filter (UPF)-optimized SS model, outperforming the BPNN, SVR, and GRNN and significantly reducing the demand for training data volume.\\u003c/p\\u003e\\n\\u003cp\\u003eCritical for distilling significant traits from raw sEMG and MMG signals is adept signal processing. Standard preprocessing involves noise and baseline drift elimination through filtering, succeeded by feature extraction methods customized to the dataset's nuances [18]. Metrics such as the mean absolute value and root mean square from the time domain, paired with frequency domain attributes like power spectral density, are routinely utilized [19]. Advanced methodologies, including ensemble empirical mode decomposition (EEMD) and its adaptive noise counterpart, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), are utilized to meticulously enhance sEMG signals by breaking them down into intrinsic mode functions for targeted feature extraction [20, 21]. It is vital to choose suitable performance indicators to gauge the efficacy of diverse predictive algorithms. Indicators like root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²) offer quantitative measures of the congruence between forecasted joint angles or limb movements and actual data points [22, 23].\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eBy analyzing the disparities and relative merits of Bidirectional Temporal Convolutional Networks (BiTCN) [24], Bidirectional Gated Recurrent Units (BiGRU) [25], and Transformer models [26], this study developed an innovative time series prediction algorithm, resulting in enhanced accuracy for forecasting shoulder joint acceleration. Utilizing the advanced hyperparameter optimization technique, specifically the Black-winged Kite Algorithm (BKA) [27], we have developed the BKA-BiTCN-BiGRU-Attention model for the prediction of shoulder joint acceleration. To mitigate the effects of random noise present in both MMG and sEMG signals, this study introduced the utilization of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm. The linear envelope extraction and full-wave rectification techniques were employed as critical preprocessing steps for the signal data. The experimental findings indicate that the proposed methodology not only reduces prediction errors but also enhances model performance relative to conventional approaches. These outcomes underscore the proposed method's extensive applicability and potential value across a wider spectrum of applications.\\u003c/p\\u003e\"},{\"header\":\"3. Experiments and Methods\",\"content\":\"\\u003cp\\u003eThis chapter primarily introduced the experimental details, MMG and sEMG extracting and pre-processing methods and shoulder joint acceleration forecasting method. Figure 1 briefly illustrated the specific process of this study.\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e3.1. Experimental Procedures\\u003c/h2\\u003e\\n \\u003cp\\u003eTwelve participants, equally divided between six males and six females, were enrolled in the experimental protocol. The participants exhibited no symptoms of arm sprain and reported an absence of painful muscle discomfort. The participant age distribution encompassed a range of 22 to 26 years, with an average age of 25.2 years, \\u0026plusmn;\\u0026thinsp;3.24 standard deviation. Their average stature was measured at 174.8 cm, \\u0026plusmn;\\u0026thinsp;8.29 cm standard deviation, and their mean body weight was recorded as 69.7 kg, \\u0026plusmn;\\u0026thinsp;10.69 kg standard deviation. All participants were fully informed regarding the study\\u0026apos;s objectives and procedures, and they provided written informed consent prior to their enrollment in the trial.\\u003c/p\\u003e\\n \\u003cp\\u003eThe study protocol mandated that participants execute forward arm raises in a sequence of 10 sets, with each set comprising 10 consecutive repetitions. Simultaneous acquisition of surface electromyography (sEMG) and mechanomyography (MMG) signals from the participants, in conjunction with shoulder joint kinematic data, was performed throughout the experimental protocol. To mitigate the impact of data variability associated with muscle fatigue, participants were instructed to undergo a 3-minute rest period subsequent to each exercise set.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e3.2. Data collection\\u003c/h2\\u003e\\n \\u003cdiv id=\\\"Sec5\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.2.1 sEMG and MMG collection\\u003c/h2\\u003e\\n \\u003cp\\u003eIn this study, the Cometa wireless myoelectricity device was employed to concurrently capture acceleration and sEMG signals, as depicted in Figs. \\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003ea and \\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eb. This advanced technology allows for a non-invasive approach to monitor muscle activity through high-resolution data acquisition, making it an ideal choice for investigating dynamic movements such as arm front raises. Subsequently, MMG signal was derived from the acceleration data [\\u003cspan class=\\\"CitationRef\\\"\\u003e28\\u003c/span\\u003e], providing additional insights into muscle mechanical properties during contraction. The sampling rate of both signals is 2000HZ\\u003c/p\\u003e\\n \\u003cp\\u003eThe primary focus of the investigation was the prediction of shoulder joint acceleration during the execution of arm front raises. To achieve this, the research hinged on the anatomical distribution of the human shoulder muscles, with specific emphasis on the anterior, middle, and posterior deltoid muscle bundles. These muscle groups were selected as the target sites for signal collection due to their pivotal role in shoulder movement and stability. Figure \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e delineates the strategic positions for sensor deployment, ensuring comprehensive coverage of the targeted muscle areas.\\u003c/p\\u003e\\n \\u003cp\\u003eBefore initiating the experimental procedure, it was crucial to prepare the designated sites adequately. The skin overlying the anterior, middle, and posterior deltoids was meticulously sanitized using medical-grade alcohol. This step is essential for reducing impedance and enhancing the quality of the acquired sEMG signals. Proper securement of the sensors to the musculature is equally important to mitigate the potential deflection of the sEMG signal collection apparatus during physical activity, thereby ensuring accurate data collection.\\u003c/p\\u003e\\n \\u003cp\\u003eFor each subject, the total duration of the experiment was approximately 45 minutes. This included preparation time, calibration of the equipment, a brief familiarization period, and multiple trials of arm front raises. However, the exact duration varied slightly among subjects due to individual differences in preparation time and the number of trials required to obtain reliable data. Despite these minor variations, all subjects underwent the same experimental protocol to ensure consistency across the study.\\u003c/p\\u003e\\n \\u003cp\\u003eTo maintain consistent movement speed among participants, a metronome set at a fixed tempo was used. Subjects were instructed to synchronize their arm movements with the auditory cues provided by the metronome, which helped standardize the pace of the arm front raises. Additionally, verbal feedback was provided to participants if deviations from the prescribed speed were observed. This method ensured that any variability in the data could be attributed primarily to physiological factors rather than differences in movement speed.\\u003c/p\\u003e\\n \\u003cp\\u003eFurthermore, maintaining consistent inter-sensor spacing at approximately 30 millimeters was critical. This practice minimizes crosstalk between adjacent electrodes, which could otherwise distort the recorded signals and compromise the integrity of the data [\\u003cspan class=\\\"CitationRef\\\"\\u003e29\\u003c/span\\u003e]. By adhering to these meticulous preparation and placement protocols, along with standardized movement speeds, the researchers ensured that the collected data accurately reflected the physiological processes under investigation, thus contributing to more reliable predictions of shoulder joint acceleration during arm front raises.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.2.2 removing random noise of MMG and sEMG signals\\u003c/h2\\u003e\\n \\u003cp\\u003eThe study introduced the utilization of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm for the purpose of removing random noise of MMG and sEMG signals. The CEEMDAN algorithm represents a sophisticated advancement in the domain of signal processing, significantly refining the Empirical Mode Decomposition (EMD) and its extension, the Ensemble Empirical Mode Decomposition (EEMD) techniques. The Comprehensive Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) facilitates the precise reconstruction of the original signal from its decomposed elements by incorporating adaptive noise into each ensemble member. This method enhances the spectral separation of the Intrinsic Mode Functions (IMFs), thereby optimizing the decomposition process. Subsequent to the isolation of MMG and sEMG signal, a comparative assessment of the envelope entropy across various extraction methodologies was conducted to ascertain the efficacy of the novel approach presented.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec7\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.2.3 Joint Acceleration data collection\\u003c/h2\\u003e\\n \\u003cp\\u003eIn the conduct of this study, the STT-IWS inertial sensor units\\u0026mdash;fabricated by Motio STT systems, in San Sebasti\\u0026aacute;n, Spain\\u0026mdash;were employed to gather acceleration metrics pertaining to the shoulder joint\\u0026apos;s movement during an anterior arm elevation. The IMU was shown in Fig. 4. These compact, wireless IMUs house a triaxial accelerometer, a triaxial gyroscope, and a triaxial magnetometer, amalgamating to offer an all-encompassing motion tracing functionality. Securing the IMU to the humerus bone facilitated the acquisition of exact three-dimensional linear acceleration data, subsequent to which this linear acceleration data was transformed into the angular acceleration values corresponding to the shoulder joint\\u0026apos;s motion.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec8\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e3.3. Data Pre-Processing Method\\u003c/h2\\u003e\\n \\u003cp\\u003eThe MMG and sEMG signal exhibited characteristics of non-stationary time series data, which required rigorous pre-processing procedures prior to the implementation of deep learning methodologies [\\u003cspan class=\\\"CitationRef\\\"\\u003e29\\u003c/span\\u003e]. Because MMG and EMG are both high-frequency vibration signals, human joint acceleration is a low-frequency signal, and the upper envelope signals of EMG and MMG are highly correlated with human joint acceleration, this study uses the upper envelope signal to realize the prediction of joint acceleration, so the MMG and EMG signals need to be preprocessed first and then used to train the acceleration prediction model. The pre-processing phase encompassed the following successive steps:\\u003c/p\\u003e\\n \\u003cp\\u003e(1) DC offset removal involves the elimination of the direct current (DC) component present in both MMG and sEMG signal.\\u003c/p\\u003e\\n \\u003cp\\u003e(2) Full-wave rectification involves the transformation of the entire signal spectrum such that all values are converted to their positive counterparts, a process applied to both MMG and sEMG signal.\\u003c/p\\u003e\\n \\u003cp\\u003e(3) Linear envelope extraction involves the isolation of the signal envelope from MMG and sEMG signal.\\u003c/p\\u003e\\n \\u003cp\\u003e(4) Normalization involves adjusting the MMG and sEMG signal to conform to a standardized scale.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec9\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e3.4. Time Series Forecasting based on BKA-BiTCN-BiGRU-Attention model\\u003c/h2\\u003e\\n \\u003cdiv id=\\\"Sec10\\\" class=\\\"Section3\\\"\\u003e\\n \\u003cp\\u003e3.4.1 Hyperparameter Optimization Algorithm: Black-winged Kite Algorithm (BKA)\\u003c/p\\u003e\\n \\u003cp\\u003eThe current study introduces an enhanced optimization methodology that is founded on the principles of the Black-winged Kite Algorithm (BKA). The algorithmic framework employs a simulation of the black-winged kite\\u0026apos;s predatory attack strategies and migratory patterns to ascertain the optimal solution. The computational model is structured into three distinct stages: initialization, the simulation of attack behaviors, and the emigration dynamics.\\u003c/p\\u003e\\u003cspan\\u003e\\n \\u003cp\\u003e1. During the initialization phase, the algorithm generates a population of candidate solutions at random. Subsequently, the solution with the highest fitness value is identified and designated as the leading individual within the population.\\u003c/p\\u003e\\n \\u003c/span\\u003e\\u003cspan\\u003e\\n \\u003cp\\u003e2. Black-winged kites exhibit an attack behavior wherein each individual modifies its positional orientation in response to its own specific location and fitness metric, optimizing the search outcomes.\\u003c/p\\u003e\\n \\u003c/span\\u003e\\u003cspan\\u003e\\n \\u003cp\\u003e3. In instances where the fitness metric of the present group is found to be inferior to that of a randomly selected group, the leading individual abdicates its leadership role and integrates into the migrating cohort. Conversely, if the fitness metric remains favorable, the leader maintains its role, directing the group\\u0026apos;s progression.\\u003c/p\\u003e\\n \\u003c/span\\u003e\\n \\u003cp\\u003eThe strategic selection process of competent leadership is instrumental in facilitating successful migratory patterns and systemic optimization.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec11\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.4.2 Bidirectional and Multi-scale Feature Extraction: Bidirectional Temporal Convolutional Networks (BiTCN)\\u003c/h2\\u003e\\n \\u003cp\\u003eBidirectional Temporal Convolutional Networks (BiTCN) are comprised of a pair of temporal convolutional networks (TCNs), configured to process data in a bidirectional manner, the structure of BiTCN was shown in Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e. The initial neural network is tasked with encoding the prospective covariates of the time series data, whereas the subsequent network is responsible for encoding the historical observations and associated covariates. This methodology maintains the integrity of temporal information inherent to sequential data, while necessitating a reduced number of sequential processing steps compared to the prevalent Bidirectional Long Short-Term Memory (BiLSTM) architectures. Consequently, it manifests as an improvement in computational efficiency\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec12\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.4.3 Contextual Information Bidirectional Processing: Bidirectional GRU (BiGRU)\\u003c/h2\\u003e\\n \\u003cp\\u003eA Gated Recurrent Unit (GRU) constitutes a variant of the recurrent neural network (RNN) architecture, enabling the preservation of information from preceding input sequences to facilitate enhanced predictive accuracy for subsequent input data. This functionality is especially pertinent in sequence processing applications, wherein the integrity of input sequence order is of paramount importance. The gated recurrent unit (GRU) architecture comprises two principal components, namely the reset gate and the update gate, which are integral to its functionality. The reset gate governs the selective discarding of information from the preceding input, whereas the update gate regulates the retention of specific elements from the current input within the memory store. Through the manipulation of these gating mechanisms throughout the training process, GRUs are capable of discerning patterns and enhancing the precision of their predictive capabilities. Bidirectional Gated Recurrent Units (BiGRUs) are designed to sequentially process input data in both a forward and reverse direction. The model incorporates a dual-Gated Recurrent Unit (GRU) architecture, wherein one GRU processes the input sequence in its conventional order, while the other processes the input in an inverted sequence. BiGRU architecture proficiently encapsulates contextual data from both antecedent and subsequent input sequences.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec13\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e3.4.4 BiTCN-BiGRU-Attention\\u003c/h2\\u003e\\n \\u003cp\\u003eThe BiTCN-BiGRU-Attention model comprises the BiTCN (Bidirectional Temporal Convolutional Network), BiGRU (Bidirectional Gated Recurrent Unit), and the Multi-head attention mechanism integrated into a cohesive architecture. Multi-head attention expands upon the self-attention mechanism by concurrently executing several self-attention processes, each utilizing distinct sets of learned weight vectors. Each individual self-attention mechanism within the parallel architecture is designated as a head. Subsequently, the outputs derived from these heads are aggregated through concatenation, followed by a linear transformation to yield the ultimate output.\\u003c/p\\u003e\\n \\u003cp\\u003eAdvantages of Multi-Head Attention:\\u003c/p\\u003e\\n \\u003cp\\u003eMulti-head attention facilitates an enhanced representation by concurrently analyzing disparate segments of the sequence, thereby enabling the capture of a broader and more varied array of features.\\u003c/p\\u003e\\n \\u003cp\\u003eefficiency is further enhanced by the ability to distribute tasks across various processing units, thereby expediting the completion of complex calculations. Parallel processing facilitates the simultaneous execution of multiple operations, significantly reducing the time required for computations.\\u003c/p\\u003e\\n \\u003cp\\u003eEnhanced Generalization Capabilities: The model\\u0026apos;s proficiency in concurrently attending to diverse facets of the input data facilitates improved generalization across a spectrum of tasks and varied datasets.\\u003c/p\\u003e\\n \\u003cp\\u003eIn the present study, the model incorporates a multi-head self-attention mechanism subsequent to the BiTCN-BiGRU layer integration. The self-attention mechanism is indispensable for facilitating the model\\u0026apos;s ability to selectively concentrate on the most salient elements within a sequence, thereby maintaining the integrity of critical information during the processing of extensive sequences. The precise methodology for establishing connections is delineated within the network structure diagram.\\u003c/p\\u003e\\n \\u003cp\\u003eThe implementation of the attention mechanism facilitates an enhancement in the model\\u0026apos;s interpretative capacity and performance metrics by dynamically allocating weighted emphasis to the most pertinent features. The allocation of weight distribution enhances the intra-model feature interactions, facilitating the acquisition of more intricate and sophisticated feature representations by the model. The structure of BiTCN-BiGRU-Attention was shown in Fig. 6.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n\\u003c/div\\u003e\"},{\"header\":\"4. Results\",\"content\":\"\\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e4.1. Results of Data Acquisition\\u003c/h2\\u003e\\n \\u003cdiv id=\\\"Sec16\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.1.1 Result of MMG extraction\\u003c/h2\\u003e\\n \\u003cp\\u003eThe analysis exhibited in Figs. \\u003cspan class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e and \\u003cspan class=\\\"InternalRef\\\"\\u003e8\\u003c/span\\u003e demonstrates that the CEEMDAN algorithm efficiently decomposes the original signal into a series of sub-signals, each with its unique center frequency characteristics. The IMF6, IMF7, and IMF8 signals, characterized by frequencies falling within the MMG signal bandwidth (10\\u0026ndash;100 Hz), are classified as MMG, distinguishing them from the residual signals, which are categorized as noise.\\u003c/p\\u003e\\n \\u003cp\\u003eIn Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e, the efficacy of the proposed method is juxtaposed with six alternative algorithms: Ensemble Synchro-squeezing Mode Decomposition (ESMD), Fast Ensemble Empirical Mode Decomposition (FEMD), Variational Mode Decomposition (VMD), Complete Ensemble Empirical Mode Decomposition (CEEMD), Ensemble Empirical Mode Decomposition (EEMD), and Empirical Mode Decomposition (EMD), to ascertain comparative performance. The empirical mode decomposition technique, specifically the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), yielded sub-signals characterized by minimal envelope entropy. This finding suggests that these derived sub-signals are associated with the lowest levels of random noise. The results indicate that the algorithm exhibits a pronounced advantage in its ability to reduce noise.\\u003c/p\\u003e\\n \\u003cp\\u003eEnvelope Entropy is a key concept in signal processing and information theory, especially for analyzing time-varying signals. It integrates signal envelope characteristics with entropy, which measures unpredictability. The envelope reflects amplitude variations over time, while entropy gauges the randomness within this envelope. This method has proven valuable in analyzing EEG and EMG signals, facilitating the detection of abnormalities and monitoring physiological states. Highly sensitive to changes in amplitude, envelope entropy excels in capturing subtle variations in non-stationary signals. By providing a clear quantitative measure of signal complexity, it aids in interpretation and decision-making processes. Thus, envelope entropy offers an effective tool for assessing signal variability and complexity in biomedical applications.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec17\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.1.2 Results of sEMG Acquisition\\u003c/h2\\u003e\\n \\u003cp\\u003eThe analysis depicted in Figs. \\u003cspan class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e and \\u003cspan class=\\\"InternalRef\\\"\\u003e11\\u003c/span\\u003e demonstrates that the CEEMDAN algorithm efficiently decomposes the original signal into a series of sub-signals, each with its unique central frequency. The IMF2-8 signals, characterized by frequencies falling within the sEMG signal band range of 10\\u0026ndash;500 Hz, are discerned as sEMG signals. Conversely, all other signals are classified as extraneous noise.\\u003c/p\\u003e\\n \\u003cp\\u003eIn Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e12\\u003c/span\\u003e, additional six algorithms were implemented for comparative analysis against the proposed method. The CEEMDAN decomposition yields sub-signals characterized by minimal envelope entropy, suggesting a lower presence of random noise within these sub-signals. The findings corroborate the algorithm\\u0026apos;s enhanced proficiency in reducing noise interference.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec18\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e4.2. Results of Data Processing\\u003c/h2\\u003e\\n \\u003cp\\u003eIn Fig. 13 and Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e, it is demonstrated that the preparation of MMG and sEMG data was accomplished through a series of four distinct procedural steps. The envelope order constitutes a critical determinant within the linear envelope model, markedly influencing its configurative morphology and, by extension, the predictive precision of the algorithmic computations. The subsequent section will delineate the influence of envelope order on the precision of predictive accuracy.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec19\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003e4.3. Results of Time Series Forecasting\\u003c/h2\\u003e\\n \\u003cp\\u003eThis study employs a six-fold cross-validation to rigorously assess various processing aspects, including signal extraction, hyperparameter optimization, and the comparative analysis of different classification algorithms. In each fold, five segments were used for training and one for testing. Performance metrics such as MSE, RMSE, MAE, MAPE, and R\\u0026sup2; were recorded. The process was iterated six times to ensure all participants\\u0026apos; data contributed equally to training and testing. Final metrics were averaged across all folds to provide a robust evaluation, minimizing bias and variance. This method ensured comprehensive model assessment while maintaining result reliability.\\u003c/p\\u003e\\n \\u003cdiv id=\\\"Sec20\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.3.1 Forecasting test result of single person and multi-person\\u003c/h2\\u003e\\n \\u003cp\\u003eThe optimal parameters for this model are detailed in Table \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e. Table \\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e delineates the performance outcomes of the BiTCN-BiGRU-Attention model when applied to single-person datasets, whereas Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e exhibits the corresponding results for multi-person datasets. The graphical representations indicate that the BiTCN-BiGRU-Attention model exhibits a high degree of prediction accuracy across both individual and collective participant datasets. For individual datasets, the highest accuracy was achieved in the case of subject S06, characterized by the metrics: mean squared error (MSE) of 0.000692, root mean squared error (RMSE) of 0.00832, mean absolute error (MAE) of 0.00664, and a R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.998. For multi-person datasets, the optimal accuracy metrics achieved were characterized by a Mean Squared Error (MSE) of 0.00153, a Root Mean Square Error (RMSE) of 0.0128, a Mean Absolute Error (MAE) of 0.0098, and a R\\u003csup\\u003e2\\u003c/sup\\u003e value of 0.990. Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e provides empirical evidence that the Black-winged Kite Algorithm (BKA) successfully optimizes the hyperparameters, thereby markedly improving the predictive accuracy of the algorithm. To evaluate whether there is a statistically significant difference in the R\\u003csup\\u003e2\\u003c/sup\\u003e between BKA-BiTCN-BiGRU-Attention and BiTCN-BiGRU-Attention, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, the P-value were significantly lower than the commonly accepted level (\\u0026alpha;\\u0026thinsp;=\\u0026thinsp;0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between BKA-BiTCN-BiGRU-Attention and BiTCN-BiGRU-Attention.\\u003c/p\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003ebest parameters\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"3\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eparameters\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eArm side raises\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eArm front raises\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eLearning rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0097\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0096\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003enumber of neurons in BiGRU\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e50\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e50\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003ekey value of attention mechanism\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eregularization parameters\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.000010093\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.000010139\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003edelay step\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eforecast span step\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eNumber of filters in BiTCN\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eFilter size\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\"\\u003e\\u003cbr\\u003e\\u003c/div\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eForecasting test result of different subjects\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"6\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eSubject number\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAPE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00448\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.00013\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0212\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0011\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n 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class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\"\\u003e\\u003cbr\\u003e\\u003c/div\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eForecasting train result of mix database\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"7\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003emethod\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAPE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eP-value\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBKA-BiTCN-BiGRU-Attention\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00153\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0003\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0128\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0012\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0098\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0142\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0017\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.990\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e/\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBiTCN-BiGRU-Attention\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00415\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0209\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0019\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0235\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0018\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0168\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0021\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.973\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0050\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0007\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec21\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.3.2 Forecasting test result of different MMG extraction methods\\u003c/h2\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 4\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eForecasting test result of different MMG extraction methods\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"7\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003emethod\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAPE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eP-value\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCEEMDAN\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00153\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0003\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0128\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan 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align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.072\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.069\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.021\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0021\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.932\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0031\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00081\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTVD_EMD\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0074\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.081\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.079\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0049\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.024\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0023\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.926\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00047\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCEEMD\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0095\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.095\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0043\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.081\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0048\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.026\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0024\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.913\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0040\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eEEMD\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0071\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0006\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.087\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.080\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0037\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.025\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0024\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.913\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0042\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eEMD\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0083\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.090\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.090\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0053\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.031\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0029\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.903\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0048\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00004\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003cp\\u003eTable \\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e delineates the predictive outcomes derived from various signal extraction methodologies when applied to multi-person datasets. The analysis yielded that the CEEMDAN algorithm demonstrated the superior predictive performance, evidenced by the metrics: mean squared error (MSE) of 0.000153, root mean squared error (RMSE) of 0.0128, mean absolute error (MAE) of 0.0098, and a R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.990. The analysis indicates that MMG and sEMG signals isolated utilizing CEEMDAN technique exhibit the highest degree of correlation with human joint acceleration. Moreover, CEEMDAN demonstrates superior noise reduction capabilities. To evaluate whether there is a statistically significant difference in the R\\u003csup\\u003e2\\u003c/sup\\u003e between CEEMDAN and other algorithms, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, the P-value were significantly lower than the commonly accepted level (\\u0026alpha;\\u0026thinsp;=\\u0026thinsp;0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between CEEMDAN and other algorithms.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec22\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.3.3 Forecasting test result of different forecast methods\\u003c/h2\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab5\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 5\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eForecasting test result of different forecast methods\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"7\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003emethod\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAPE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eP-value\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBiTCN-BiGRU-Attention\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00415\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0209\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0019\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0235\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0018\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0168\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0021\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.973\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0050\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e/\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBP\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00419\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0007\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0615\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0043\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0831\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0069\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0261\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0029\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.943\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00069\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCNN\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00468\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0727\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0053\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0757\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0056\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0241\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0028\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.938\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0037\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00031\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eSVM\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00329\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0006\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0536\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0631\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0216\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0022\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.953\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0017\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBiLSTM\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00478\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0011\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0709\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0042\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0857\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0056\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0294\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0026\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.939\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0042\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00032\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eELM\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00513\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0012\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0736\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0803\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0051\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0254\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.938\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0035\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRF\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00651\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0016\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0787\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0049\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0801\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0052\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0253\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.935\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0051\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00026\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRBF\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00452\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0007\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0693\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0037\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0641\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0036\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0209\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0018\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.941\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0060\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00039\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eLSTM\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00528\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0014\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0772\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0051\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0784\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0046\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0219\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0017\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.940\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0056\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00027\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003cp\\u003eTable \\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e presents the forecasting results of different methods using multi-person datasets. The BiTCN-BiGRU-Attention algorithm demonstrated the best performance, with the following metrics: MSE\\u0026thinsp;=\\u0026thinsp;0.00415, RMSE\\u0026thinsp;=\\u0026thinsp;0.0209, MAE\\u0026thinsp;=\\u0026thinsp;0.0235, and R\\u003csup\\u003e2\\u003c/sup\\u003e\\u0026thinsp;=\\u0026thinsp;0.973.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003cdiv id=\\\"Sec23\\\" class=\\\"Section3\\\"\\u003e\\n \\u003ch2\\u003e4.3.4 Forecasting test result of different input signals\\u003c/h2\\u003e\\n \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u0026nbsp;\\u003ctable id=\\\"Tab6\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 6\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eForecasting test result of different input signals\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003ccolgroup cols=\\\"7\\\"\\u003e\\u003c/colgroup\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003esignal\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRMSE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMAPE\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eP-value\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMMG\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00247\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0007\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0492\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0372\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0046\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0178\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0026\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.945\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0035\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003esEMG\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00238\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0008\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0471\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0046\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0384\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0179\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0021\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.948\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0032\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0006\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMMG\\u0026thinsp;+\\u0026thinsp;sEMG\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.00153\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0003\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0128\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0012\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0098\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0009\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.0142\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0017\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.990\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\pm\\\\:\\\\)\\u003c/span\\u003e\\u003c/span\\u003e0.0041\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e/\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003c/div\\u003e\\n \\u003cp\\u003eTable \\u003cspan class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e delineates the outcomes of single MMG signal, single sEMG signal, and the integrated signal of MMG and sEMG, utilizing multi-subject datasets. The findings suggest that the integration of MMG and sEMG signals confers optimal predictive accuracy, as evidenced by the following performance metrics: Mean Squared Error (MSE) equaled 0.00153, Root Mean Squared Error (RMSE) was 0.0128, Mean Absolute Error (MAE) was recorded at 0.0098, and a R\\u003csup\\u003e2\\u003c/sup\\u003e was 0.990. MMG and sEMG were utilized to capture distinct forms of data resultant from muscle contraction, with MMG focusing on the vibration signals and sEMG detecting the associated electrical activity. The two datasets exhibit a significant positive correlation with joint acceleration; however, the integrity of this correlation is compromised by the aliasing artifacts introduced by noise signals, resulting in a partial loss of correlation. Thus, the amalgamation of the two signals serves to mutually complement one another, thereby enhancing the precision of predictive outcomes. To evaluate whether there is a statistically significant difference in the R\\u003csup\\u003e2\\u003c/sup\\u003e between MMG\\u0026thinsp;+\\u0026thinsp;sEMG and other signal resources, two-sample T-test was employed. This method is suitable for comparing the means of two independent samples under the assumption that both sets of data are normally distributed. According to Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, the P-value were significantly lower than the commonly accepted level (\\u0026alpha;\\u0026thinsp;=\\u0026thinsp;0.05). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between MMG\\u0026thinsp;+\\u0026thinsp;sEMG and other signal resources.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n\\u003c/div\\u003e\"},{\"header\":\"5. Discussion\",\"content\":\"\\u003cp\\u003eIn this research, an innovative dual-modality approach for enhancing the precision of human movement intention detection was proposed through the integration of surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing nerve potential activity and the vibrational characteristics of muscle contractions respectively, are utilized to train a predictive model for estimating arm joint rotational acceleration.\\u003c/p\\u003e \\u003cp\\u003eKey Contributions of this research:\\u003c/p\\u003e \\u003cp\\u003eDual-Modality Approach: The study uniquely integrates sEMG and MMG signals for predicting shoulder joint acceleration. This combination leverages the strengths of both signal types to improve the accuracy of predictions.\\u003c/p\\u003e \\u003cp\\u003eAdvanced Algorithm Development: The BiTCN-BiGRU-Attention algorithm, which combines Bidirectional Temporal Convolutional Networks (BiTCN), Bidirectional GRU (BiGRU) architecture, and Multi-Attention layer, was developed. The optimization of this algorithm's hyperparameters was achieved through the Black-winged Kite Algorithm (BKA).\\u003c/p\\u003e \\u003cp\\u003eNoise Reduction Techniques: To mitigate random noise in the acquired data, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm was employed, leading to improved signal quality and thus more accurate predictions.\\u003c/p\\u003e \\u003cp\\u003eThe application of the CEEMDAN algorithm for noise reduction led to significant improvements in signal quality, as evidenced by lower envelope entropy compared to other decomposition techniques like EMD, VMD, and CEEMD. This enhancement in signal fidelity directly contributed to more precise predictions of arm joint rotational acceleration. Moreover, the integration of the BKA-BiTCN-BiGRU-Attention model demonstrated superior predictive performance metrics (MSE\\u0026thinsp;=\\u0026thinsp;0.00153, RMSE\\u0026thinsp;=\\u0026thinsp;0.0128, MAE\\u0026thinsp;=\\u0026thinsp;0.0098, R\\u0026sup2; = 0.990), highlighting its effectiveness over traditional models like BPNN, RF, and SVM. Limitations of this research: Restricted Application Scope: The current investigation is centered on the prediction of acceleration patterns in shoulder joint motion. Subsequent investigations may be directed towards exploring additional joints and varying types of movements to corroborate the generalizability of the model across a wider range of conditions. The kinematic attributes of shoulder joint articulation exhibit distinct characteristics when compared to other synovial joints, which underscores the need for additional investigation into the distinct signal features and specialized processing techniques applicable to this joint and its unique dynamics. Practical Application Validation: Subsequent to the model's validation within a controlled laboratory setting, additional assessments are imperative to ascertain its efficacy in operational scenarios. Specifically, the model's resilience and its capability to maintain real-time performance in intricate environmental conditions necessitate thorough evaluation. Diverse perturbations can arise in real-world applications, necessitating the verification of the model's efficacy across a spectrum of operational conditions. Hardware Implementation: The present model is predominantly executed within a computational simulation framework. Subsequent research endeavors should focus on the integration of the proposed methodologies within embedded systems, in order to satisfy the stringent constraints of real-time operation and energy efficiency. Constraints imposed by the hardware of embedded systems can compromise the efficacy of computational models, thereby mandating additional algorithmic optimization to ensure compatibility with the specific characteristics of the hardware substrates.\\u003c/p\\u003e\"},{\"header\":\"6. Conclusion\",\"content\":\"\\u003cp\\u003eThis research underscores the potential of integrating advanced signal processing techniques with deep learning methodologies to enhance the accuracy of human movement prediction models. The findings suggest that the proposed approach not only reduces prediction errors but also significantly improves model performance compared to traditional methods. The methodology presented offers extensive applicability across various domains, particularly in wearable exoskeletons and robotic appendages, paving the way for more intuitive human-machine interactions. Future work could explore the scalability of these methods to other joints and movements, further broadening their impact on rehabilitation technologies and beyond. Several directions for future research emerge from this study:\\u003c/p\\u003e \\u003cp\\u003eScalability and Generalization: Expanding the scope to include various types of movements and joints will test the robustness and versatility of the proposed methodology. This would involve collecting diverse datasets and potentially adapting the model architecture to accommodate different kinematic patterns.\\u003c/p\\u003e \\u003cp\\u003eReal-Time Applications: Developing more efficient implementations of the BKA-BiTCN-BiGRU-Attention model to enable real-time applications in wearable exoskeletons and robotic appendages. This could involve hardware optimization or software improvements to reduce latency and computational overhead.\\u003c/p\\u003e \\u003cp\\u003eIndividualized Models: Investigating personalized models tailored to individual users' physiological characteristics could improve prediction accuracy. Machine learning techniques capable of adapting to user-specific patterns over time may offer enhanced performance.\\u003c/p\\u003e \\u003cp\\u003eInterdisciplinary Collaboration: Collaborating with experts in biomechanics, rehabilitation medicine, and human-computer interaction could provide valuable insights for refining the model and extending its applications. Such collaborations could also facilitate the translation of this technology into clinical practice.\\u003c/p\\u003e \\u003cp\\u003eLongitudinal Studies: Conducting longitudinal studies to assess the long-term stability and adaptability of the model under varying conditions (e.g., fatigue, injury recovery) is crucial. Understanding how the model performs over extended periods can inform its reliability and utility in practical settings.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003eAcknowledgments\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors are grateful to the editors and anonymous reviewers for their valuable comments and suggestions, the creators of the source code for generously providing it, and the researchers whose findings are cited in this paper for serving as a reference and inspiration, the experiment participant and Nanjing University of Science and Technology for their support of this study. Thanks to the experiment participants and Postgraduate Research Practice Innovation Program of Jiangsu Province for their support of this study.\\u003c/p\\u003e\\n\\u003cp\\u003eConflict of Interest:\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\\u003c/p\\u003e\\n\\u003cp\\u003eAuthor Contributions:\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eYu Bai:\\u0026nbsp;\\u003c/strong\\u003eConceptualization, methodology, data curation, writing original draft.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eXiaorong Guan:\\u0026nbsp;\\u003c/strong\\u003eFunding acquisition, supervision, resources.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eShi Cheng:\\u0026nbsp;\\u003c/strong\\u003eFormal analysis, visualization.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eRui Zhang:\\u0026nbsp;\\u003c/strong\\u003eData curation, investigation.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eLong He:\\u0026nbsp;\\u003c/strong\\u003eValidation, resources.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eHui Bin Li:\\u0026nbsp;\\u003c/strong\\u003eSupervision, software.\\u003c/p\\u003e\\n\\u003cp\\u003eFunding:\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThis project is funded by Postgraduate Research Practice Innovation Program of Jiangsu Province (Grant NO. KYCX23_0512).\\u003c/p\\u003e\\n\\u003cp\\u003eAvailability of Data and Materials:\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThe code and data used during the current study are available from: https://gitee.com/baiyu1928/b-b-b-a.\\u003c/p\\u003e\\n\\u003cp\\u003eAuthor confirm for Ethical review\\u003c/p\\u003e\\n\\u003cp\\u003eI confirm that all methods were performed in accordance with the relevant guidelines and regulations by including a statement in the methods section to this effect.\\u003c/p\\u003e\\n\\u003cp\\u003e[Author Name] Yu Bai, Xiao Rong Guan, Long He, Shi Cheng, Rui Zhang and Hui Bin Li\\u003c/p\\u003e\\n\\u003cp\\u003e[Date] 2024 11 18\\u003c/p\\u003e\\n\\u003cp\\u003eSubject statement\\u0026nbsp; \\u0026nbsp; \\u0026nbsp; \\u0026nbsp; \\u0026nbsp; \\u0026nbsp; \\u0026nbsp; \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAll subjects are agreed for publication of identifying information/images in an online open-access publication.\\u003c/p\\u003e\\n\\u003cp\\u003e[Subject Name] Yu Bai, Xiao Rong Guan, Long He, Shi Cheng, Rui Zhang, Hui Bin Li, Zhong Li, Zheng Wang, Chang Long Jiang, Xiang Lei Li, Peng Fei Liu and Ding Zhe Li.\\u003c/p\\u003e\\n\\u003cp\\u003e[Date] 2024 11 18\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n \\u003cli\\u003eQiu S, Pei Z, Wang C, et al. 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M. van der Krogt; \\u0026quot;Interpreting Joint Moments and Powers in Gait\\u0026quot;, 2018.\\u003c/li\\u003e\\n \\u003cli\\u003eHualong Xie; Guanchao Li; Xiaofei Zhao; Fei Li; \\u0026quot;Prediction of Limb Joint Angles Based on Multi-Source Signals By GS-GRNN For Exoskeleton Wearer\\u0026quot;, SENSORS (BASEL, SWITZERLAND), 2020.\\u003c/li\\u003e\\n \\u003cli\\u003eShiyin Qiu; Wei Guo; Darwin Caldwell; Fei Chen; \\u0026quot;Exoskeleton Online Learning and Estimation of Human Walking Intention Based on Dynamical Movement Primitives\\u0026quot;, IEEE TRANSACTIONS ON COGNITIVE AND DEVELOPMENTAL SYSTEMS, 2021.\\u003c/li\\u003e\\n \\u003cli\\u003eBin Ren; Zhiqiang Zhang; Chi Zhang; Silu Chen; \\u0026quot;Motion Trajectories Prediction of Lower Limb Exoskeleton Based on Long Short-Term Memory (LSTM) Networks\\u0026quot;, ACTUATORS, 2022.\\u003c/li\\u003e\\n \\u003cli\\u003eWenjuan Zhong; Xueming Fu; Mingming Zhang; \\u0026quot;A Muscle Synergy-Driven ANFIS Approach to Predict Continuous Knee Joint Movement\\u0026quot;, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2022.\\u003c/li\\u003e\\n \\u003cli\\u003eAndrea Merlo; I. Campanini; \\u0026quot;Technical Aspects of Surface Electromyography for Clinicians\\u0026quot;, THE OPEN REHABILITATION JOURNAL, 2010. (IF: 3)\\u003c/li\\u003e\\n \\u003cli\\u003eFang Wang; Jianing Jin; Zhiren Gong; Wentao Zhang; Guangyao Tang; Zesen Jia; \\u0026quot;Gesture Recognition Based on SEMG and Support Vector Machine\\u0026quot;, 2021 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS, AUTOMATION, 2021.\\u003c/li\\u003e\\n \\u003cli\\u003eXiangdong Peng; Xiao Zhou; Huaqiang Zhu; Zejun Ke; Congcheng Pan; \\u0026quot;MSFF-Net: Multi-Stream Feature Fusion Network for Surface Electromyography Gesture Recognition\\u0026quot;, PLOS ONE, 2022. (IF: 3)\\u003c/li\\u003e\\n \\u003cli\\u003eX. Xi, C. Yang, S. M. Miran, Y.-B. Zhao, S. Lin, and Z. Luo, \\u0026ldquo;SEMG-MMG state-space model for the continuous estimation of multi-joint angle,\\u0026rdquo; Complexity, vol. 2020, pp. 1\\u0026ndash;12, Feb. 2020, doi:10.1155/2020/4503271.\\u003c/li\\u003e\\n \\u003cli\\u003eZhou, J., Sun, Y., Luo, L., Zhang, W., \\u0026amp; Wei, Z. (2024). Human\\u0026ndash;Robot Cooperation Control Strategy Design Based on Trajectory Deformation Algorithm and Dynamic Movement Primitives for Lower Limb Rehabilitation Robots. Processes.\\u003c/li\\u003e\\n \\u003cli\\u003eLiu, X., Wang, J., Liang, T., Lou, C., Wang, H., \\u0026amp; Liu, X. (2023). SE-TCN Network for Continuous Estimation of Upper Limb Joint Angles. Mathematical Biosciences and Engineering, 20(2), 3237-3260.\\u003c/li\\u003e\\n \\u003cli\\u003eXie, H., Li, G., Zhao, X., \\u0026amp; Li, F. (2020). Prediction of Limb Joint Angles Based on Multi-Source Signals by GS-GRNN for Exoskeleton Wearer. Sensors (Basel, Switzerland), 20.\\u003c/li\\u003e\\n \\u003cli\\u003eZhang, P., Wu, P., \\u0026amp; Wang, W. (2023). Research on Lower Limb Step Speed Recognition Method Based on Electromyography. Micromachines, 14.\\u003c/li\\u003e\\n \\u003cli\\u003ePeng, C., Yang, D., Ge, Z., \\u0026amp; Liu, H. (2023). Wrist Autonomy Based on Upper-Limb Synergy: A Pilot Study. Medical \\u0026amp; Biological Engineering \\u0026amp; Computing, 61, 1149-1166.\\u003c/li\\u003e\\n \\u003cli\\u003eLee, J., Kwon, K., Soltis, I., et al. (2024). Intelligent Upper-Limb Exoskeleton Integrated with Soft Bioelectronics and Deep Learning for Intention-Driven Augmentation. NPJ Flexible Electronics\\u003c/li\\u003e\\n \\u003cli\\u003eSprangers O, Schelter S, de Rijke M. Parameter-efficient deep probabilistic forecasting[J]. International Journal of Forecasting, 2023, 39(1): 332-345.\\u003c/li\\u003e\\n \\u003cli\\u003eZhu Q, Zhang F, Liu S, et al. A hybrid VMD\\u0026ndash;BiGRU model for rubber futures time series forecasting[J]. Applied Soft Computing, 2019, 84: 105739.\\u003c/li\\u003e\\n \\u003cli\\u003eDu S, Li T, Yang Y, et al. Multivariate time series forecasting via attention-based encoder\\u0026ndash;decoder framework[J]. Neurocomputing, 2020, 388: 269-279.\\u003c/li\\u003e\\n \\u003cli\\u003eWang J, Wang W, Hu X, et al. Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems[J]. Artificial Intelligence Review, 2024, 57(4): 98.\\u003c/li\\u003e\\n \\u003cli\\u003eQuan J, Uchitomi H, Shigeyama R, et al. High-sensitivity acceleration sensor detecting micro-mechanomyogram and deep learning approach for parkinson\\u0026rsquo;s disease classification[J]. Scientific Reports, 2024, 14(1): 22941.\\u003c/li\\u003e\\n \\u003cli\\u003eZhu M, Guan X, Li Z, et al. sEMG-based lower limb motion prediction using CNN-LSTM with improved PCA optimization algorithm[J]. Journal of Bionic Engineering, 2023, 20(2): 612-627.\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Mechanomyography, surface electromyography, signal fusion, Bidirectional Temporal Convolutional Networks, Bidirectional GRU, Attention mechanism, Black-winged Kite algorithm, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise algorithm\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5384176/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5384176/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eIn the present investigation, to enhance the precision of human movement intention detection, a dual-modality approach was proposed, integrating both surface electromyography (sEMG) and mechanomyography (MMG) signals. These signals, representing the nerve potential activity and the vibrational characteristics of muscle contractions, respectively, were utilized to train a predictive model for estimating arm joint rotational acceleration. Participants with intact shoulder joints were enrolled in this study, during which both MMG and sEMG signal were acquired using wireless sensor technology. In this research, The BiTCN-BiGRU-Attention algorithm, an integration of Bidirectional Temporal Convolutional Networks (BiTCN), Bidirectional GRU (BiGRU) architecture and Muti-Attention layer, was proposed for acceleration prediction. What\\u0026rsquo;s more, the BiTCN-BiGRU-Attention algorithm was developed by combining the Black-winged Kite Algorithm (BKA) for the optimization of hyperparameters. The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm was employed to remove random noise of both MMG and sEMG signal from the acquired data. Various methodologies were employed to substantiate the superior performance of the CEEMDAN and BKA-BiTCN-BiGRU-Attention algorithm. Utilizing comparative analyses with conventional algorithms, including backpropagation neural networks (BP), random forests (RF), and support vector machines (SVM), the BKA-BiTCN-BiGRU-Attention model demonstrated superior predictive performance, yielding a prediction accuracy with mean squared error (MSE) of 0.00153, root mean squared error (RMSE) of 0.0128, mean absolute error (MAE) of 0.0098, and a R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.990.The comparative analysis with conventional signal decomposition techniques, including Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Concurrent Ensemble Empirical Mode Decomposition (CEEMD), has revealed that the MMG and sEMG signal processed via the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm exhibit the minimum envelope entropy. This finding indicates that the resultant sub-signals derived from CEEMDAN decomposition are characterized by the lowest levels of random noise. The amalgamation of the sub-signals residing within the respective frequency band was executed, resulting in the formation of MMG and sEMG signal.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Investigation into the prediction of arm joint rotation acceleration utilizing signal fusion and time-series network methodologies\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-04-04 10:48:50\",\"doi\":\"10.21203/rs.3.rs-5384176/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"a288ff19-b7b3-4676-a311-543f12728d4b\",\"owner\":[],\"postedDate\":\"April 4th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":46607364,\"name\":\"Biological sciences/Biological techniques\"},{\"id\":46607365,\"name\":\"Physical sciences/Engineering\"}],\"tags\":[],\"updatedAt\":\"2025-05-20T03:53:27+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2025-04-04 10:48:50\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-5384176\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-5384176\",\"identity\":\"rs-5384176\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}