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At present, the traditional sports training management mode is obsolete, which can’t do the scientific guidance for athletes’ training. This paper proposes a movement prediction system based on self-organizing mapping network, which firstly adopts a filter combining jitter clear and bi-exponential smoothing to filter the skeletal data of athletes collected by KinectV2. Then an automatic coding and decoding network model is designed, which accomplishes the task of extracting athlete-related motion information by dividing human limb parts and extracting independent features of each part. The extracted athlete movement information is matched with the standard movement template by combining the dynamic time regularization algorithm with the Euclidean distance to achieve the evaluation of the athlete’s training data, and finally, the self-organizing mapping network is introduced to predict the clustering of the athlete’s training performance. The score reliability of this paper’s algorithm is above 97%, and the self-reported movement states of the athletes participating in the test are consistent with the training state clustering results under the cascade self-organizing mapping network clustering. It shows that the model established in this paper is characterized by high accuracy, objectivity, and scientificity, which can accurately predict the performance of athletes and provide scientific training guidance.

Movement disorders are the main symptoms of neurological diseases such as Parkinson’s disease and deep learning-related methods can provide some intelligent solutions for the assessment and diagnosis of Parkinson’s movement disorders. In this paper, we propose a Kinect-based movement disorder assessment and analysis method, which uses the Kinect algorithm to capture and inverse kinematics analysis of human skeletal points, and further suggests the study of movement disorder assessment method based on dynamic time regularization algorithm so as to further achieve the effect of movement disorder assessment. Through the clinical experimental research on Parkinson’s disease patients and healthy subjects of the same age group, the use of the algorithm proposed in this paper is 15.18% higher than the GaitSet method in the CL state. The error of the algorithm proposed in this paper in the experiments comparing the gait parameter with the gold-standard motion capture system is close to 0.03s, which is a better improvement and upgrade compared with the advanced skeleton-based methods. In summary, the algorithm proposed in this paper is valuable and feasible for use in the assessment of Parkinson’s dyskinesia.

This paper investigates music education, where an efficient and accurate performance evaluation system in the piano teaching and performance ecosystem is increasingly becoming an essential tool for improving teaching quality and performance level. The objective evaluation of students’ performance skills can be achieved by carefully analyzing piano performances using the network flow optimization technique. This technique optimizes the performance evaluation system’s audio recognition ability by analyzing the piano audio signal and solving the multi-constraint nonlinear optimization problem in a limited time domain. This paper establishes a network flow optimization model, applies the multi-constraint nonlinear optimization technique, and combines the non-negative matrix decomposition and dynamic time regularization algorithm to analyze the piano performance for experiments. After optimization processing, hundreds of piano audio samples were collected, and the audio recognition accuracy was improved by 20%. By optimizing and processing the audio signals from the network stream, the evaluation system could detect polyphony more accurately and track the musical score effectively, improving accuracy and efficiency. Using the non-negative matrix decomposition algorithm, the accuracy of detecting polyphony can reach 85%, while the dynamic temporal regularization algorithm can match the position of the musical score with 95% accuracy. The accuracy of piano performance evaluation is optimized by this network flow optimization method, providing new technical means for music education, and promoting the quality of teaching and performance.

Currently, the alarm functions of existing levee seepage monitoring systems are limited to single-parameter monitoring and lack rate-of-change alarms and correlation alarms. This can lead to false alarms, missed alarms, equipment failures, or unnecessary downtime. To enhance the intelligence of levee safety monitoring and seepage alarms, a levee seepage intelligent alarm system based on a Bidirectional Long Short-Term Memory (BILSTM) network model was designed and implemented. Firstly, data cleaning and preprocessing are carried out on the engineering safety monitoring operation data to reduce the influence of dirty data such as outliers and repetitive values on the accuracy of alarms. Secondly, for the correlation between the piezometric tube water levels of the levee and the Yangtze River water levels, a correlation analysis based on Mutual Information (MI) theory was conducted to minimize the effect of piezometric tube water level change delays on correlation. Finally, the BILSTM model was used to predict trends in these potentially abnormal data intervals. Based on engineering application requirements, alarm thresholds were established, and a multi-level alarm module was developed. Field operation test results show that the proposed method can accurately predict the piezometric tube water levels of levees, achieving intelligent alarms within the engineering safety monitoring system.

The current sports training lacks data-based scientific training tools, and the use of action recognition technology to collect and mine sports data can effectively identify and evaluate sports skill actions. In this paper, a Transformer-based convolutional neural human action recognition network is proposed, which integrates the C3D convolutional network with the visual Transformer structure, using the 3D convolutional kernel for the extraction of time-domain features and using the Transformer network to accurately classify the feature sequences. The OpenPose algorithm is used to extract the essential points of the skeletal joints to estimate the human action posture. Through the dynamic time regularization algorithm, athletes’ sports movements are matched with standard movements to achieve a quantitative assessment of sports skill movements. The experimental results show that the method in this paper has better performance than similar neural network models in the task of sports action recognition and evaluation, and its class average accuracy mAP value and GFLOPs/V value are 0.9291 and 25.01, respectively, which substantially improves the recognition efficiency of sports skill actions.

We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new Regularized Inertial Proximal Algorithm obtained by means of a convenient finite-difference discretization. These systems are the counterpart to accelerated forward–backward algorithms in the context of maximally monotone operators. A proper tuning of the parameters allows us to prove the weak convergence of the trajectories to zeroes of the operator. Moreover, it is possible to estimate the rate at which the speed and acceleration vanish. We also study the effect of perturbations or computational errors that leave the convergence properties unchanged. We also analyze a growth condition under which strong convergence can be guaranteed. A simple example shows the criticality of the assumptions on the Yosida approximation parameter, and allows us to illustrate the behavior of these systems compared with some of their close relatives.

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 ( 1990 ); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992 ); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007 ) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010 ). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.

Electrical load forecasting is of the utmost significance in the power business since it may serve as a reference for downstream operations such as power grid dispatch, resulting in substantial financial advantages. Presently, the urban energy sector incorporates the functioning of multiple load demand clusters, which contributes to the reduction of utility grid strain. However, the integrated functioning of numerous users results in dynamic load needs, necessitating accurate electric load forecasting for monitoring operations. Load forecasting is a multifaceted task that necessitates the use of approaches beyond statistical methods. The concept of cluster load demand forecasting is a novel application that is seldom addressed in the literature. This article examines different machine learning techniques, such as linear regression, support vector machines, Gaussian process regression, and artificial neural networks (ANN), to determine the most efficient approach for predicting short-term load demand in cluster loads. The effectiveness of these solutions is evaluated by quantifying several aspects, such as error metrics and computing time. This discovery demonstrates that the artificial neural network (ANN) produces highly accurate forecasting outcomes. Furthermore, three separate optimization strategies are utilized to choose the most effective ANN training algorithm: Bayesian regularization, Levenberg–Marquardt, and scaled conjugate gradient. We assess the efficacy of optimization methods by running training, testing, validation, and error analysis. The results indicate that the ANN models based on the BR and LM optimization algorithms yield the most accurate electrical load demand forecasting results.

The determination of structural dynamic characteristics can be challenging, especially for complex cases. This can be a major impediment for dynamic load identification in many engineering applications. Hence, avoiding the need to find numerous solutions for structural dynamic characteristics can significantly simplify dynamic load identification. To achieve this, we rely on machine learning. The recent developments in machine learning have fundamentally changed the way we approach problems in numerous fields. Machine learning models can be more easily established to solve inverse problems compared to standard approaches. Here, we propose a novel method for dynamic load identification, exploiting deep learning. The proposed algorithm is a time-domain solution for beam structures based on the recurrent neural network theory and the long short-term memory. A deep learning model, which contains one bidirectional long short-term memory layer, one long short-term memory layer and two full connection layers, is constructed to identify the typical dynamic loads of a simply supported beam. The dynamic inverse model based on the proposed algorithm is then used to identify a sinusoidal, an impulsive and a random excitation. The accuracy, the robustness and the adaptability of the model are analyzed. Moreover, the effects of different architectures and hyperparameters on the identification results are evaluated. We show that the model can identify multi-points excitations well. Ultimately, the impact of the number and the position of the measuring points is discussed, and it is confirmed that the identification errors are not sensitive to the layout of the measuring points. All the presented results indicate the advantages of the proposed method, which can be beneficial for many applications.

We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions’ cumulative payoffs over time—specifically, by playing mixed strategies that maximize their expected cumulative payoff minus a regularization term. A widely studied example is exponential reinforcement learning, a process induced by an entropic regularization term which leads mixed strategies to evolve according to the replicator dynamics. However, in contrast to the class of regularization functions used to define smooth best responses in models of stochastic fictitious play, the functions used in this paper need not be infinitely steep at the boundary of the simplex; in fact, dropping this requirement gives rise to an important dichotomy between steep and nonsteep cases. In this general framework, we extend several properties of exponential learning, including the elimination of dominated strategies, the asymptotic stability of strict Nash equilibria, and the convergence of time-averaged trajectories in zero-sum games with an interior Nash equilibrium.