Online Distributed Parameter Optimization Method and System for Intelligent Modeling of Complex Systems

Abstract

This invention discloses an online distributed parameter optimization method and system for intelligent modeling of complex systems, relating to the field of electronic digital data processing technology. The method includes: on the edge side, an adaptive recursive ridge regression algorithm is used to recursively update the weights of the output layer of the feedforward neural network in real time to quickly track data flow dynamics; when the edge side detects a continuous decline in performance, node pruning, selection, and random configuration of node growth based on the optimal dataset are triggered; when concept drift is detected, the edge side uploads data and model status, and the cloud side performs anti-forgetting deep optimization on the feature extraction module, and then downloads the optimized parameters for collaborative reconstruction and deployment. This invention solves the problems of insufficient adaptability to dynamic operating conditions, low computational resource efficiency, and susceptibility to knowledge forgetting in existing technologies, achieving an optimal balance between model accuracy, adaptation speed, and resource consumption, and is particularly suitable for online modeling of complex dynamic systems such as intelligent control of high-speed trains.

Description

Technical Field

[0001] This application relates to the field of electronic digital data processing technology, and in particular to an online distributed parameter optimization method and system for intelligent modeling of complex systems. Background Technology

[0002] With the increasing maturity of deep learning technology, data-driven modeling methods have been widely applied to various complex real-world systems. Benefiting from the powerful data fusion and nonlinear modeling capabilities of multi-source sensor data and neural networks, data-driven modeling schemes based on machine learning or deep learning have become an important research direction for predicting the future state of complex systems.

[0003] However, real-world complex systems typically operate in highly dynamic and perturbation-prone environments, with tightly coupled internal states and significant time-varying characteristics. Frequent fluctuations in external operating conditions, natural degradation of equipment performance, and even sudden failures can all cause drastic and continuous drift in the statistical properties of system operating data, a phenomenon known as "concept drift." This leads to a rapid decline in the predictive accuracy or even failure of offline static models trained on fixed historical datasets.

[0004] To cope with such rapid changes, traditional centralized cloud-based model update solutions typically require global fine-tuning using massive amounts of data, a time-consuming and resource-inefficient process that struggles to meet the stringent real-time adaptability requirements of complex systems. In recent years, the synergy between edge computing and cloud computing has been widely studied as a more efficient model update paradigm. For example, existing technologies achieve online model updates by using historical data for global correction in the cloud and real-time window data for local correction at the edge. Another approach accelerates correction by constructing an optimization problem and distributing different layers of the deep learning model across the edge, cloud, and edge layers. However, most of these existing distributed optimization algorithms still rely entirely on gradient-based iterative learning, whose convergence speed and accuracy are highly dependent on parameter initialization and the choice of learning rate. In edge-side scenarios with small sample sizes, they are prone to getting trapped in local minima and experiencing knowledge forgetting.

[0005] In contrast, stochastically weighted neural networks, such as stochastically configured networks, have attracted attention as a non-iterative learning algorithm due to their extremely fast learning speed and ability to avoid getting trapped in local optima. Representative studies ensure their general approximation through inequality constraints and use recursive least squares to update output parameters, while also designing online structure adjustment mechanisms to adapt to data flow. However, existing stochastically configured network schemes still have significant drawbacks: First, their node contribution evaluation criteria may not be applicable in complex tasks, and fixed-ratio pruning strategies are prone to knowledge forgetting; second, their single network expansion method has limited modeling ability when facing high-dimensional strongly nonlinear systems, easily generating a large number of inefficient nodes and exacerbating multicollinearity problems; third, although existing studies have used methods such as ridge regression to deal with collinearity, their fixed forgetting factors and regularization parameters are difficult to maintain optimal performance under strongly time-varying conditions.

[0006] Because the architecture of randomly configured networks is similar to that of feedforward neural networks, they are naturally suitable as lightweight, fast-adjustable output modules for various deep models. Combining deep feature extraction modules based on convolutional or linear layer stacking with the output module can accelerate the deployment of deep neural networks at the edge. However, the feature extraction module needs to be optimized based on gradient descent, while the output module is based on random configuration theory; their optimization paradigms are quite different. Therefore, designing and implementing an online strategy that can collaboratively update these two modules based on actual computing power distribution is a significant challenge. The core difficulty lies in:

[0007] First, how to implement online anti-forgetting pruning of output module nodes to dynamically optimize the structure and retain useful knowledge;

[0008] Second, how to design an advanced linear output weight recursive update algorithm that can adaptively adjust the forgetting factor and regularization factor to effectively handle the multicollinearity problem under strongly time-varying conditions.

[0009] Third, how to design a collaborative update framework between the edge-side output module and the cloud-based feature extraction module to achieve efficient integration and optimal global performance of modules with different optimization paradigms and update frequencies. Summary of the Invention

[0010] The purpose of this application is to provide an online distributed parameter optimization method and system for intelligent modeling of complex systems. It aims to solve the technical problems of insufficient adaptability to dynamic operating conditions, low computational resource efficiency, and easy knowledge forgetting in existing online neural network model update methods. It enables the neural network model to quickly track the time-varying nature of operating conditions, adaptively simplify structural redundancy, retain historical knowledge against forgetting, and coordinately correct concept drift, thereby significantly improving the accuracy, robustness, and resource utilization efficiency of online prediction models for complex systems.

[0011] To achieve the above objectives, this application provides the following solution:

[0012] Firstly, this application provides an online distributed parameter optimization method for intelligent modeling of complex systems, including:

[0013] The device acquires data streams in real time and continuously updates the output layer weight parameters at the end of the feedforward neural network module based on the adaptive recursive ridge regression algorithm.

[0014] The edge continuously monitors the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds a first threshold for G consecutive times, a structural adjustment of the hidden layer of the feedforward neural network module is triggered, where G≥1. The structural adjustment includes: constructing an optimal dataset based on new data streams and historical data, performing node pruning and selection operations combined with sparsity constraints; and adding new hidden layer nodes using a random configuration algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection, and updating the output layer weight parameters at the end of the feedforward neural network module.

[0015] After the structural adjustment is triggered at the edge, N consecutive data points are newly acquired from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud side along with the verification dataset and a subset of data collected from historical data. Based on the received data, the cloud side uses an incremental learning algorithm based on low-rank decomposition to optimize and update the parameters of the feature extraction module.

[0016] The cloud side verifies the validity of the optimized feature extraction module parameters. If the verification is successful, the parameters are transmitted to the edge side. The edge side uses the received feature extraction module parameters and the cached current state parameters of the feedforward neural network module to reconstruct the complete prediction model and trigger local structural adjustments of the feedforward neural network module in the prediction model. After the adjustments are completed, the final neural network model is deployed to the edge side.

[0017] Secondly, this application provides an online distributed parameter optimization system for intelligent modeling of complex systems, including: an end-side execution module, an edge-side execution module, and a cloud-side execution module;

[0018] The edge execution module is used to recursively update the output layer weight parameters of the feedforward neural network module based on the adaptive recursive ridge regression algorithm.

[0019] The edge-side execution module is used to monitor the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds a first threshold (G≥1) for G consecutive times, it triggers a structural adjustment of the hidden layer of the feedforward neural network module. This structural adjustment includes: constructing an optimal dataset based on new data streams and historical data; performing node pruning and selection operations combined with sparsity constraints; adding new hidden layer nodes using a randomized allocation algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection; and updating the output layer weight parameters of the feedforward neural network module. After triggering the structural adjustment, it collects N consecutive data streams from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud execution module along with the verification dataset and a subset of data collected from historical data. The optimized feature extraction module parameters are received from the cloud execution module and reconstructed into a complete prediction model with the cached current state parameters of the feedforward neural network module. The local structure adjustment of the feedforward neural network module in the prediction model is triggered. After the adjustment is completed, the final neural network model is deployed to the edge execution module.

[0020] The cloud-side execution module is used to receive the current state parameters, verification dataset, and historical data subset of the feedforward neural network module uploaded from the edge-side execution module. Based on the received data, it optimizes and updates the parameters of the feature extraction module using an incremental learning algorithm based on low-rank decomposition. It then verifies the validity of the optimized feature extraction module parameters, and if the verification passes, it downloads them to the edge-side execution module.

[0021] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0022] This application provides an online distributed parameter optimization method and system for intelligent modeling of complex systems. By recursively updating the output layer weight parameters of the feedforward neural network module on the edge side using an adaptive recursive ridge regression algorithm, it solves the problem of parameter tracking lag in time-varying systems, achieving millisecond-level real-time response and accurate tracking of dynamic data flows. By triggering node pruning, selection, and random configuration of node growth based on the optimal dataset on the edge side when performance degradation is detected, it solves the problem that fixed-structure models cannot adaptively adjust capacity to match different operating conditions, achieving online self-organization and compaction of the network structure, effectively avoiding overfitting and resource waste. By triggering incremental learning optimization based on low-rank decomposition on the cloud side after detecting concept drift in the underlying feature extraction module on the edge side, and transmitting the optimized parameters down for collaborative reconstruction and correction, it solves the problems of catastrophic forgetting, update delays, and low resource efficiency caused by traditional global fine-tuning. It achieves deep and forgetting-resistant correction for fundamental concept drift, as well as efficient collaboration between edge, cloud, and end-user computing power and optimization tasks, ultimately achieving an optimal balance between model accuracy, adaptation speed, and system resource consumption in complex online learning scenarios. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart of the edge-cloud collaborative operation in an online distributed parameter optimization method for intelligent modeling of a complex system according to an embodiment of this application.

[0025] Figure 2 This is a schematic diagram of the speed-speed limit matching curve of a high-speed train provided in an embodiment of this application;

[0026] Figure 3(a) is a timing diagram of control commands for a high-speed train power unit 1 provided in an embodiment of this application;

[0027] Figure 3(b) is a timing diagram of control commands for a high-speed train power unit 2 provided in an embodiment of this application;

[0028] Figure 3(c) is a timing diagram of control commands for a high-speed train power unit 3 provided in an embodiment of this application;

[0029] Figure 3(d) is a timing diagram of control commands for a high-speed train power unit 4 provided in an embodiment of this application;

[0030] Figure 4(a) is a timing diagram of the dynamic response of output electrical power provided in an embodiment of this application;

[0031] Figure 4(b) is a timing diagram of the dynamic response of the input voltage signal provided in an embodiment of this application;

[0032] Figure 5 A comparison diagram showing the dynamic changes in the number of hidden nodes as parameters between the OSOSCN model and the OSLSCN model provided in an embodiment of this application;

[0033] Figure 6 A comparison chart of prediction results of various neural network models for electrical power provided in another embodiment of this application;

[0034] Figure 7 A three-dimensional comparison diagram of the prediction errors of various neural network models provided in an embodiment of this application;

[0035] Figure 8 A fitting comparison diagram of the actual output electrical power and the output power of the OSOSCN and OSLSCN models provided for an embodiment of this application;

[0036] Figure 9 A comparison chart showing the change in the number of hidden nodes in the model over time for two methods (EECC method and EEC method) provided in an embodiment of this application;

[0037] Figure 10 Timing diagrams of the corrected signals for two methods (EECC method and literature method) provided in an embodiment of this application;

[0038] Figure 11 A comparison graph of the errors over time for three methods (document method, EEC method and EECC method) provided in an embodiment of this application. Detailed Implementation

[0039] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0040] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] The basic building blocks of the "deep neural network model" in this application are as follows:

[0042] Deep neural networks are machine learning models with multiple layers of nonlinear transformations. Their core lies in abstracting and learning features from input data layer by layer through a stacked layer structure. Depth refers to the number of layers in the network. The deep neural network model involved in this application mainly consists of two functionally defined, collaborative core modules: a feature extraction module and an output module (i.e., a feedforward neural network module). The following provides a detailed description of each module:

[0043] I. Feature Extraction Module (i.e., Pre-network)

[0044] The feature extraction module typically consists of stacked linear layers (fully connected layers) and / or convolutional layers, responsible for automatically extracting high-level, abstract feature representations from the raw input data. Its parameters (such as weights and biases) usually need to be trained using gradient-based iterative optimization algorithms (such as backpropagation).

[0045] 1. Linear layer

[0046] Linear layers are used to perform linear transformations of features. They multiply the input feature vector by a learnable weight matrix and add a learnable bias vector to generate an output vector. Mathematically, this is expressed as:

[0047]

[0048] in, The input feature vector has a dimension of , Input feature dimension;

[0049] The weight matrix is ​​a learnable matrix with dimension . , To output the feature dimension, the weight matrix Each element in the vector represents the importance of the corresponding input feature vector to the output vector;

[0050] It is a learnable bias vector;

[0051] The output vector of the linear layer;

[0052] Due to their fully connected nature (each output neuron is connected to all inputs), linear layers excel at capturing global correlations and complex interactions between input features. They are often used as a fundamental component of multilayer perceptrons or at the end of the network to synthesize all abstract features and map them to the final output space. In this application, linear layers form the basis of a depth-optimizable dynamic feature extraction module.

[0053] 2. Convolutional layer

[0054] Convolutional layers are specifically designed for processing grid data with spatial or temporal structures (such as images and time series). They slide a set of learnable convolutional kernels across the input data and perform locally weighted summations to extract local features (such as edges, textures, or short-term temporal patterns). Convolutional layers significantly reduce the number of parameters in deep neural network models through parameter sharing and local connectivity, and endow deep neural network models with a certain degree of invariance to input data translation, thus being widely used in computer vision and temporal signal processing. In this application, convolutional layers can also be used as components of a feature extraction module to extract effective primary spatiotemporal features from raw sensor time-series data.

[0055] II. Output Module (i.e., Final-stage Network)

[0056] The output module receives high-dimensional abstract features from the feature extraction module and transforms them into the final prediction output (such as regression values ​​or classification labels). One of the core innovations of this application lies in the unique construction method and efficient optimization strategy of the output module. Structurally, the output module is equivalent to a single-hidden-layer feedforward neural network module, and its input is the feature vector output by the feedforward feature extraction module. Unlike traditional neural networks, this module has the following significant characteristics:

[0057] Parameter initialization and generation: The weights and biases from the input layer to the hidden layer in the output module are randomly generated based on inequality constraints and fixed thereafter, eliminating the need for gradient-based iterative training and greatly reducing computational overhead.

[0058] Parameter optimization method: The weight parameters from the hidden layer to the output layer are efficiently determined by analytical methods such as solving linear equations or recursive least squares, which avoids the problems of gradient-based optimization methods that are prone to getting trapped in local optima and slow convergence, and has extremely fast training speed.

[0059] Online Adaptability: This application further expands the capabilities of the output module by designing a recursive estimation algorithm for adaptive adjustment of the forgetting factor and regularization parameters, as well as a dynamic structure adjustment strategy (including node pruning and growth), enabling it to quickly track dynamic changes in the system in online streaming data scenarios while maintaining the compactness and generalization ability of the network structure.

[0060] III. Inter-module collaboration and optimized architecture

[0061] In the overall architecture proposed in this application, the two modules have clear division of labor and work together to form a highly efficient distributed update system:

[0062] Feature extraction module: responsible for deep, transferable feature extraction. Its parameters are periodically optimized through a gradient descent algorithm in the cloud to cope with fundamental conceptual shifts at the system's underlying level.

[0063] Output module: responsible for quickly fitting the nonlinear mapping from features to the final target. Its parameters and structure are adjusted online and quickly through analytical methods on the edge side and lightweight rules to track the time-varying dynamics of the data in real time.

[0064] In this embodiment, modules with different optimization methods (gradient optimization vs. random configuration + analytical solution) and different optimization levels (cloud vs. edge vs. terminal) are coordinated, and a complete triggering, updating and integration mechanism is designed to achieve a balance between accuracy, speed and resource efficiency of complex system neural network models as a whole.

[0065] In one exemplary embodiment, such as Figure 1 As shown, an online distributed parameter optimization method for intelligent modeling of complex systems is provided. Its core lies in constructing a three-level collaborative optimization framework involving the end, edge, and cloud. This method is executed by a computer device, specifically by a terminal or server alone, or by both. In this embodiment, the method is described using a server as an example, including the following steps S1 to S4. Wherein:

[0066] S1】Data stream is collected in real time at the edge and the output layer weight parameters at the end of the feedforward neural network module are continuously updated based on the adaptive recursive ridge regression algorithm.

[0067] S2】The edge continuously monitors the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds the first threshold for G consecutive times, the structure adjustment of the hidden layer of the feedforward neural network module is triggered, where G≥1. The structure adjustment includes: constructing an optimal dataset based on new data streams and historical data, performing node pruning and selection operations combined with sparse constraints; and adding new hidden layer nodes using a random configuration algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection, and updating the output layer weight parameters at the end of the feedforward neural network module.

[0068] S3】After the structural adjustment is triggered at the edge, N consecutive data points are newly collected from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud side along with the verification dataset and a subset of data collected from historical data. Based on the received data, the cloud side uses an incremental learning algorithm based on low-rank decomposition to optimize and update the parameters of the feature extraction module.

[0069] S4】The cloud side verifies the validity of the optimized feature extraction module parameters. If the verification is successful, it is transmitted to the edge side. The edge side reconstructs the complete prediction model by receiving the feature extraction module parameters and the current state parameters of the cached feedforward neural network module, and triggers the local structure adjustment of the feedforward neural network module in the prediction model. After the adjustment is completed, the final neural network model is deployed to the edge side.

[0070] Implementing steps S1 to S4 above, firstly, on the edge side, the output layer weight parameters of the feedforward neural network module are recursively updated in real time using an adaptive recursive ridge regression algorithm to achieve rapid tracking of the time-varying dynamics of the data flow. Based on this, on the edge side, by continuously monitoring the absolute prediction error, dynamic structural adjustments to the feedforward neural network module are triggered when performance continues to decline. These adjustments include node pruning and selection based on the optimal dataset and random node growth based on residuals, thereby adaptively changing the capacity of the feedforward neural network module to cope with changes in local operating conditions. If the model performance still does not meet the requirements after structural adjustments, then... The edge determines that the underlying feature extraction module has experienced concept drift through the newly acquired data window, and then uploads its state and data to the cloud. The cloud uses an incremental learning algorithm based on low-rank decomposition to perform deep parameter optimization on the feature extraction module to cope with fundamental concept changes. Finally, the cloud downloads the optimized and verified parameters down, and the edge integrates them with the cached feedforward neural network module state. By triggering local structural adjustments, the final model is quickly adapted and deployed to the edge, thus forming a complete closed-loop correction process that connects the edge, cloud, and edge layers and integrates lightweight recursive updates, dynamic structural adjustments, and deep anti-forgetting optimization.

[0071] Furthermore, the collaborative correction framework provided in this application possesses high versatility and scalability, not limited to high-speed train data stream scenarios, but also applicable to other complex dynamic systems with similar characteristics, such as: Industrial IoT and predictive maintenance: used for online analysis of multi-dimensional time-series data such as vibration and temperature of large rotating machinery (e.g., fans, pumps), real-time prediction of remaining service life, and adaptation to model degradation caused by equipment wear and environmental changes through a collaborative mechanism. Intelligent transportation and autonomous driving: used for fusion and situation prediction of vehicle surrounding environment perception data (e.g., cameras, LiDAR), and rapid adaptation to the impact of different weather, lighting, and road conditions on the perception model through edge-cloud collaboration. Smart energy and grid dispatch: used for ultra-short-term prediction of distributed photovoltaic / wind power output, regional load, etc., and real-time correction of the prediction model through the framework to adapt to the strong uncertainty brought about by sudden weather changes and emergencies. Fintech and risk monitoring: used for real-time anomaly detection and risk prediction of high-frequency trading data or user behavior data streams, rapidly adjusting at the edge to respond to changes in market microstructure, and deeply optimizing at the cloud to address concept drift caused by macro-financial cycles or new fraud models.

[0072] In another exemplary embodiment of this application, in order to adaptively and recursively update the linear weights between the hidden layer and the output layer in the feedforward neural network module, a two-factor (forgetting factor and regularization factor) alternating adaptive recursive ridge regression algorithm is adopted. The implementation process of step S1] specifically includes the following steps S11 to S15, wherein:

[0073] S11, Model Definition and Problem Construction:

[0074] Output matrix of the hidden layer of the feedforward neural network module With sample label vector The following linear parameterized model is established:

[0075]

[0076] in, The size of the sample label at each time step;

[0077] For the current moment, ;

[0078] The output layer weight parameters to be estimated at the current moment;

[0079] To be independent of the output matrix System noise;

[0080] Construct an exponentially weighted matrix and regularization factor The core of this regularized weighted least squares optimization problem is:

[0081]

[0082] in, This provides an estimate of the output layer weight parameters at the current moment.

[0083] Represents the independent variable that minimizes the objective function;

[0084] The square of the standard Euclidean norm;

[0085] For the square of the weighted Euclidean norm , As a weighted variable;

[0086] It is a diagonal matrix. , This indicates the construction of a diagonal matrix, with diagonal elements... Forgetting factors of Power of 1 ;

[0087] As a regularization factor, ;

[0088] Furthermore, the output matrix , , The first The hidden layer output vector at time step 1. The number of nodes in the hidden layer. ; For the real number field, Indicates transpose; sample label vector , , The first Sample label vector at time step; output layer weight parameters to be estimated , , The first Output weight parameters of each hidden node; system noise , .

[0089] S12, Derivation and execution of the recursive update formula:

[0090] Solve the optimization problem, derive and execute the output layer weight parameters. The recursive update calculation; where the recursive update utilizes Time, i.e., parameter estimation at the previous time. Current hidden layer output vector Prior error and inverse matrix ( Update;

[0091] Specifically, this will be implemented through the following steps:

[0092] S121, Calculate the prior error :

[0093]

[0094] in, This represents the sample label vector at the current moment;

[0095] This is the output vector of the hidden layer at the current time step;

[0096] S122, Define the autocorrelation matrix and its inverse matrix :

[0097]

[0098] in, For the first The hidden layer output vector at each time step ;

[0099] Forgetting factor of Power of;

[0100] This is the autocorrelation matrix from the previous time step;

[0101] S123, based on the principle of matrix inversion, the inverse matrix can be obtained. The recurrence relation:

[0102]

[0103] in, The autocorrelation matrix of the previous time step The inverse matrix;

[0104] For the observed variables at the current moment, ;

[0105] S124, based on prior error and inverse matrix The recursive update formula for the output layer weight parameters is obtained as follows:

[0106]

[0107] in, These are the estimated values ​​for the output layer weight parameters;

[0108] It is the identity matrix;

[0109] S125, the inverse matrix With weight parameter estimates This serves as the initial state for parameter updates in the next moment;

[0110] S13, Adaptive adjustment of forgetting factor:

[0111] Based on the variance estimation of system noise and prior error, the forgetting factor at the current time is dynamically adjusted using the following formula. :

[0112]

[0113] in, For variance estimation;

[0114] For the current time of system noise Variance estimation;

[0115] and The prior errors at the current time and the previous time are respectively... variance estimation, Prior error The estimate;

[0116] and The observed variables at the current time and the previous time are respectively Variance estimation;

[0117] and The sample labels are for the current time and the previous time respectively. Variance estimation;

[0118] and The sample labels are for the current time and the previous time respectively. The estimated value variance estimation, The sample label vector at the current time. The estimated value, ;

[0119] Forgetting factor The preset upper limit, For positive integers, Smoothing factor (usually taken as...) );

[0120] When the system undergoes drastic dynamic changes (prior error variance estimation) When the noise level increases, the forgetting factor automatically decreases to speed up tracking; when the system is stable, the forgetting factor automatically increases to smooth noise and improve estimation accuracy.

[0121] S14, Regularization factor adaptively adjusted:

[0122] Output matrix based on hidden layer The singular value decomposition and estimation mean square error minimization criterion are obtained by dynamically adjusting the regularization factor at the current time using the following formula. :

[0123]

[0124] in, Autocorrelation matrix The maximum singular value;

[0125] For the weight parameter estimates In the autocorrelation matrix The maximum component after projection onto the singular vector space;

[0126] Characterizes the effective sample size;

[0127] When the effective sample size is small (i.e., the autocorrelation matrix) Small, leading to Small) or problematic pathological (maximum singularity) When the matrix is ​​large, the regularization factor automatically increases to enhance regularization; conversely, it decreases. The effect of the regularization factor is integrated into the recursive process in one of the following ways: setting the inverse matrix during initialization. ( (as the initial regularization factor), or periodically reset the current inverse matrix to Or, equivalently, introduce during the inverse matrix update process. The impact.

[0128] S15, parameters updated in real time:

[0129] Using the adaptive forgetting factor obtained in steps S13 and S14 With regularization factor The recursive update formula for the output layer weight parameters in step S12 is used to complete the update of the output layer weight parameters. Online, adaptive optimal estimation enables real-time tracking of the time-varying dynamics of the data stream.

[0130] Through the steps S11–S15 described above, efficient and fully automated online learning of the output weights is achieved. The two-factor adaptive mechanism enables the recursive estimation algorithm to self-adjust in real time based on system dynamics and the state of the neural network model, significantly improving the robustness and predictive performance of the neural network model in complex time-varying data stream environments.

[0131] In another exemplary embodiment of this application, in order to achieve adaptive structural adjustment of the hidden layer of the feedforward neural network module, the implementation process of step S2] specifically includes the following steps S21 to S26, wherein:

[0132] S21, Performance monitoring and structural adjustment trigger:

[0133] S211, Edge-side continuous monitoring step S1: Upload the current time sample label vector. and the corresponding absolute prediction error , ;

[0134] S212, Judgment ( Does the first threshold hold true?

[0135] If true, then the counter maintained on the edge side Increasing: ;

[0136] If this is not true, then reset the counter. 0;

[0137] When the counter When the consecutive count reaches G (G≥1), the structure adjustment flag is triggered. and reset the counter 0. Initiate the structural adjustment process;

[0138] S22, Optimal Dataset Construction:

[0139] S221, collect the latest real-time data samples from the trigger time to form the current new data stream. ;

[0140] S222, based on the current new data stream Construct a local regression model and select a subset of samples from historical data based on its fitting error. ;

[0141] S223, to enhance anti-forgetting performance, from historical datasets... Uniform sampling was used to obtain the historical sample set. ;

[0142] S224, the current new data stream Subsample set With historical sample sets The dataset is then pieced together to form an optimal dataset for guiding structural adjustments. ;

[0143] S23, Node Contribution Assessment and Set Partitioning:

[0144] S231, based on the optimal dataset Calculate the hidden layer node in the current feedforward neural network module. Contribution :

[0145]

[0146] in, For the optimal dataset Total number of samples;

[0147] Subscript For sample indexing, for the optimal dataset All of them Iterate through each sample and sum them. ;

[0148] and They are nodes Input weights and biases, ;

[0149] To hide nodes The output layer weights;

[0150] To hide nodes Activation function;

[0151] For the optimal dataset The Middle The nth input sample is used to calculate the nth... The hidden node pairs the _th Activation value of each sample Input;

[0152] S232, divide all M hidden nodes into three sets:

[0153] Permafrost Collection (Pre-training initial node). This represents the total number of permanently frozen nodes;

[0154] Freeze candidate set , This represents the total number of currently frozen nodes;

[0155] Pruning candidate set ;

[0156] S24, Node thawing decision and freeze output calculation:

[0157] S241, regarding freezing the candidate set Each node in Determine thawing conditions ( Does the thawing threshold hold true?

[0158]

[0159] in, For the optimal dataset Mean of the middle label, subscript Traverse the frozen candidate set All nodes in;

[0160] If true, then the node will be... Thaw and remove it from the frozen candidate set. Removed from the default settings and added to the preset defrost collection. ;

[0161] If this is not true, then the node will be... Keep it frozen and retain it in the frozen candidate set. In, a frozen set is formed. ;

[0162] S242, Calculate the permafrost set With Keep Frozen Set Total contribution of frozen nodes in And update the pruning candidate set. :

[0163]

[0164] Among them, subscript Traversing the Permafrost Set With Keep Frozen Set All nodes in;

[0165] S25, Important node selection based on sparse constraints:

[0166] S251, from the updated pruning candidate set In this paper, the set of important nodes is selected by solving the following sparse constraint optimization problem, and the objective function is:

[0167]

[0168] Among them, subscript For the updated pruning candidate set Node index in ;

[0169] For the updated pruning candidate set The first in The contribution of each node;

[0170] Optimize variables for nodes, and ;

[0171] S252, the greedy iterative sieving method is used to solve the above optimization problem:

[0172] Initialize an empty set Used to store the updated pruning candidate set The nodes selected from the [selection list]. In each iteration, [the nodes are] selected from the updated pruning candidate set. From the remaining nodes, select the node that maximizes the decrease in the current objective function value and add it to the set. And from the updated pruning candidate set Removed from the residual when the objective function value drops below the residual threshold. Stop iterating when the time comes. Finally, permanently freeze the set. Keep the frozen collection With the selected set of nodes Taking the union of the sets yields the set of important nodes. And update the total number of currently frozen nodes. .

[0173] S26, Node Growth and Output Weight Update:

[0174] S261, based on the set of important nodes Calculate the current feedforward neural network module on the optimal dataset. residuals :

[0175]

[0176]

[0177] in, For the optimal dataset Input, ;

[0178] Subscript Set of important nodes Node index in ;

[0179] For the first The optimal dataset The output vector, .

[0180] and Each is a set of important nodes. The Middle The input weights and biases of each node; Set of important nodes The Middle The activation function for each node;

[0181] S262, if the residual does not meet the preset performance requirements, a random configuration algorithm is used to grow new nodes:

[0182] Randomly generate multiple sets of candidate parameters The selection process makes the following inequality constraints hold and The set with the largest value is used as the parameter for the new node:

[0183]

[0184] in, As a pre-defined increasing sequence, ,satisfy ;

[0185] For dynamic parameters, satisfying and ;

[0186] For the first The optimal dataset The output vector;

[0187] S263, after adding a new node, recalculate the feedforward neural network module on the optimal dataset based on the ridge regression closed-form solution. Output weights Repeat the node growth steps S262 to S263 until the model meets the preset performance requirements.

[0188] Through steps S21 to S26 above, the adaptive structural adjustment of the feedforward neural network module on the edge side is realized. It can quickly adapt to new working conditions while retaining key historical knowledge, effectively improving the robustness and prediction accuracy of the neural network model in dynamic data flow environments.

[0189] In another exemplary embodiment of this application, in order to perform online concept drift detection and anti-forgetting incremental optimization on the feature extraction module, the implementation process of step S3] specifically includes the following steps S31 to S35, wherein:

[0190] S31, Edge-side concept drift delay detection and data preparation:

[0191] When the edge side triggers a structural adjustment of the feedforward neural network module (i.e. And the temporary storage space is in an unoccupied state (i.e., the storage status flag). When ), perform the following operations:

[0192] S311, cache the state parameters of the current feedforward neural network module It contains the structure and weight information of the feedforward neural network module;

[0193] S312 continuously collects future data from real-time data streams. N w The data points constitute the validation dataset. D w ;

[0194] S313, in the validation dataset D w Above, calculate the current complete model (from the current feature extraction module). The mean absolute error (consisting of the state parameters of the feedforward neural network module) ;

[0195] S314, judgment ( Does the second threshold hold true?

[0196] If true, then the feature extraction module is determined to have experienced concept drift, and a storage status flag is set. Cache the state parameters Validate dataset D w and from historical datasets H d A subset of historical data obtained according to preset rules (such as equal-interval sampling). D d Package and upload to the cloud;

[0197] If the condition is not met, it is determined that no concept drift has occurred, storage space is immediately released, and storage status flags are set. The process has ended.

[0198] S32, Cloud-based model reconstruction and training dataset construction:

[0199] The cloud side receives data packets (i.e., status parameters) uploaded from the edge side. Validate dataset D w and subsets of historical data D d After that, perform the following operations:

[0200] S321, parse the data packet to obtain the state parameters of the feedforward neural network module. Validate dataset D w and subsets of historical data D d ;

[0201] S322, utilizing state parameters Reconstruct the feedforward neural network module and connect it to the current feature extraction module in the cloud. and basic feature extraction module (Pre-trained versions) are concatenated to form two models to be evaluated: ( )and ( );

[0202] S323 will validate the dataset. Dw subset of historical data Dd Merge to form the cloud-side training dataset .

[0203] S33, Incremental learning optimization based on low-rank decomposition:

[0204] right Feature extraction module in Perform incremental learning based on low-rank decomposition to optimize its parameters:

[0205] S331, for the feature extraction module Any linear layer weight matrix to be optimized Reconstruct it into the following form:

[0206]

[0207] in, The base weight matrix for offline pre-training. , The number of output channels for the linear layer. This represents the number of input channels for the linear layer.

[0208] and These are the scaling diagonal matrices for the output and input channels, respectively. , , The scaling diagonal matrix elements for the output channels. The elements of the scaled diagonal matrix for the input channels;

[0209] It is a low-rank bias matrix. , Let be the rank of the low-rank bias matrix;

[0210] S332, low-rank bias matrix By using the learnable bias matrix Perform singular value decomposition and retain the first few elements. The principal singular component yields:

[0211]

[0212] in, , Singular value matrices The left and right singular vector matrices;

[0213] For the first A singular value, , For the corresponding singular vectors;

[0214] During the optimization process, , , It is learned directly as a low-rank incremental component.

[0215] S333, the optimal rank of each level is determined by a hierarchical rank selection criterion. :

[0216] By solving the following optimization problem, the parameter increment is minimized while satisfying the performance approximation constraints:

[0217]

[0218] in, J is the layer index, and J is the total number of layers;

[0219] For the first The first layer One singular value;

[0220] This represents the gradient of the loss function with respect to the initial reconstruction weights;

[0221] As a performance approximation threshold, ;

[0222] st is Restrictions.

[0223] S334, based on the training dataset The scaling matrix is ​​solved by an optimization algorithm. , and low-rank increment components The parameters are fixed, while the base weight matrix is ​​also fixed. The process remains unchanged until convergence, resulting in the optimized feature extraction module. .

[0224] S34, Optimization effect verification and parameter distribution:

[0225] S341, the feature extraction module With state parameters By splicing the parts together, we obtain the model to be evaluated. In the validation dataset Dw The above calculation is used to evaluate the model. Mean absolute error Meanwhile, in the validation dataset Dw The above calculation is used to evaluate the model. Mean absolute error ;

[0226] S342, judgment Is it true or false?

[0227] If the condition is met, the optimization is considered effective, and the optimized feature extraction module is used. The parameters are used as the state of the new feature extraction module. and update the cloud Then, the status of the new feature extraction module is determined. The data is then transmitted down to the edge as a response to the concept drift determination request in step S314.

[0228] Otherwise, if the optimization is deemed insufficient, the original feature extraction module will be retained. And send an optimization failure command to the edge side.

[0229] S35, Edge-side Model Reconstruction and Collaboration:

[0230] The edge side receives the new feature extraction module status from the cloud side. Then, combine the status parameters of the local cache. Reconstruct the complete model. To further restore model performance, set a flag to trigger structural adjustments. This triggers local structural adjustments to the feedforward neural network module on the edge side (i.e., the process in step S2). After the correction is completed, the final model is deployed to the edge side.

[0231] Through the above steps, incremental and forgetting-resistant optimization of the feature extraction module was achieved, effectively addressing the fundamental changes in the underlying feature distribution (concept drift). At the same time, through coordination with edge-side structural adjustments, the overall model's continuous high performance in dynamic data flow environments was ensured.

[0232] In another exemplary embodiment of this application, in order to complete the coordination of cloud optimization and edge-side adaptive adjustment and deploy the final model, the implementation process of step S4] specifically includes the following steps S41 to S45, wherein:

[0233] S41, Verification of cloud-side optimization effects:

[0234] The feature extraction module obtained by the cloud side after optimization in step S3 Given the parameters, perform the following verification operation:

[0235] S411, the optimized feature extraction module State parameters of the feedforward neural network module uploaded from the edge side The parts are pieced together to form the model to be evaluated. ;

[0236] S412, in the validation dataset Dw (Uploaded from the edge) Calculate the model to be evaluated. Mean absolute error ;

[0237] S413, Obtain the feature extraction module calculated in step S313. (Concatenated from the original feature extraction module and state parameters), on the same validation dataset Dw Mean absolute error ;

[0238] S414, Conditions for determining the effectiveness of optimization Is / 2 true?

[0239] If the validity condition is met, the cloud optimization is considered successful, and the optimized feature extraction module parameters are used as the new feature extraction module status. And update the current feature extraction module in the cloud. ; and change the status of the new feature extraction module The message is sent to the edge via the downlink channel as a response to the concept drift determination request in step S31.

[0240] If the validity condition is not met, it is determined that the cloud optimization has not met expectations, and the current feature extraction module is retained. It remains unchanged, and sends an optimization failure command to the edge side.

[0241] S42, Edge-side model reconstruction and performance recovery trigger:

[0242] The edge side receives the new feature extraction module status from the cloud side. Then, perform the following operations:

[0243] S421, Read the state parameters of the feedforward neural network module cached in step S311 from the local temporary storage. ;

[0244] S422, the received new feature extraction module status With cached state parameters The data are then pieced together to reconstruct a complete prediction model.

[0245] S423, Set trigger structure adjustment flag Initiate a local structural adjustment procedure for the feedforward neural network module in the reconstructed model to enable the module to quickly adapt to the new feature extraction environment.

[0246] S43, Local structural adjustments on the edge side are executed:

[0247] S431, based on the latest real-time data stream, constructs a small-scale optimal dataset. This is used for local structural adjustments (the construction method is the same as step S22, but the amount of data can be reduced; the local structural adjustment here refers to the structural adjustment process with a more relaxed threshold or a limited range for rapid adaptation).

[0248] S432, using a greedy iterative screening method, perform fast node selection and pruning operations on the feedforward neural network module in the reconstructed model (refer to step S25, but a more lenient threshold can be used).

[0249] S433, if the network residual after pruning still does not meet the performance requirements, a random configuration algorithm is used to grow a small number of nodes (refer to step S26, but the maximum number of nodes to be grown can be limited).

[0250] S434. After the structural adjustment is completed, the output layer weights are recalculated based on ridge regression to obtain the final optimized feedforward neural network module.

[0251] S44, Final Model Integration and Deployment:

[0252] S441, Connect the locally structured adjusted feedforward neural network module with the newly issued feature extraction module state. Integrate the components to form the target neural network model;

[0253] S442 serializes the target neural network model and deploys it to the edge runtime environment, replacing the original edge model;

[0254] S443, clear the temporary cache on the edge side (including state parameters). ), reset related flags ( , ,counter 0), the collaborative correction process ends.

[0255] Through the above steps, the collaboration between deep optimization in the cloud and rapid adaptation at the edge was achieved. While effectively dealing with concept drift, the compatibility and overall performance between model modules were ensured through local structural adjustments. Ultimately, the model was smoothly updated and deployed at the edge, ensuring the continuous accuracy and robustness of online prediction for complex systems.

[0256] This application also provides an application scenario, applying the above-mentioned online distributed parameter optimization method for intelligent modeling of complex systems to the online adaptive modeling and optimization of high-speed train intelligent control systems. In this complex dynamic system, the optimal traction / braking commands need to be dynamically calculated based on real-time track conditions, load, and dispatch instructions. Because the train operating environment (such as gradient, curves, and wind resistance) and vehicle status (such as equipment wear and wheel-rail adhesion changes) are highly time-varying, the neural network model invoked by the control algorithm is required to possess online adaptability.

[0257] Step 1, System Deployment and Initialization

[0258] The device is defined as an on-board control unit, and a lightweight neural network model is deployed on it to collect real-time time-series data such as train speed, acceleration, and traction / braking commands, and to perform millisecond-level speed prediction.

[0259] The edge side is defined as the edge server along the line, and edge nodes with strong computing power are deployed on it to monitor the performance of the neural network model of multiple trains and perform structural adjustments to the neural network model.

[0260] The cloud is defined as the railway data center AI platform, which stores massive amounts of historical operation data and high-performance computing resources, and is responsible for deep training and optimization of the feature extraction module;

[0261] Initial neural network model: In the cloud, using historical multi-line and multi-condition data, a hybrid architecture neural network model is pre-trained, consisting of a feature extraction module (composed of stacked convolutional and linear layers, used to extract spatiotemporal coupled features) and an output module (used to quickly map features to prediction speed); the neural network model is then offline and distributed to the edge side and the device.

[0262] Step 2: Online collaborative optimization of the operation process

[0263] During online operation, the train operates according to the following collaborative mechanism:

[0264] S2.1, Continuous recursive calibration on the device side

[0265] The onboard control unit collects data every second and runs an adaptive recursive ridge regression algorithm. For example, when the train enters a long, steep, or uphill section, the traction characteristics change. The algorithm dynamically adjusts the forgetting factor and rapidly adjusts the output weights of the neural network model, enabling the output weights to adapt to new dynamic relationships in real time, maintain prediction accuracy, and achieve rapid adaptation to short-term time-varying dynamics.

[0266] S2.2, Edge-side trigger structure adjustment

[0267] Assume a significant change in train operating conditions. Edge servers along the line detect multiple consecutive prediction errors exceeding a threshold, triggering structural adjustments. The edge servers execute:

[0268] Constructing the optimal dataset: Integrating historical datasets with the current dataset;

[0269] Node pruning: Based on the freezing mechanism and progressive projection optimization, redundant hidden layer nodes under the current working conditions are pruned;

[0270] Node growth: Based on residuals, a random configuration algorithm is used to add hidden layer nodes that adapt to the current train dynamics characteristics;

[0271] Update weights: Use ridge regression to recalculate the output weights of the entire network based on the optimal dataset;

[0272] This process is completed at the edge and takes only seconds, allowing the neural network model structure to adapt to moderate operating conditions and avoiding continuous performance degradation caused by a fixed structure.

[0273] S2.3, Cloud-based Deep Feature Optimization

[0274] If, after a long period of operation, the wheel-rail adhesion coefficient systematically decreases or the power system experiences abnormal operation (a fundamental conceptual drift), although edge-side structural adjustments can fully restore the accuracy of the neural network model, the decreased effectiveness of the feature extraction module will lead to continuous growth of the edge-side network structure. Therefore, the feature extraction module also needs to be updated. At this point, the edge side detects the continuous performance degradation of the original neural network model before structural adjustments, triggering cloud optimization.

[0275] Cloud-based retraining: Based on historical and current running data, the training dataset is reconstructed, and only the feature extraction module is retrained using gradient descent. Through parameter transfer, the overall neural network model is adapted to the new dynamics.

[0276] Parameter distribution: The optimized feature extraction module parameters are distributed to the edge side. The edge side integrates these parameters with the original output module and adjusts the new structure to ensure the neural network model meets the pre-defined performance requirements for deployment.

[0277] This process addresses long-term, fundamental system changes. Although it takes a long time (tens of seconds), the edge structure adjustment before cloud correction ensures the short-term effectiveness of deploying the neural network model, and the background updates in the cloud ensure the efficient feature extraction capability of the neural network model.

[0278] S2.4, Collaborative Integration and Closed-Loop Update

[0279] After the optimized complete neural network model is validated at the edge (edge ​​servers along the route), it is deployed back to the device (vehicle control unit). The system state is reset, and monitoring mechanisms at all levels are restarted, forming a continuously running "perception-optimization-deployment" closed loop.

[0280] To verify the effectiveness of the hierarchical collaborative correction framework and its algorithm characteristics, experiments were conducted on a micro gas turbine benchmark dataset and a high-speed train real-world dataset.

[0281] To verify the effectiveness of the method in online adaptive modeling and optimization of high-speed train intelligent control systems, experiments were conducted on a micro gas turbine benchmark dataset and actual high-speed train data. The abbreviations of the models involved in this experiment, their full English names, and Chinese annotations are detailed in Table 1 below.

[0282] Table 1 Explanation of each model

[0283]

[0284] Figure 2 This is a speed-speed limit matching curve for high-speed trains, showing the correspondence between the train's (Speed ​​of Trains) operating speed and the speed limits of the track section. The horizontal axis represents time (in seconds), and the vertical axis represents speed (in km / h). The red line represents the speed limit of the track section, and the green line represents the actual speed of the high-speed train. Figure 2 As can be seen, the trends of the train's actual speed (green) and the section speed limit (red) almost completely overlap, indicating that the train strictly adheres to the section speed limit and there are no speeding incidents. The train's actual speed fluctuates periodically, with intervals of approximately 650 seconds (e.g., 0-650s, 650-1300s), exhibiting a pattern of "increasing → maintaining (peak speed close to 300km / h) → decreasing," corresponding to the speed limit changes in different sections (e.g., higher speed limits on highways, lower speed limits at stations / curves). This curve reflects that the train's operation fully complies with the section speed limit requirements, and the speed adjusts synchronously with the interval changes in the section speed limit.

[0285] Figures 3(a) to 3(d) The timing diagrams of control commands for the four power units (Power Units 1-4) of a high-speed train illustrate the coordinated dynamic switching pattern of traction and braking commands, demonstrating the complexity of the system control. Figures 3(a) to 3(d) These correspond to the four power units, "Power Unit 1" through "Power Unit 4". The horizontal axis represents operating time (in seconds, covering 0-7150 seconds), and the vertical axis represents control command intensity (in kN). The three curves represent: Air Brake Setpoint (red), Traction Motor Setpoint (yellow), and Electric Brake Setpoint (blue). Figures 3(a) to 3(d) It can be seen that the three curves of the four power units show a high degree of consistency, indicating good overall system control coordination. The traction motor setpoint (yellow) and the two types of braking setpoints (red and blue) exhibit "mutually exclusive fluctuations": when the traction motor setpoint is high, the air brake and electric brake setpoints are close to 0; when the air brake and electric brake setpoints rise, the traction motor setpoint decreases synchronously, reflecting the dynamic switching of the "traction-braking" mode. All three curves show high-frequency fluctuations, especially at the switching nodes in the time interval (such as around 650s and 1300s), where the fluctuations are more concentrated, indicating that the system needs to adjust the setpoints in real time to adapt to changes in train speed and the switching requirements of operating conditions.

[0286] Figures 4(a) and 4(b) are timing diagrams of the system's input voltage-output power dynamic response, demonstrating the highly synchronized changes in system output power and input signal, illustrating the nonlinearity and time-varying nature of the system response. The horizontal axis of both Figures 4(a) and 4(b) represents time nodes (labeled as 444, 888, etc.), while the vertical axis of Figure 4(a) represents output electrical power (unit: kW), presented as a green curve. The vertical axis of Figure 4(b) represents the input voltage signal (…). Voltage (unit: V) is represented by a yellow curve. The output electrical power curve (green) in Figure 4(a) exhibits periodic fluctuations (peak value close to 3.5kW, valley value close to 0), reflecting the dynamic changes in system output power over time, with a clear undulating rhythm. The stepped curve of the input voltage signal in Figure 4(b) (light yellow) shows periodic step changes (peak value close to 10V, valley value close to 0). Its rhythm is highly synchronized with the fluctuations in output power. Step adjustments in the input signal directly trigger fluctuations in output power; therefore, the dynamic changes in the input signal are the core driving factor for the output power response.

[0287] Figure 5 This graph compares the dynamic changes in the number of hidden nodes of the OSOSCN model (the neural network model proposed in this application) and the OSLSCN model with parameter N. The OSOSCN model is represented by an orange dashed line, and the OSLSCN model by a green dashed line, illustrating the pattern of complexity adjustment for both models. The horizontal axis represents parameter N (range 0-500); the vertical axis represents the number of hidden nodes for both models. As parameter N increases, the number of hidden nodes in both models increases in a stepwise manner, indicating that both the OSOSCN and OSLSCN models dynamically increase their complexity according to changes in parameter N to adapt to different task requirements. Within the same parameter N range, the number of hidden nodes in the OSLSCN model is generally higher than that in the OSOSCN model, meaning that the OSLSCN model has a more complex structure and higher resource consumption at the corresponding parameter N. The "stepwise switching" of hidden nodes in the two models corresponds to a basically synchronized parameter N, reflecting the similarity in their structural adjustment logic. The results show that the node pruning strategy of this application can retain more effective nodes, thus enabling the neural network model to meet the preset performance with fewer new nodes added by the random allocation algorithm.

[0288] Figure 6 This chart compares the prediction results of various neural network models for electrical power, used to evaluate the matching degree between the output of different models and the true value. The horizontal axis represents the parameter N (range 0~500), and the vertical axis represents electrical power (unit: kW). The black curve represents the true output electrical power (True curve), and the other curves correspond to the output results of different models (SCN, ARSCN, RRSCN, OSLSCN, OSOSCN). The output curves of each model highly overlap with the True curve, indicating that these models have high prediction accuracy for electrical power and can reproduce the variation pattern of true power well. The enlarged image in the upper left corner shows the details of the region where the parameter N is small: the initial output of each model also has a good fit with the true value; the differences between the curves of different models are slight within the overall range, reflecting the consistent performance of these models on this task. All curves show synchronous fluctuations, indicating that the neural network model obtained by the method of this application can effectively capture the dynamic variation characteristics of the true output electrical power.

[0289] Figure 7This is a 3D comparison chart of prediction errors for various neural network models, illustrating the distribution characteristics of prediction errors for different models as parameter N varies. The horizontal axis represents parameter N (range 0-500), the vertical axis represents model type (including SCN, ARSCN, RRSCN, OSLSCN, and OSOSCN), and the vertical axis represents model error (unit: kW; a smaller error indicates higher model accuracy). The prediction errors of each model fluctuate with parameter N, with most errors concentrated in the low range of 0-1.0 kW. However, some models (such as OSOSCN and OSLSCN) exhibit error peaks at specific parameter N nodes (such as around 200 and 400). Among them, the prediction errors of SCN, ARSCN, and RRSCN models are generally smoother, with a higher proportion of low error ranges. The misprediction errors of OSOSCN and OSLSCN fluctuate more significantly, with peak errors much higher than other models, indicating relatively weaker stability. Nodes such as N=200 and 400 represent the peak prediction error points for multiple models, indicating that these parameter ranges have a more significant impact on model accuracy.

[0290] Combination Figure 6 and Figure 7 Analysis shows that the neural network model (OSOSCN model) proposed in this application has better tracking ability and lower steady-state error in most cases.

[0291] Figure 8 This chart compares the actual output electrical power with the output power of the OSOSCN and OSLSCN models to evaluate the accuracy of the two models in reproducing electrical power. The horizontal axis represents the parameter N (range 0~1725), and the vertical axis represents the output electrical power (unit: kW). The solid green line represents the true value curve of the output electrical power (i.e., the True curve), the dashed orange line represents the output electrical power curve of the OSOSCN model, and the dashed blue line represents the output electrical power curve of the OSLSCN model. The output curves of both models are highly consistent with the trends of the true value curves, accurately reproducing the periodic fluctuation pattern of the actual output electrical power from "peak (nearly 3.5kW) to valley (approximately 1.0kW)," indicating that the models have a strong ability to capture dynamic changes in power. At key nodes of power fluctuation (such as the valley region near N=690), there is a slight deviation between the model output and the true value, but the overall deviation is small and does not deviate from the trend of actual power change. After initial calibration using the same calibration data, the OSOSCN model showed superior anti-forgetting performance compared to the OSLSCN model for predictions under various working conditions. This verifies that the OSOSCN model's anti-forgetting performance and cross-working-condition generalization are better than the comparison algorithms.

[0292] Figures 5-8The corresponding ablation experiment performance data are detailed in Table 2. As shown in Table 2, the OSOSCN model is the best in terms of mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), and requires fewer hidden nodes, which proves the effectiveness of the device-side adaptive algorithm and the edge-side structure adjustment strategy.

[0293] Table 2 Ablation Experiment Performance Data

[0294]

[0295] Figure 9 This chart compares the number of hidden nodes in the model over time for two methods (EECC method and EEC method), illustrating the dynamic adjustment of model complexity under different methods. The horizontal axis represents time (unit: seconds, range 0~4000), and the vertical axis represents the number of hidden nodes (the core indicator reflecting model complexity). The red dashed line represents the time-varying curve of the EECC method (edge-cloud collaborative method), and the yellow dashed line represents the time-varying curve of the EEC method (edge-cloud collaborative method). The number of hidden nodes in the EECC method remains generally stable, consistently around 30 with only minor fluctuations, indicating strong controllability of model complexity under this method. The number of hidden nodes in the EEC method is similar to that of the EECC method for most of the time, but experiences a sharp jump (peaking close to 130) in the 1500-2000 second range, before falling back to a stable range. Therefore, this method significantly increases model complexity at specific time points. The complexity of the EEC method fluctuates significantly, leading to a sharp increase in resource consumption during specific periods; in contrast, the complexity of the EECC method is stable, with a more gradual increase in resource consumption. Therefore, this demonstrates that the collaborative framework proposed in this application can more stably control the complexity of neural network models and achieve higher resource utilization efficiency.

[0296] Figure 10The graphs show the time points at which the correction signal is triggered by the two methods (EECC method and literature method). The horizontal axis represents time (in seconds, ranging from 0 to 4000), and the vertical axis represents the correction signal (values ​​of 0 or 1, where 1 represents the triggering of the correction operation). The red vertical bars represent the correction signal curve of the EECC method, and the blue vertical bars represent the correction signal curve of the literature method (e.g., Liu Y, Chai T. Demandpeak forecasting of the fused magnesia furnace group with model prediction and adaptive deep learning[J]. IEEE Transactions on Neural Networks and Learning Systems, 2024, 35(11):15920-15931). The correction signal is a discrete 0 / 1 signal: when the correction signal is 1, the corresponding method triggers a correction operation; when the correction signal is 0, no correction operation is performed. The correction triggering periods of the two methods overlap (such as at the beginning of the time, around 1500 seconds), and there are also cases where they are triggered separately. However, the EECC method triggers significantly fewer times.

[0297] Figure 11 This graph compares the errors of three methods (the literature method, the EEC method, and the EECC method) over time, used to evaluate the model accuracy and error stability of different methods. The horizontal axis represents time (in seconds, ranging from 0 to 4000), and the vertical axis represents model error (in seconds, ranging from 0 to 4000). The blue solid line represents the model error of the literature method over time, the yellow dashed line represents the model error of the EEC method over time, and the red dotted line represents the model error of the EECC method over time. Figure 11 It can be seen that the error of the literature method (as above) is mainly negative, with large fluctuations, and the lowest error is close to -1.5. The overall error range is more dispersed; the errors of both the EEC method and the EECC method are predominantly positive, concentrated in the range of 0 to 0.5. Within the interval, the fluctuation amplitude is much smaller than that of the former, and the error is more convergent. Therefore, its error fluctuation is gentle, the interval is concentrated, and the stability is stronger. In contrast, the error fluctuation of the literature method is violent and the stability is poor. The error fluctuation of the EECC method is smaller and more concentrated, and the stability is the strongest.

[0298] Figures 9-11 Table 3 details the performance comparison of the corresponding collaborative framework. The results show that the EECC method in this application achieves the lowest prediction error while having significantly fewer cloud correction triggers (4.2 ± 0.699 times) than the methods in the literature (13.4 ± 1.549 times), and the average number of nodes in the neural network model is also less. This demonstrates that the proposed collaborative framework significantly improves the utilization efficiency of communication and computing resources while ensuring accuracy.

[0299] Table 3 Comparison of Quantitative Indicators of Different Collaborative Algorithms

[0300]

[0301] Through the above examples, the method of this application has achieved the following: In ablation experiments on a micro gas turbine dataset, the OSOSCN model reduces the mean absolute error by approximately 27.8% compared to the OSLSCN model, and requires fewer nodes; In high-speed train simulation, the edge-cloud collaborative framework (EECC method) reduces the number of cloud communication triggers by approximately 68.7% compared to methods in the literature that require frequent cloud updates. This verifies the comprehensive advantages of the proposed method in improving the tracking accuracy, structural efficiency, and resource utilization efficiency of neural network models.

[0302] This example demonstrates that the online distributed parameter optimization method for intelligent modeling of complex systems can effectively support the lifelong learning and adaptive evolution of intelligent neural network models for complex dynamic systems such as high-speed trains. While ensuring high accuracy, it achieves efficient utilization of computing and communication resources and has significant industrial application value.

[0303] Based on the same inventive concept, this application also provides a system for implementing the online distributed parameter optimization method for intelligent modeling of complex systems described above. The solution provided by this system is similar to the implementation scheme described in the above method. Therefore, the specific limitations of one or more embodiments of the online distributed parameter optimization system for intelligent modeling of complex systems provided below can be found in the limitations of the online distributed parameter optimization method for intelligent modeling of complex systems described above, and will not be repeated here.

[0304] In one exemplary embodiment, an online distributed parameter optimization system for intelligent modeling of complex systems is provided, comprising: an edge execution module, an edge execution module, and a cloud execution module;

[0305] The aforementioned edge execution module is used to recursively update the output layer weight parameters of the feedforward neural network module based on the adaptive recursive ridge regression algorithm.

[0306] The aforementioned edge-side execution module is used to monitor the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds a first threshold (G≥1) for G consecutive times, it triggers a structural adjustment of the hidden layer of the feedforward neural network module. This structural adjustment includes: constructing an optimal dataset based on new data streams and historical data; performing node pruning and selection operations combined with sparsity constraints; adding new hidden layer nodes using a randomized allocation algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection; and updating the output layer weight parameters of the feedforward neural network module. After triggering the structural adjustment, it collects N consecutive data streams from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud execution module along with the verification dataset and a subset of data collected from historical data. The optimized feature extraction module parameters are received from the cloud execution module and reconstructed into a complete prediction model with the cached current state parameters of the feedforward neural network module. The local structure adjustment of the feedforward neural network module in the prediction model is triggered. After the adjustment is completed, the final neural network model is deployed to the edge execution module.

[0307] The aforementioned cloud-side execution module is used to receive the current state parameters, verification dataset, and historical data subset of the feedforward neural network module uploaded from the edge-side execution module. Based on the received data, it optimizes and updates the parameters of the feature extraction module using an incremental learning algorithm based on low-rank decomposition. It then verifies the validity of the optimized feature extraction module parameters, and if the verification passes, it downloads them to the edge-side execution module.

[0308] In another exemplary embodiment, an online distributed parameter optimization system for intelligent modeling of complex systems includes: a device, an edge server, and a cloud server;

[0309] The edge device is configured to recursively update the output layer weight parameters of the feedforward neural network module based on the adaptive recursive ridge regression algorithm.

[0310] The edge device is configured to: monitor the absolute prediction error of the feedforward neural network module; when the absolute prediction error exceeds a first threshold (G≥1) for G consecutive times, trigger a structural adjustment of the hidden layer of the feedforward neural network module; wherein, the structural adjustment includes: constructing an optimal dataset based on new data streams and historical data, performing node pruning and selection operations combined with sparsity constraints; based on the residuals of the feedforward neural network module on the optimal dataset after selection, adding new hidden layer nodes using a random configuration algorithm, and updating the output layer weight parameters of the feedforward neural network module; after triggering the structural adjustment, collecting N consecutive data streams from the real-time data stream. w The validation dataset consists of N data points, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud server along with the verification dataset and a subset of historical data. The optimized feature extraction module parameters are received from the cloud server and reconstructed into a complete prediction model with the cached current state parameters of the feedforward neural network module. The local structure adjustment of the feedforward neural network module in the prediction model is triggered. After the adjustment is completed, the final neural network model is deployed to the edge device.

[0311] The cloud-side server is configured to: receive the current state parameters, verification dataset, and historical data subset of the feedforward neural network module uploaded from the edge-side device; optimize and update the parameters of the feature extraction module based on the received data using an incremental learning algorithm based on low-rank decomposition; verify the validity of the optimized feature extraction module parameters; and if the verification passes, download them to the edge-side device.

[0312] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, memory, input / output interfaces (I / O), and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is connected to the system bus via the I / O interfaces. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the computer device stores video tag processing data. The I / O interfaces of the computer device are used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements an online distributed parameter optimization method for intelligent modeling of complex systems.

[0313] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0314] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0315] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0316] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0317] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0318] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0319] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0320] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. An online distributed parameter optimization method for intelligent modeling of complex systems, characterized in that, Includes the following steps: The edge acquires data streams in real time and continuously updates the output layer weight parameters at the end of the feedforward neural network module based on the adaptive recursive ridge regression algorithm. The edge continuously monitors the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds a first threshold for G consecutive times, a structural adjustment of the hidden layer of the feedforward neural network module is triggered, where G≥1. The structural adjustment includes: constructing an optimal dataset based on new data streams and historical data, performing node pruning and selection operations combined with sparsity constraints; and adding new hidden layer nodes using a random configuration algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection, and updating the output layer weight parameters at the end of the feedforward neural network module. After the structural adjustment is triggered at the edge, N consecutive data points are newly acquired from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module concatenated with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud side along with the verification dataset and a subset of data collected from historical data. Based on the received data, the cloud side uses an incremental learning algorithm based on low-rank decomposition to optimize and update the parameters of the feature extraction module. The optimization of the parameters of the feature extraction module specifically includes: When the edge-side triggers structural adjustments and the temporary storage space is unoccupied, the state parameters of the feedforward neural network module are cached; future N data are continuously collected from the real-time data stream. w The validation dataset consists of N data points, and the mean absolute error of the current full model is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that concept drift has occurred, and the cached state parameters, verification dataset, and historical data subset are uploaded to the cloud. After receiving the data on the cloud side, the feedforward neural network module is reconstructed using the state parameters, and then concatenated with the current feature extraction module and the basic feature extraction module on the cloud side to form two models to be evaluated; the validation dataset and the historical data subset are combined to form the cloud side training dataset. Incremental learning based on low-rank decomposition is performed on the basic feature extraction module to optimize its parameters, resulting in an optimized feature extraction module. The optimized feature extraction module is concatenated with the state parameters to obtain the model to be evaluated. Its mean absolute error is calculated on the validation dataset and compared with the mean absolute error before optimization to verify the optimization effect. If the verification is effective, the optimized parameters are passed down to the edge side. After receiving parameters from the cloud side, the edge side reconstructs the complete model by combining the state parameters cached locally, and triggers local structural adjustments to the feedforward neural network module. The cloud side verifies the validity of the optimized feature extraction module parameters. If the verification is successful, the parameters are transmitted to the edge side. The edge side uses the received feature extraction module parameters and the cached current state parameters of the feedforward neural network module to reconstruct the complete prediction model and trigger local structural adjustments of the feedforward neural network module in the prediction model. After the adjustments are completed, the final neural network model is deployed to the edge side.

2. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 1, characterized in that, The method of continuously updating the output layer weight parameters at the end of the feedforward neural network module based on the adaptive recursive ridge regression algorithm specifically includes: Based on the output matrix of the hidden layer of the feedforward neural network module and the sample label vector, a linear parameterized model is established, and a regularized weighted least squares optimization problem based on the exponential weighted matrix and the regularization factor is constructed. Solve the regularized weighted least squares optimization problem, derive and execute the recursive update calculation of the output layer weight parameters; Based on the variance estimation of system noise and prior error, the forgetting factor at the current moment is dynamically adjusted. Based on the singular value decomposition of the output matrix and the criterion for minimizing the mean square error of the estimation, the regularization factor at the current time is dynamically adjusted. By using the adaptively adjusted forgetting factor and regularization factor, the recursive update calculation of the output layer weight parameters is driven, thereby completing the online estimation of the output layer weight parameters.

3. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 1 or 2, characterized in that, The structural adjustment of the hidden layer of the feedforward neural network module specifically includes: The absolute error of prediction is continuously monitored at the edge. When the error exceeds the first threshold for G consecutive times, a structural adjustment is triggered, where G≥1. The latest real-time data samples are collected to form the current new data stream, and a local regression model is constructed based on the current new data stream. A sub-sample set is selected from the historical data according to its fitting error. At the same time, a historical sample set is obtained by uniformly sampling from the historical dataset. The current new data stream, the sub-sample set and the historical sample set are concatenated to form the optimal dataset. Based on the optimal dataset, the contribution of each hidden layer node in the current feedforward neural network module is calculated, and all hidden nodes are divided into a permanent set, a frozen candidate set, and a pruning candidate set. For each node in the frozen candidate set, an unfreezing decision is made, and the total contribution of the frozen nodes is calculated to update the pruning candidate set; From the updated pruning candidate set, the set of important nodes is selected by solving an optimization problem with sparse constraints; Based on the set of important nodes, the residual of the current feedforward neural network module on the optimal dataset is calculated; if the residual does not meet the preset performance requirements, a random configuration algorithm is used to grow new nodes and recalculate the output layer weight parameters until the performance requirements are met.

4. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 1, characterized in that, The incremental learning based on low-rank decomposition specifically includes: For the linear layer weight matrix W to be optimized in the feature extraction module, it is reconstructed as follows: in, This is the base weight matrix for offline pre-training; and These are the scaling diagonal matrices for the output and input channels, respectively; It is a low-rank bias matrix. Let be the rank of the low-rank bias matrix.

5. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 2, characterized in that, The recursive update calculation of the output layer weight parameters is specifically implemented through the following formula: in, and These are the estimated values ​​of the output layer weight parameters at the current and previous time steps, respectively. It is the identity matrix; As a regularization factor; Forgetting factor; The autocorrelation matrix at the current time step The inverse matrix; The autocorrelation matrix of the previous time step The inverse matrix; This is the output vector of the hidden layer at the current time step; This represents the prior error at the current moment; For the observed variables at the current moment.

6. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 2, characterized in that, The dynamic adjustment of the regularization factor at the current moment is specifically achieved through the following formula: in, The regularization factor at the current moment; The forgetting factor at the current moment; Autocorrelation matrix The maximum singular value; For the current time of system noise Variance estimation; For the weight parameter estimates In the autocorrelation matrix The maximum component after projection onto the singular vector space.

7. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 3, characterized in that, The contribution of the hidden layer nodes is calculated using the following formula: in, Hidden layer node Contribution , Hidden layer node The total number; For the optimal dataset Total number of samples; subscript For sample index, ; and They are nodes Input weights and biases; To hide nodes The output layer weights; To hide nodes Activation function; For the optimal dataset The Middle The nth input sample is used to calculate the nth... The hidden node is the first Activation value of each sample Input.

8. The online distributed parameter optimization method for intelligent modeling of complex systems according to claim 1, characterized in that: The first threshold and / or the number of consecutive occurrences G are dynamically adjusted based on the historical prediction error statistical characteristics of the feedforward neural network module.

9. An online distributed parameter optimization system for implementing the online distributed parameter optimization method for intelligent modeling of complex systems as described in claim 1, characterized in that, include: End-side execution module, edge-side execution module, and cloud-side execution module; The edge execution module is used to recursively update the output layer weight parameters of the feedforward neural network module based on the adaptive recursive ridge regression algorithm. The edge-side execution module is used to monitor the absolute prediction error of the feedforward neural network module. When the absolute prediction error exceeds a first threshold (G≥1) for G consecutive times, it triggers a structural adjustment of the hidden layer of the feedforward neural network module. This structural adjustment includes: constructing an optimal dataset based on new data streams and historical data; performing node pruning and selection operations combined with sparsity constraints; adding new hidden layer nodes using a randomized allocation algorithm based on the residuals of the feedforward neural network module on the optimal dataset after selection; and updating the output layer weight parameters of the feedforward neural network module. After triggering the structural adjustment, it collects N consecutive data streams from the real-time data stream. w N data points are used to form a validation dataset, and its mean absolute error is calculated. w ≥1; If the mean absolute error exceeds the second threshold, it is determined that the feature extraction module spliced ​​with the feedforward neural network module has experienced concept drift. The current state parameters of the feedforward neural network module are cached and uploaded to the cloud execution module along with the verification dataset and a subset of data collected from historical data. The optimized feature extraction module parameters are received from the cloud execution module and reconstructed into a complete prediction model with the cached current state parameters of the feedforward neural network module. The local structure adjustment of the feedforward neural network module in the prediction model is triggered. After the adjustment is completed, the final neural network model is deployed to the edge execution module. The cloud-side execution module is used to receive the current state parameters, verification dataset, and historical data subset of the feedforward neural network module uploaded from the edge-side execution module. Based on the received data, it optimizes and updates the parameters of the feature extraction module using an incremental learning algorithm based on low-rank decomposition. It then verifies the validity of the optimized feature extraction module parameters, and if the verification passes, it downloads them to the edge-side execution module.

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