Intelligent drive material hysteresis modeling method based on knowledge-driven neural network

Abstract

The application discloses a kind of intelligent drive material hysteresis modeling methods based on knowledge-driven neural network, it is related to intelligent manufacturing and drive control technical field, including: the fractional order Backlash-GRUNN hybrid model of fusion material physical mechanism is constructed;The multiscale physical characteristics of intelligent drive material are input into the fractional order Backlash-GRUNN hybrid model, and model training is carried out, to obtain the fractional order Backlash-GRUNN hybrid model after training;The fractional order Backlash-GRUNN hybrid model after training is used as the hysteresis model of intelligent drive material, to describe the hysteresis characteristics of intelligent drive material under different drive signals.The application solves the problems of high modeling complexity, strong parameter dependence, low model precision and poor interpretability of existing methods.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and drive control technology, specifically to an intelligent drive material hysteresis modeling method based on a knowledge-driven neural network. Background Technology

[0002] Piezoelectric materials are a type of smart actuation material that generates mechanical strain under the influence of an electric field, and are used in sensors and actuators. Another type of smart actuation material—dielectric elastomers—is a novel soft smart material. Based on the Maxwell stress effect induced by an electric field, it drives a dielectric thin film under polarization, causing its thickness to compress and its planar surface to expand, thus achieving large deformation output. This demonstrates excellent driving strain, high energy density, and superior energy efficiency, providing a new path to overcome the kinematic and dynamic bottlenecks of traditional electromechanical systems. These smart actuation materials enable efficient, precise, and flexible control and operation, possessing unique physical properties and engineering applications in the fields of intelligent manufacturing and drive control technology. However, their response mechanisms to external stimuli (such as electric fields, magnetic fields, temperature, or stress) are complex, often exhibiting hysteresis and nonlinear characteristics. For example, the mechanical strain or charge output generated by piezoelectric materials under the influence of an electric field is affected by historical excitation; the deformation of dielectric elastomers under the influence of an electric field also exhibits hysteresis and nonlinear characteristics.

[0003] Common mathematical modeling methods for describing the hysteresis nonlinear properties of smart materials can be categorized into differential equation models, integral operator models, and artificial intelligence models. Differential equation models and integral operator models belong to physical knowledge models, possessing good interpretability in terms of physics and knowledge, and are suitable for describing the dynamic evolution and physical mechanisms of systems. However, they have high modeling complexity and strong parameter dependence, resulting in relatively low accuracy. Artificial intelligence models have powerful nonlinear modeling capabilities and adaptability, capable of handling big data and complex systems, but suffer from poor interpretability and high demands on data volume and computational resources. In particular, model performance is poor when the amount of data is limited. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides an intelligent driving material hysteresis modeling method based on a knowledge-driven neural network, which solves the problems of high modeling complexity, strong parameter dependence, low model accuracy, and poor interpretability of existing methods.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a smart driving material hysteresis modeling method based on a knowledge-driven neural network, comprising the following steps:

[0006] S1: Construct a fractional-order Backlash-GRUNN hybrid model that integrates material physics mechanisms;

[0007] S2: Input the multi-scale physical characteristics of the intelligent driving material into the fractional Backlash-GRUNN hybrid model, train the model, and obtain the trained fractional Backlash-GRUNN hybrid model;

[0008] S3: The trained fractional-order Backlash-GRUNN hybrid model is used as the hysteresis model of the intelligent driving material to describe the hysteresis characteristics of the intelligent driving material under different driving signals.

[0009] Furthermore, the fractional Backlash-GRUNN hybrid model in S1 is composed of interconnected fractional Backlash neural network sub-models and GRUNN neural network sub-models;

[0010] The fractional-order Backlash neural network sub-model includes 9 input layers, 20 hidden layers, and 1 output layer;

[0011] The input layer includes the excitation signals of the real system. The derivative of the excitation signal and 7 input sequences consisting of a constant 1 , , where, when the excitation signal When connected to an absolute value activation function layer, its connection weight is set to a constant value of 1, and the excitation signal... When connected to the additive layer, the connection weights are set to 1, 0.8, 0.08, 0.032, and 0.0176, respectively.

[0012] Input sequence The outputs of the connected neurons are the seven parameters of the hysteresis model, and the input weights of each neuron are as follows: The corresponding custom activation function is:

[0013]

[0014] in, The parameters for the corresponding equations are respectively , , , , , , , For the corresponding neurons, The weights corresponding to each neuron. For the corresponding weight index, , This is the input to the neuron;

[0015] The expression for the absolute value activation function layer is:

[0016]

[0017] in, For absolute value activation functions, To perform the absolute value operation on the input signal of this neuron;

[0018] Each hidden layer contains one neuron;

[0019] The output layer is used to generate the network's output signal.

[0020] Furthermore, the fractional-order Backlash-GRUNN hybrid model is expressed as:

[0021]

[0022]

[0023] in, For the output variables of the fractional-order Backlash neural network sub-model, For time, The symbol for fractional calculus operators. For order, For the output variables of the fractional Backlash-GRUNN mixture model;

[0024] According to the definition of backward difference, after discretization, we get:

[0025]

[0026]

[0027] in, , and The first , and The output variables of the time-series fractional-order Backlash neural network submodel. The sampling interval is... For the first Constantly provide stimulus signals. For the first The output variables of the time-series fractional Backlash-GRUNN mixture model For the first Constantly provide stimulus signals. For the first The derivative of the excitation signal at time t.

[0028] Furthermore, the GRUNN neural network sub-model uses the output of the fractional-order Backlash neural network sub-model as an extended input to the GRUNN neural network sub-model input sequence, along with the excitation signal. and the derivative of the excitation signal Together they act on the GRUNN neural network sub-model;

[0029] The calculation process of the GRUNN neural network sub-model is as follows:

[0030]

[0031] in, To reset the door in Output at any moment To update the door Output at any moment It is the sigmoid activation function. To reset the weight matrix of the gate, To update the gate weight matrix, for The output of the time loop unit, for The input to the GRUNN model at time 10:00. To reset the gate's bias vector, To update the bias vector of the gate;

[0032]

[0033] in, for The output of the time loop unit, These are candidate values ​​for the current hidden state. The hyperbolic tangent activation function is used. Let be the weight matrix of the candidate hidden states. It is the bias vector of the candidate hidden state. This represents element-wise product.

[0034] Furthermore, the fractional-order Backlash neural network sub-model is trained using the LM algorithm.

[0035] A knowledge-driven neural network-based intelligent hysteresis modeling system for driven materials includes a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the knowledge-driven neural network-based intelligent hysteresis modeling method for driven materials.

[0036] The beneficial effects of this invention are:

[0037] (1) Knowledge-driven mechanism with prior constraints: Backlash differential equations in fractional form, which are more conducive to describing non-local memory, are used to describe the macroscopic evolution of hysteresis behavior. This is further transformed into a Backlash neural network model (BacklashNN), mapping the differential equation parameters to network weights, thus transforming the parameter determination problem into a weight optimization problem for the neural network. This transformation constrains the network's solution space, ensuring that the overall model learning process satisfies prior mathematical laws. This transparent model emphasizes strong interpretability, clear mathematical meaning, and a simple structure.

[0038] (2) Enhanced data-driven compensation for time-series capture: The GRU module with reset and update gates, specially designed in deep learning, is introduced to selectively retain or ignore historical information, aiming to finely capture the hysteresis effect and comprehensively correct unmodeled dynamic errors. The combination of knowledge-driven and data-driven approaches significantly improves the performance of the Backlash model in capturing long-term dependencies, achieving synergistic optimization of model transparency and prediction accuracy, and demonstrating a new perspective on combining prior knowledge with deep learning methods.

[0039] (3) The model has high accuracy, low computational cost, short time, small data requirement, and high interpretability. The significant advantages of this method in terms of modeling accuracy and dynamic consistency, this hybrid modeling method that combines prior knowledge constraints and data-driven compensation, provides a new perspective for modeling the driving properties of smart materials. Attached Figure Description

[0040] Figure 1 This is a flowchart of the intelligent driving material hysteresis modeling method based on knowledge-driven neural networks of the present invention.

[0041] Figure 2 This is a topology diagram of a fractional Backlash model.

[0042] Figure 3 This is a diagram of a fractional-order Backlash neural network model.

[0043] Figure 4 This is a structural diagram of GRUNN.

[0044] Figure 5 This is a structural diagram of a fractional Backlash-GRUNN.

[0045] Figure 6 The graph shows the predictive regression analysis of the fractional Backlash submodel on different datasets.

[0046] Figure 7 A graph comparing the modeling performance of different models.

[0047] Figure 8 This is a simulation diagram of a variable frequency signal.

[0048] Figure 9 This is a simulation diagram of a variable amplitude signal.

[0049] Figure 10 The simulation diagram shows significant asymmetry.

[0050] Figure 11 This is a simulation diagram of butterfly-shaped hysteresis. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0052] Example 1, as Figure 1 As shown, an intelligent driving material hysteresis modeling method based on a knowledge-driven neural network includes the following steps:

[0053] S1: Construct a fractional-order Backlash-GRUNN hybrid model that integrates material physics mechanisms;

[0054] The fractional Backlash-GRUNN hybrid model in S1 is composed of interconnected fractional Backlash neural network sub-models and GRUNN neural network sub-models.

[0055] Unlike traditional rigid smart materials, dielectric elastomers possess strong nonlocal memory characteristics. Furthermore, the interaction between material deformation and the influence of the electric field during mechanical loading leads to multiphysics coupling, complicating the establishment of a unified model. In addition, the inhomogeneity and defects of material properties in real-world applications must also be considered, resulting in multiple challenges in modeling dielectric elastomers. Based on these considerations, this invention proposes a fractional-order Backlash-GRUNN model.

[0056] The fractional Backlash-GRUNN hybrid model is represented as follows:

[0057]

[0058] This formula is responsible for providing basic nonlinear expressive power. The fractional derivative can not only capture the effects of long-term memory, but also provide more comprehensive rate-related information.

[0059]

[0060] The damping term in this formula It affects the degree to which the system responds to changes in input. This represents the energy loss caused by time-varying input, further emphasizing the importance of state changes in rate systems, which are crucial to the system's stability and dynamic response. External force term. This reflects the external influences on the system in practical applications, compensating for unmeasured disturbances or noise to enhance the model's practical applicability. This comprehensive dynamic framework takes into account the interactions between variables, enabling it to more accurately describe and predict complex nonlinear responses in real-world systems.

[0061] in, For the output variables of the fractional-order Backlash neural network sub-model, For time, The symbol for fractional calculus operators. For order, For the fractional Backlash-GRUNN hybrid model, represents the output variable.

[0062] Discretizing continuous differential equations is a key step in solving complex dynamic system problems. First, discretization provides the foundation for computer implementation, enabling modern computers to perform complex numerical calculations quickly and efficiently, meeting the needs of large-scale data processing. Simultaneously, by appropriately selecting the grid partitioning and time step, the discretization process significantly improves the accuracy of the model solution, better capturing the dynamic behavior and physical characteristics of the system.

[0063] The Finite Difference Method (FDM) is one of the most commonly used discretization methods for complex engineering and physics problems. It approximates the numerical solution of continuous differential equations by replacing the derivatives with difference quotients at discrete nodes. The basic process involves dividing time and space into uniform or non-uniform grids, expressing the derivatives using forward difference, backward difference, or central difference formulas, and substituting their discrete expressions into the original equations to form a system of discrete equations. In the solution process, iterative or direct methods are typically used to obtain the numerical solution. Here, a first-order backward difference form is used, where... Indicates the sampling interval, when When the size is sufficiently small, the difference equation is defined as:

[0064]

[0065]

[0066]

[0067] According to the definition of backward difference, after discretization, we get:

[0068]

[0069]

[0070] in, , and The first , and The output variables of the time-series fractional-order Backlash neural network submodel. The sampling interval is... For the first Constantly provide stimulus signals. For the first The output variables of the time-series fractional Backlash-GRUNN mixture model For the first Constantly provide stimulus signals. For the first The derivative of the excitation signal at time t.

[0071] In the numerical discretization of fractional calculus, larger orders (such as 10, 20, etc.) can more comprehensively reflect the historical information of the system, thereby improving the approximation accuracy of the model, but also significantly increasing the computational burden. Conversely, smaller orders (such as 2) greatly shorten the computation time, making them suitable for real-time applications or situations with limited storage, but may sacrifice some approximation accuracy. We found that taking the first four terms as the difference approximation can meet the high accuracy requirements, ensure the stability of the algorithm, and effectively control the computational load. Based on this, after extensive experimental comparisons, we systematically evaluated the choice of order λ, including 0, 0.5, 0.8, 1, 1.3, and 5 other different orders, and finally determined that the order value is 0.8. This choice effectively balances the modeling accuracy with computational efficiency, meeting the dual requirements of accuracy and performance in practical engineering applications. The discretized fractional-order input information is shown below:

[0072]

[0073] Based on the above discretized model expression, and considering the transmission relationship from the input signal to the output signal, as well as the structural relationship between the model parameters and the terms of the expression, a custom neural network topology is defined, such as... Figure 2 As shown.

[0074] The fractional-order Backlash neural network sub-model includes 9 input layers, 20 hidden layers, and 1 output layer;

[0075] The input layer includes the excitation signals of the real system. The derivative of the excitation signal and 7 input sequences consisting of a constant 1 , Its length is related to the input signal The lengths are the same. Strictly based on the discretized differential equations, this network adopts an intermediate structure with 20 hidden layers, specially designed so that each layer contains only one neuron. This unique architectural design aims to reduce computational complexity and optimize model performance. and These represent the node addition operator and the node multiplication operator, respectively. Denotes the delay operator, where The unit of discrete-time signal is used, and this design effectively captures the nonlinear hysteresis characteristics of dynamic systems. Finally, the 21st layer is designed as the output layer, responsible for generating the network's output signal. This innovative network structure enables more flexible and efficient modeling of complex nonlinear dynamic systems, achieving higher prediction accuracy and stronger adaptability.

[0076] Among them, when the excitation signal When connected to an absolute value activation function layer, its connection weight is set to a constant value of 1, and the excitation signal... When connected to the additive layer, since the inputs are accumulated at different times in the time series, the connection weights are set to 1, 0.8, 0.08, 0.032, and 0.0176, respectively. The connection weights between layers in this neural network are 1, -1, and T, respectively. Here, T is the sampling time interval, and 1 and -1 represent the sensitivity of the neurons in that layer to the corresponding input signal; 1 represents a positive response, and -1 represents the inhibition of signal flow.

[0077] Input sequence The outputs of the connected neurons are the seven parameters of the hysteresis model, and the input weights of each neuron are as follows: The corresponding custom activation function is:

[0078]

[0079] in, The parameters for the corresponding equations are respectively , , , , , , , For the corresponding neurons, The weights corresponding to each neuron. For the corresponding weight index, , This is the input to the neuron;

[0080] Weights corresponding to 7 neurons This design allows for adaptive adjustment during network training. After being processed by specific activation functions, the weights of these neurons correspond one-to-one with the parameters in the differential equation model, giving the neural network model actual physical constraints and principles, making it interpretable, and enhancing the transparency of understanding how the neural network identifies and extracts complex features of the modeled system. In contrast, the connection weights between other layers are fixed and do not update during training; this design also reduces the difficulty of identifying neural network parameters.

[0081] Furthermore, to further enhance the flexibility and robustness of neural network models in handling nonlinear features, this invention designs corresponding activation functions for neural network layers requiring special operations. This design not only accelerates the training speed of the neural network but also ensures the accuracy of describing nonlinear features. Specifically, the expression for the absolute value activation function we use is:

[0082]

[0083] in, For absolute value activation functions, To perform the absolute value operation on the input signal of this neuron;

[0084] Each hidden layer contains one neuron;

[0085] The output layer is used to generate the network's output signal.

[0086] Based on the above design of the neural network topology and activation function, the neural network finally obtained by this invention is as follows: Figure 3 As shown, the constructed fractional-order Backlash neural network model has 20 hidden layers and 1 output layer, which is consistent with... Figure 2 The topology corresponds to that in the model. Each layer has only one neuron, and the network size and complexity are considered acceptable for network training. Furthermore, an ideal property is that the internal structure of the proposed fractional-order Backlash neural network is known, making it interpretable.

[0087] Mathematical models based on differential equations and their custom neural network structures provide strong prior knowledge constraints. However, when dealing with the complex nonlinear hysteresis relationships of smart material actuators, this method struggles to fully capture the dynamic characteristics of the system globally, especially exhibiting instability at extreme points. Therefore, there is an urgent need to explore more advanced modeling techniques to improve the accuracy and adaptability of models, thereby more effectively revealing the behavior of smart materials. Gated recurrent units (GRUs) are a special type of recurrent neural network that utilizes its gating mechanism to achieve effective information fusion and can effectively alleviate the gradient vanishing problem in standard RNNs, making them an ideal choice for handling time delays and hysteresis phenomena.

[0088] This invention features targeted customization and extensions in the design of the GRUNN model. Specifically, it introduces an input augmentation mechanism that incorporates fractional order concepts. The output of the Backlash neural network model, containing fractional order information, is used as an extended input to the GRUNN input sequence. This enhances the network's ability to perceive "non-local dynamic characteristics" and constrains the GRUNN solution space, improving the training efficiency of deep neural networks. Further data normalization is also implemented to serve the requirements of conserving computational resources and ensuring modeling stability. Furthermore, in the design of the GRU layer, based on past experience and extensive experimental testing, we adjusted the number of hidden layer units and the activation function configuration. The number of hidden layer units was set to 50, the initial learning rate to 0.005, and the learning rate adjustment factor every 10 epochs to 0.6. The training objective was set to 10. -7 .

[0089] The GRUNN neural network sub-model uses the output of the fractional-order Backlash neural network sub-model as an extended input to the input sequence of the GRUNN neural network sub-model, along with the excitation signal. and the derivative of the excitation signal Together they act on the GRUNN neural network sub-model;

[0090] Figure 4 The structure of GRUNN in this invention is shown. , They represent time The model input and the output of the loop unit.

[0091] The calculation process of the GRUNN neural network sub-model is as follows:

[0092]

[0093] The Reset Gate controls the impact of past hidden states on the current candidate hidden state;

[0094] in, To reset the door in Output at any moment To update the door Output at any moment It is the sigmoid activation function. To reset the weight matrix of the gate, To update the gate weight matrix, for The output of the time loop unit, for The input to the GRUNN model at time 10:00. To reset the gate's bias vector, To update the bias vector of the gate;

[0095] The calculation of the hidden state in GRUNN combines the effects of the reset gate and the update gate, as shown in the following formula:

[0096]

[0097] in, for The output of the time loop unit, These are candidate values ​​for the current hidden state. The hyperbolic tangent activation function is used. Let be the weight matrix of the candidate hidden states. It is the bias vector of the candidate hidden state. This represents element-wise product.

[0098] This invention extends neural network modeling methods to the domain of multi-valued hysteresis mappings, specifically in the expanded input space constructed by the input, input derivative, and output of the fractional-order BacklashNN model. Above, the output of the hysteresis system Coordinates in the input space It is uniquely determined, forming a one-to-one mapping relationship.

[0099] like Figure 5 As shown, the fractional-order Backlash-GRUNN hybrid model has 9 inputs, among which For the excitation signal of the real system, It is the derivative of the input signal and is responsible for providing rate-related information. The output of the backNN model, and , As a unified input sequence applied to the GRUNN model, As the output of the GRUNN model, it also represents the response of the fractional-order Backlash-GRUNN hybrid model. The remaining connections within the hybrid model are consistent with those described above. By using the prior knowledge of the fractional-order BacklashNN for guidance, combined with the powerful temporal capture capabilities of GRUNN, the fractional-order Backlash-GRUNN hybrid model maintains high transparency while also ensuring accurate modeling capabilities.

[0100] S2: Input the multi-scale physical characteristics of the intelligent driving material into the fractional Backlash-GRUNN hybrid model, train the model, and obtain the trained fractional Backlash-GRUNN hybrid model;

[0101] After constructing the fractional-order Backlash-GRUNN hysteresis model, appropriate network training configuration is also essential for improving model accuracy. In this embodiment, the dielectric elastomer experimental data is randomly allocated as the training set, validation set, and test set in a ratio of 70%, 15%, and 15%, respectively. This random partitioning helps improve the model's generalization ability. Table 1 clearly shows the key parameter settings of the model. The number of iterations for the fractional-order BacklashNN sub-model is set to 200. Fewer iterations prevent overfitting of the simple neural structure. The training objective is set to 10⁻⁴, and the learning rate is set to 0.08, aiming to accelerate the training process and save training time without affecting the provision of pre-constraints. The number of iterations for the GRUNN sub-model is set to 500 because more iterations are needed to learn effective features for fine-tuning the model. The smaller training objective of 10⁻⁴ is used. -7 A lower initial learning rate of 0.005 better corrects for unmodeled dynamic errors; these parameters were determined based on experimental validation and research experience. In neural network design, the number of neurons in the hidden layer is a crucial parameter. Generally, increasing the number of neurons in the hidden layer allows the network to uncover deeper data features, thereby improving model performance. However, this often comes with higher energy consumption and longer training time. Therefore, a trade-off must be made between model performance and complexity when designing a network. Extensive experimental testing revealed that when the number of hidden layer neurons in the GRUNN model is 50, it can largely balance modeling accuracy and training efficiency, achieving satisfactory overall performance.

[0102] It should be noted that while this setup has not undergone global optimization and may not be the theoretically optimal solution, it has achieved a high performance level in current application scenarios. This is thanks to the powerful feature learning capabilities of neural networks, which can automatically extract effective information from large-scale data and exhibit excellent generalization ability and robustness. As long as the training objective is set reasonably, a fully optimized neural network can often meet task requirements with stable performance.

[0103] Table 1 Key parameter settings for the fractional-order Backlash-GRUNN neural network model

[0104]

[0105] This invention borrows and improves upon a two-step training method. In the first step, the Levenberg-Marquardt algorithm (LM algorithm) is used to train the fractional-order BacklashNN sub-model. The LM algorithm is an iterative optimization method for nonlinear least squares problems. By combining the efficiency of the Gauss-Newton method with the stability of gradient descent, it aims to balance fast convergence and stability in optimization problems with high nonlinearity and complexity, and is one of the most commonly used algorithms for training neural networks. The experimental data used for training should cover sufficient amplitude and bandwidth to ensure that the sub-model can fully capture the system's response characteristics under different conditions. In the second step, the input data and derivatives of the experimental system, along with the output of the fractional-order BacklashNN sub-model, are used as the input to GRUNN, and the output data of the experimental system is used as the output of GRUNN. GRUNN's unique gated loop mechanism can effectively handle complex dependencies in sequential data, achieving accurate modeling of nonlinear systems by integrating historical data. Setting different parameters for different sub-models provides flexibility and adaptability for model training to meet different characteristic requirements. This strategy allows for a better balance between training time and model performance.

[0106] S3: The trained fractional-order Backlash-GRUNN hybrid model is used as the hysteresis model of the intelligent driving material to describe the hysteresis characteristics of the intelligent driving material under different driving signals.

[0107] In one embodiment of the present invention, Figure 6 The analysis results of the fractional-order Backlash sub-model are presented. The training data for the model were generated from a set of sinusoidal signals with fixed frequencies and amplitudes. The figure compares the model's predictions with the actual system responses. In the regression analysis, the correlation coefficient R-value is used to measure the linear correlation between the model's predictions and the actual target values. The correlation coefficient R-value for the training set is 0.99841, for the validation set it is 0.99824, and for the test set it is 0.99844. Overall, the data points are closely distributed around the regression line, with no obvious outliers. The predicted output is highly correlated with the target value, further validating the model's stability and accuracy.

[0108] To overcome the aforementioned limitations, a gated recurrent unit neural network (GRUNN) was introduced to construct a fractional-order Backlash-GRUNN model. This model integrates the knowledge-driven mechanism of fractional-order Backlash with the advantages of GRUNN in time-series data processing and information integration, thereby effectively compensating for the shortcomings of fractional-order BacklashNN in modeling peaks, troughs, and transition segments.

[0109] Figure 7This study demonstrates a significant performance improvement over the fractional Backlash-GRU model, particularly in predicting accuracy at extrema and in their vicinity. The model is able to more effectively capture subtle changes and identify complex nonlinear behaviors that traditional fractional BacklashNNs struggle to learn independently, exhibiting stronger modeling capabilities and generalization performance.

[0110] To further improve modeling accuracy and computational efficiency, the model selectively incorporates key attributes of the excitation signal (such as amplitude and frequency) as input features. Since GRUNN relies on a gating mechanism to dynamically adjust temporal dependency information, the appropriate selection of input features is crucial for enhancing the model's ability to characterize the system's dynamic behavior. By carefully selecting input variables, the model's ability to identify nonlinear and rate-dependent behaviors is improved, while effectively controlling model complexity and reducing training costs.

[0111] The results show that the proposed fractional-order Backlash-GRUNN model exhibits higher modeling accuracy and robustness in characterizing the asymmetry and rate-dependent hysteresis in dielectric elastomer systems.

[0112] This embodiment systematically explores the hysteresis characteristics of dielectric elastomers under various working environments and deeply verifies the modeling capability and adaptability of the fractional-order Backlash-GRUNN model in dealing with different hysteresis behaviors and parameter variations. The simulation data acquisition process is as follows: First, a mathematical model of the dielectric elastomer system is built using the MATLAB / Simulink platform, and representative excitation signals are selected to obtain the model output. The four sets of simulation data obtained finally show amplitude variation, frequency variation, significant asymmetry, and typical "butterfly-shaped" hysteresis curve characteristics, respectively. These data are then used to train the fractional-order Backlash-GRUNN model to comprehensively evaluate its modeling accuracy and generalization ability.

[0113] However, existing research often focuses on single or partial types of hysteresis behavior, making it difficult to uniformly model multiple complex behaviors such as amplitude correlation, rate correlation, significant asymmetry, and typical "butterfly" hysteresis. Against this backdrop, this embodiment selects the four typical hysteresis phenomena mentioned above and constructs test datasets with different dynamic characteristics to more realistically represent hysteresis phenomena in DEA systems. Subsequently, a fractional-order Backlash-GRUNN model is used to model and fit these representative hysteresis behaviors, and the simulation performance is systematically evaluated in terms of modeling accuracy and response consistency to verify the model's effectiveness and generalization ability in handling complex nonlinear hysteresis scenarios.

[0114] Figures 8 to 11This visually demonstrates the superior fitting ability of the fractional-order Backlash-GRUNN model to simulate various hysteresis characteristics of dielectric elastomers in different practical applications. Each set of figures consists of four parts: Figure 8 (a) Figure 9 (a) Figure 10 (a) and Figure 11 (a) shows different input excitation conditions; corresponding Figure 8 (b) Figure 9 (b) Figure 10 (b) and Figure 11 (b) shows the model's fit to the output under these conditions, with the black dashed line representing the actual simulated response curve and the red dashed line representing the model's prediction. Next, each subplot (c) in each group reflects the model's fitting ability to handle complex input-output relationships (hysteresis behavior), with the black dashed line showing the theoretical input-output response path and the red dashed line representing the model's prediction curve. Finally, subplot (d) shows in detail the error distribution between the model's predicted output and simulated data response under different operating conditions, intuitively demonstrating the model's high accuracy. Clearly, regardless of changes in operating conditions, the fractional-order Backlash-GRUNN model consistently demonstrates a powerful ability to capture and fit hysteresis behavior.

[0115] In this study, the average error (AVG) was used as the core indicator to measure the model's accuracy, as shown in Table 2. The results show that the fractional-order Backlash-GRU model exhibits average errors on the order of 1e-2 or lower under various hysteresis types, fully reflecting its excellent performance in complex nonlinear hysteresis behavior. Furthermore, the robustness of the model was assessed using peak-valley error (PV) and standard deviation (STD). Although the peak-valley error was the largest (5.4852) in the third set of complex signal simulations, the fluctuation accounted for less than 8% of the full range, and the STD value was 0.8067, ensuring the model's stability under different operating conditions. Notably, even when facing highly nonlinear dynamics such as butterfly hysteresis, the model can still complete accurate fitting in less than one minute, demonstrating excellent computational efficiency. Overall, the fractional-order Backlash-GRU model, with its high accuracy, excellent robustness, and fast computation speed, fully demonstrates its strong adaptability and application potential in modeling complex hysteresis behavior.

[0116] Table 2 Error Analysis of Different Lag Phenomena

[0117]

[0118] Example 2: A knowledge-driven neural network-based intelligent driving material hysteresis modeling system includes a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the knowledge-driven neural network-based intelligent driving material hysteresis modeling method described above.

[0119] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A method for intelligent driving material hysteresis modeling based on knowledge-driven neural networks, characterized in that, Includes the following steps: S1: Construct a fractional-order Backlash-GRUNN hybrid model that integrates material physics mechanisms; The fractional Backlash-GRUNN hybrid model is represented as follows: in, For the output variables of the fractional-order Backlash neural network sub-model, For time, The symbol for fractional calculus operators. For order, For the output variables of the fractional Backlash-GRUNN mixture model, As an excitation signal, The derivative of the excitation signal, , , , , , These are the parameters of the corresponding equation; According to the definition of backward difference, after discretization, we get: in, and The first and The output variables of the time-series fractional-order Backlash neural network submodel. The sampling interval is... For the first Constantly provide stimulus signals. For the first The output variables of the time-series fractional Backlash-GRUNN mixture model For the first Constantly provide stimulus signals. For the first The derivative of the excitation signal at time t; S2: Input the multi-scale physical characteristics of the intelligent driving material into the fractional Backlash-GRUNN hybrid model, train the model, and obtain the trained fractional Backlash-GRUNN hybrid model; S3: The trained fractional-order Backlash-GRUNN hybrid model is used as the hysteresis model of the intelligent driving material to describe the hysteresis characteristics of the intelligent driving material under different driving signals.

2. The intelligent driving material hysteresis modeling method based on knowledge-driven neural networks according to claim 1, characterized in that, The fractional Backlash-GRUNN hybrid model in S1 is composed of interconnected fractional Backlash neural network sub-models and GRUNN neural network sub-models. The fractional-order Backlash neural network sub-model includes 9 input layers, 20 hidden layers, and 1 output layer; The input layer includes the excitation signals of the real system. The derivative of the excitation signal and 7 input sequences consisting of a constant 1 , , where, when the excitation signal When connected to an absolute value activation function layer, its connection weight is set to a constant value of 1, and when the excitation signal... When connected to an additive layer, the connection weights are set to 1, 0.8, 0.08, 0.032, and 0.0176, respectively. Input sequence The outputs of the connected neurons are the seven parameters of the hysteresis model, and the input weights of each neuron are as follows: The corresponding custom activation function is: in, The parameters for the corresponding equations are respectively , , , , , , , For the corresponding neurons, The weights corresponding to each neuron. For the corresponding weight index, , This is the input to the neuron; The expression for the absolute value activation function layer is: in, For absolute value activation functions, To perform the absolute value operation on the input signal of this neuron; Each hidden layer contains one neuron; The output layer is used to generate the network's output signal.

3. The intelligent driving material hysteresis modeling method based on knowledge-driven neural networks according to claim 2, characterized in that, The GRUNN neural network sub-model uses the output of the fractional-order Backlash neural network sub-model as an extended input to the input sequence of the GRUNN neural network sub-model, along with the excitation signal. and the derivative of the excitation signal Together they act on the GRUNN neural network sub-model; The calculation process of the GRUNN neural network sub-model is as follows: in, To reset the door in Output at any moment To update the door Output at any moment It is the sigmoid activation function. To reset the weight matrix of the gate, To update the gate weight matrix, for The output of the time loop unit, for The input to the GRUNN model at time 10:

00. To reset the gate's bias vector, To update the bias vector of the gate; in, for The output of the time loop unit, These are candidate values ​​for the current hidden state. The hyperbolic tangent activation function is used. Let be the weight matrix of the candidate hidden states. It is the bias vector of the candidate hidden state. This represents element-wise product.

4. The intelligent driving material hysteresis modeling method based on knowledge-driven neural networks according to claim 2, characterized in that, The LM algorithm was used to train the fractional-order Backlash neural network sub-model.

5. A smart driving material hysteresis modeling system based on a knowledge-driven neural network, characterized in that, It includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of the intelligent driving material hysteresis modeling method based on a knowledge-driven neural network as described in any one of claims 1-4.

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