A method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks

Abstract

This invention belongs to the field of deep learning modeling technology, and particularly relates to a method for inverse dynamics modeling of MRE isolators based on deep fusion networks. The method includes the following steps: S1, constructing an inverse dynamics model of the MRE isolator based on a deep fusion network; S2, performing dynamic mechanical performance tests on the MRE isolator, collecting and recording the raw data of the device; and preprocessing the raw data to obtain training data; S3, using the obtained training data to train the constructed inverse dynamics model of the MRE isolator; S4, using the trained inverse dynamics model of the MRE isolator to control the MRE isolator; wherein, steps S1 and S2 can be interchanged. This method overcomes the problems of traditional parametric phenomenological models being difficult to inverse and the limited research and low accuracy of non-parametric neural network models, providing strong support for the intelligent control of MRE isolators.

Description

Technical Field

[0001] This invention belongs to the field of deep learning modeling technology, and in particular relates to a method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks. Background Technology

[0002] MRE (Magnetorheological elastomer) vibration isolators, as semi-active control devices based on magnetorheological elastomers (MREs), have shown great application potential in vibration reduction and isolation technology due to their simple structure, fast response speed, low energy consumption, and self-protection against control failure. However, the dynamic characteristics of MRE vibration isolators are not static; they are affected by multiple factors such as the motion state, excitation conditions, and electromagnetic environment, exhibiting significant nonlinear and hysteretic characteristics. This complexity poses a great challenge to the dynamic modeling of MRE vibration isolators, especially inverse dynamic modeling, which involves predicting the control signal based on the device's motion state and actuation force, making it even more difficult.

[0003] Dynamic modeling of MRE (Mechanical Resistor) vibration isolators is crucial for describing the relationship between their motion state, control signals, and output parameters. Forward modeling calculates the actuated force using control signals and motion state, primarily used to reveal the mechanical working mechanism of the device, device substitution in numerical simulations, and the role of force sensors in actual control. Inverse modeling, on the other hand, focuses on predicting the control signal based on the motion state and actuated force, which is essential for achieving intelligent and controllable MRE vibration isolation systems.

[0004] In the dynamic modeling research of MRE isolators, phenomenological models based on numerical equations, such as the Koh-Kelly model, modified Bouc-Wen model, LuGre model, and strain-stiffening model, can effectively describe the forward nonlinear dynamic characteristics of the device, but they suffer from problems such as too many parameters to be identified, large computational load, and difficulty in deriving and solving inverse models. Furthermore, the accuracy of inverse parameterized models is generally low, failing to meet the needs of practical control systems. With the rapid development of artificial intelligence technology, machine learning and deep learning models have been gradually applied to the forward dynamic modeling of MRE isolators, achieving significant results. However, in inverse dynamic modeling, because inverse models need to predict control inputs from desired outputs, their establishment is far more difficult than that of forward models, resulting in relatively few related studies. For example, although Yang et al. attempted to use recurrent neural networks (RNNs) to capture the inverse dynamic behavior of MRE isolators, the generalization ability and robustness of the model were affected by the discontinuity of current data in the experimental dataset. While Gu et al. used continuous signals as the dataset and established an optimal generalized regression neural network (GRNN) to describe the inverse dynamic characteristics, the accuracy of the model still needs improvement. These problems stem from the complexity and nonlinearity of the dynamic characteristics of MRE isolators, the inherent difficulty of inverse dynamic modeling, and the limitations of existing models in handling continuous, high-precision control signal prediction.

[0005] Therefore, how to utilize advanced deep learning technology to construct an inverse dynamic model that can accurately and efficiently predict the control signal of MRE vibration isolators, in order to overcome the problems of traditional parametric phenomenological models being difficult to inverse and non-parametric neural network models having limited research and low accuracy, and to provide strong support for the intelligent control of MRE vibration isolators, has become an urgent problem to be solved. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a method for inverse dynamic modeling of MRE isolators based on deep fusion networks. This method overcomes the difficulties in inverting traditional parametric phenomenological models and the limited research and low accuracy of non-parametric neural network models, thus providing strong support for the intelligent control of MRE isolators.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks includes the following steps:

[0009] S1. Construct an inverse dynamics model for the MRE isolator based on a deep fusion network; the inverse dynamics model for the MRE isolator includes:

[0010] The local feature extraction unit is used to extract local features from the input multivariate time series using multi-scale convolution;

[0011] The global feature extraction unit is used to extract the forward-backward sequence-dependent global features of the dynamic performance of the MRE vibration isolator based on the output signal of the local feature extraction unit. The global feature extraction unit includes a two-layer Bi-LSTM model, which includes two LSTMs for forward and backward propagation, respectively, to obtain feature values ​​in the forward and backward propagation directions.

[0012] The attention mechanism unit is used to assign weights to each channel of the output features of the global feature extraction unit.

[0013] The fully connected layer is used to receive the output signal of the attention mechanism and output the control current signal of the device.

[0014] S2. Perform dynamic mechanical performance tests on the MRE vibration isolator, collect and record the raw data of the device; and preprocess the raw data to obtain training data.

[0015] S3. Use the obtained training data to train the constructed MRE vibration isolator inverse dynamics model;

[0016] S4. Use the trained MRE isolator inverse dynamics model to control the MRE isolator;

[0017] Steps S1 and S2 can be interchanged.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] 1. Effective Extraction of Local and Global Features. Through a local feature extraction unit employing multi-scale convolution technology, the local dynamic characteristics of the MRE vibration isolator can be accurately captured from the input multivariate time series. This not only improves the efficiency of network training to a certain extent but also reduces the risk of model overfitting, while enhancing the extraction of local features from signals within the nonlinear time series neighborhood. Compared to traditional methods, this approach allows for more detailed analysis of time series data and improves the accuracy of feature extraction.

[0020] The global feature extraction unit utilizes a two-layer Bi-LSTM model, considering not only the forward dependencies but also the backward dependencies of the time series, thus comprehensively capturing the global features of the dynamic performance of the MRE isolator. By leveraging the bidirectional structural association context information of the Bi-LSTM, effective data features are extracted from long-term series, revealing the forward and backward dependencies of the sequence. This emphasizes the learning of the nonlinear hysteresis global features of the MRE isolator's time-series data. This design offers significant advantages in capturing sequence dependencies compared to unidirectional LSTMs or traditional RNNs.

[0021] 2. Introduction of the Attention Mechanism. The attention mechanism unit assigns weights to the output features of the global feature extraction unit, enabling the model to focus on more important feature channels and further improving its ability to predict the dynamic performance of MRE vibration isolators. Furthermore, by combining the attention mechanism with weight calculations, the correlation between the prediction target and the input features is obtained. This combination of structures adapts to predictions at multiple time steps, thereby improving the algorithm's convergence and generalization capabilities. Compared to models without the attention mechanism, this approach is more intelligent and efficient in feature selection.

[0022] 3. This method organically combines MRE vibration reduction and isolation technology with cutting-edge deep learning technology to construct a mapping relationship between the displacement, velocity, force, and control current of the MRE isolator. It is very suitable for reverse modeling of MRE isolators where expert experience is lacking.

[0023] In summary, this method constructs an inverse dynamic model capable of accurately and efficiently predicting the control signal of MRE isolators. Through effective extraction of local and global features, the introduction of an attention mechanism, the flexibility and efficiency of model training, and the realization of intelligent control, this method overcomes the difficulties of inverting traditional parametric phenomenological models and the limited research and low accuracy of non-parametric neural network models. This innovative technical solution provides strong support for the intelligent control of MRE isolators, promoting the application and development of MRE isolator technology in the field of intelligent control.

[0024] Preferably, the local feature extraction unit includes multiple parallel convolutional paths; each convolutional path includes a convolutional layer, a normalization layer, and an activation layer, and the convolutional layers of each convolutional path use convolutional kernels of different sizes; in any convolutional path, the convolutional layer is used to extract features from the input signal matrix, the normalization layer is used to process the features extracted by the convolutional layer using the Batch Normalization method to alleviate the gradient divergence problem and accelerate the convergence of the initial features; the activation layer is used to perform a nonlinear transformation on the batch normalized output using the SeLU activation function;

[0025] The output features of each convolutional path are superimposed in the vertical channel dimension using the Concat function to obtain the output features of the local feature extraction unit.

[0026] This setup, by using multiple parallel convolutional paths, each with a different kernel size, enables multi-scale feature extraction from the input signal matrix. This design captures feature information at different frequencies and scales, enhancing the model's ability to represent complex data.

[0027] 2. The normalization layer employs Batch Normalization to process the features extracted by the convolutional layers. This step effectively alleviates the gradient divergence problem, especially in deep networks where gradient vanishing or exploding are common training challenges. Batch Normalization normalizes the input of each layer, making the model more stable during training and accelerating the convergence speed of initial features. The activation layer uses the SeLU (Scaled Exponential Linear Unit) activation function to perform a non-linear transformation on the batch-normalized output. The SeLU activation function has self-normalization properties, ensuring that the output distribution remains within a certain range even in the early stages of training, avoiding overfitting and gradient vanishing problems. Furthermore, the SeLU activation function introduces non-linear characteristics into the model, enhancing its expressive power.

[0028] 3. The output features of each convolutional path are superimposed along the vertical channel dimension using the Concat function, achieving feature fusion. This fusion method can fully utilize the feature information extracted by convolutional kernels of different scales, generating richer and more comprehensive local feature representations. This is crucial for subsequent global feature extraction and final control signal prediction.

[0029] In summary, through multi-scale feature extraction, stability of feature processing, nonlinear feature transformation, and feature fusion in the local feature extraction unit, this technique significantly enhances the model's ability to represent the dynamic characteristics of MRE isolators. This not only improves the model's accuracy and robustness but also provides strong support for subsequent global feature extraction and intelligent control. This innovative design enables the model to more effectively extract key features from the input signal, providing a more accurate and efficient solution for the intelligent control of MRE isolators.

[0030] Preferably, the local feature extraction unit includes three convolutional paths, wherein the convolutional kernel of the convolutional layer in the first convolutional path has 3 channels, 3 widths, and 1 height; the convolutional kernel of the convolutional layer in the second convolutional path has 3 channels, 4 widths, and 1 height; and the convolutional kernel of the convolutional layer in the third convolutional path has 3 channels, 4 widths, and 1 height.

[0031] This setup, by using three convolutional paths with different kernel sizes, allows the local feature extraction unit to capture features of the input signal at different scales, enhancing the model's feature representation capabilities. Simultaneously, this design balances computational efficiency with model complexity and performance. A (3,3,1) kernel (number of channels, width, height) is suitable for capturing more detailed and localized features, while a (3,4,1) kernel can capture a wider range of feature information. Although the third kernel has the same size as the second, this may indicate that this path is designed to capture slightly different features through different weight initializations or subsequent processing steps, or it could be a redundant design to enhance the model's robustness. This innovative design enables the local feature extraction unit to more effectively provide rich feature information for subsequent global feature extraction and intelligent adjustment stages.

[0032] Preferably, the LSTM of the two-layer Bi-LSTM model regulates the data flow through three gating mechanisms: forget gate, input gate, and output gate;

[0033] For the time series output features of the local feature extraction unit; the forget gate allows the LSTM to forget previously unused information, based on the current input x. t Previous state C t-1 and output h t-1 The system determines the memory portion that needs to be forgotten; after the LSTM forgets the portion from the previous state, the input gate replenishes the most recent memory unit from the candidate memory units. It is based on x t C t-1 and h t-1 Decide which part will enter the current state C t The output gate generates an output for the LSTM after calculating the new state, based on C. t h t-1 and x t Determine the current output h t The calculation process is as follows:

[0034]

[0035] h t =o t tanh(C t );

[0036] In the formula, W f W i W o and W c b is the weight parameter. f b i b o and bc Here, σ and tanh are the bias parameters, representing the sigmoid and hyperbolic tangent activation functions, respectively.

[0037] This setup, by introducing three gating mechanisms—forget gate, input gate, and output gate—enables the LSTM units in the two-layer Bi-LSTM model to more effectively handle noise and outliers in time-series data. These gating mechanisms enhance the model's memory capacity, flexibility, and robustness by dynamically adjusting the information flow; based on this gating mechanism, the vanishing and exploding gradient problems are effectively mitigated. Simultaneously, the bidirectional structure design allows the model to capture forward and backward dependencies in the time series, further improving the model's accuracy and generalization ability. This technology provides strong support for the inverse dynamic modeling of MRE vibration isolators, enabling the model to more accurately predict control signals and achieve intelligent regulation.

[0038] Preferably, the forward and backward propagation LSTMs are combined simultaneously to obtain the global output features H of the two-layer Bi-LSTM model. t :

[0039]

[0040] in and These are the outputs of the forward and backward LSTM, respectively. and These are the weights for the forward and backward LSTMs, respectively; b H These are the bias parameters for the Bi-LSTM model.

[0041] This setup combines the forward and backward propagation LSTMs simultaneously to obtain the global output features of a two-layer Bi-LSTM model. This technique demonstrates significant effects in enhancing feature representation capabilities, improving model accuracy, strengthening robustness and generalization ability, providing flexibility and scalability, and maintaining computational efficiency. These advantages make Bi-LSTM models promising for applications in natural language processing, time series analysis, and other fields. Although Bi-LSTM models increase computational cost compared to unidirectional LSTMs, their ability to capture bidirectional dependencies typically allows them to converge within a fewer iterations, thus improving overall training efficiency. Furthermore, with advancements in hardware computing power and optimization of deep learning frameworks, the computational efficiency of Bi-LSTM models continues to improve.

[0042] Preferably, the input of the MRE vibration isolator inverse dynamic model is a three-dimensional signal matrix consisting of the displacement, velocity, and actuation force of the MRE vibration isolator, and the output is the device control current.

[0043] This setup, by receiving real-time displacement, velocity, and force signals from the MRE isolator, allows the inverse model to quickly calculate the required control current. This real-time feedback mechanism ensures that the isolator can respond rapidly to external excitation, thereby effectively suppressing vibration. Through precise modeling and training, the inverse model can accurately predict the required control current under different operating conditions, thus achieving precise vibration control.

[0044] Preferably, in S2, the training data is further divided into a training set, a validation set, and a test set according to a preset ratio, and the training set is augmented with a sliding window and an input matrix is ​​constructed.

[0045] This setup, 1. utilizes sliding window data augmentation, which effectively increases the amount of training data by truncating fixed-length subsequences at different positions as training samples. This helps the model learn more features, improving its generalization ability and robustness. Through sliding window data augmentation, the model can access subsequences of different positions and lengths, thus enhancing its adaptability to different input data. This helps improve the model's robustness, enabling it to maintain stable performance when facing noisy data or outliers.

[0046] 2. Constructing training data into an input matrix makes it easier to input into the neural network model for processing. Each row of the input matrix represents a training sample, and each column represents a feature dimension of the sample. This structured data format helps the model learn and understand the data better. Constructing the input matrix allows the model to perform matrix operations more efficiently when processing data, thereby improving the model's training and prediction speed. This is especially important for processing large-scale datasets.

[0047] Preferably, in S2, when performing sliding window data augmentation on the training set, for the preprocessed dataset: displacement s = {s1, s2, ..., s...} n}, velocity v = {v1, v2, ..., v n Damping force f = {f1, f2, ..., f n} and control current i={i1,i2,…,i n}; Set the sliding window size to T and the step size to stp; The constructed sample sequence is represented as:

[0048]

[0049] The above formula represents the displacement S constructed after data augmentation. t Speed ​​V t Execution F t Control current sample I t The set of the t-th sequence is set N = (nT) / stp+1;

[0050] The N*3 signals obtained after data augmentation are expanded to a dimension of 1*N*3 to construct a three-dimensional matrix, which serves as the three-dimensional signal matrix for inputting the inverse dynamic model of the MRE vibration isolator.

[0051] This setup allows for two main advantages: 1) By using the sliding window technique, a large number of new samples can be generated from the preprocessed dataset. These new samples have some temporal continuity, but different starting and ending points, thus increasing data diversity. This diversity helps the model learn more features and improves its generalization ability. 2) Because the samples generated by the sliding window include various variations from the original dataset, the model is exposed to more situations during training. This helps the model maintain stable performance when facing noisy data or outliers, thereby improving the model's robustness.

[0052] 2. Constructing the enhanced data into a three-dimensional matrix makes it easier to input into neural network models for processing. This structured data format helps the model better understand and process the data, improving training efficiency and prediction accuracy. Each row of the three-dimensional matrix represents data at a time step, and each column represents a feature dimension (displacement, velocity, execution force). This representation fully utilizes the information in the original dataset, enabling the model to learn more comprehensive features. Using a three-dimensional matrix as input supports more complex neural network models, such as Convolutional Neural Networks (CNNs) or Recurrent Neural Networks (RNNs). These models can handle long-term dependencies in time series data, further improving model performance.

[0053] Preferably, in S2, when performing dynamic mechanical performance testing on the MRE vibration isolator, the equipment used includes an excitation system, a displacement sensor, a force sensor, a data acquisition instrument, a computer, and a double-end clamping fixture; the process of performing dynamic mechanical performance testing includes: applying different excitation conditions to perform dynamic mechanical performance testing on the MRE vibration isolator, and simultaneously acquiring and recording the device current, displacement, velocity, and force signals to construct the original dataset.

[0054] This setup, along with the technical content of S2 for dynamic mechanical performance testing of MRE vibration isolators, utilizes high-precision testing equipment and a comprehensive testing process to accurately evaluate the dynamic mechanical performance of the isolators, providing a reliable foundation for subsequent data processing and model building. This helps optimize the design and performance of the vibration isolators, improving their stability and reliability in practical applications.

[0055] Preferably, in S2, when preprocessing the original data, the preprocessing includes filtering and noise reduction.

[0056] This setup, through filtering and noise reduction techniques used in the preprocessing of raw data, significantly improves data quality, optimizes subsequent analysis processes, and enhances model performance and robustness. This is of great significance for improving the accuracy and reliability of the inverse dynamics model of MRE vibration isolators. Attached Figure Description

[0057] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0058] Figure 1 This is a flowchart of the method;

[0059] Figure 2 This is a schematic diagram of the inverse dynamics model of the MRE vibration isolator in the embodiment;

[0060] Figure 3 This is a schematic diagram of the inverse dynamics model of the MRE vibration isolator in the embodiment;

[0061] Figure 4 This is a schematic diagram of the data flow of the inverse dynamics model of the MRE vibration isolator in the embodiment;

[0062] Figure 5 This is a schematic diagram of the LSTM structure in the embodiment;

[0063] Figure 6 This is a diagram showing the effect of the dynamic performance test data of the MRE vibration isolator in step S2 of the embodiment.

[0064] Figure 7 This is a schematic diagram of the inverse dynamics model training process for the MRE vibration isolator in the embodiment;

[0065] Figure 8 This is a schematic diagram illustrating the control current test effect of the MRE vibration isolator in the embodiment. Detailed Implementation

[0066] The following detailed explanation illustrates the specific implementation methods:

[0067] Example 1

[0068] like Figure 1 As shown, this embodiment discloses a method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks, including the following steps:

[0069] S1. Construct an inverse dynamic model for the MRE isolator based on a deep fusion network. The input to the MRE isolator inverse dynamic model is a three-dimensional signal matrix consisting of the displacement, velocity, and actuation force of the MRE isolator, and the output is the device control current. Thus, by receiving the displacement, velocity, and actuation force signals of the MRE isolator in real time, the inverse model can quickly calculate the required control current. This real-time feedback mechanism ensures that the isolator can respond quickly to external excitation, thereby effectively suppressing vibration. Through precise modeling and training, the inverse model can accurately predict the required control current under different operating conditions, thereby achieving precise vibration control of the MRE isolator.

[0070] A schematic diagram of the inverse dynamics model of the MRE vibration isolator is shown below. Figure 2 As shown in the figure, s, v, f, and i represent the displacement, velocity, actuation force, and control current of the MRE isolator, respectively, obtained from the dynamic performance testing module and processed by the dynamic signal preprocessing module and the training data preparation module. The CBi-AM fusion network inverse model (i.e., the MRE isolator inverse dynamic model constructed by this method) is a three-input single-output model, where s, v, and f constitute a three-dimensional signal matrix as the model input. Let i and y be the model's predicted output and the actual output, respectively. The error between them is used to update and optimize the model parameters.

[0071] like Figure 3 , Figure 4 As shown, the inverse dynamic model of the MRE vibration isolator includes a local feature extraction unit, a global feature extraction unit, an attention mechanism unit, and a fully connected layer connected in sequence.

[0072] The local feature extraction unit is used to extract local features from the input multivariate time series using multi-scale convolution.

[0073] The global feature extraction unit is used to extract forward-backward sequence-dependent global features of the dynamic performance of the MRE vibration isolator based on the output signal of the local feature extraction unit. The global feature extraction unit includes a two-layer Bi-LSTM model, which includes two LSTMs for forward and backward propagation, respectively, to obtain feature values ​​in the forward and backward propagation directions.

[0074] The attention mechanism unit is used to assign weights to each channel of the output features of the global feature extraction unit.

[0075] The fully connected layer is used to receive the output signal of the attention mechanism and output the control current signal of the device.

[0076] In specific implementation, the local feature extraction unit includes multiple parallel convolutional paths; each convolutional path includes a convolutional layer, a normalization layer, and an activation layer, and the convolutional layers of each convolutional path use convolutional kernels of different sizes; in any convolutional path, the convolutional layer is used to extract features from the input signal matrix, the normalization layer is used to process the features extracted by the convolutional layer using the Batch Normalization method to alleviate the gradient divergence problem and accelerate the convergence of the initial features; the activation layer is used to perform nonlinear transformation on the batch normalized output using the SeLU activation function.

[0077] The output features of each convolutional path are superimposed in the vertical channel dimension using the Concat function to obtain the output features of the local feature extraction unit.

[0078] By setting up multiple parallel convolutional paths, each using a different kernel size, multi-scale feature extraction of the input signal matrix can be achieved. This design captures feature information at different frequencies and scales, enhancing the model's ability to represent complex data. The normalization layer employs Batch Normalization to process the features extracted by the convolutional layers. This step effectively alleviates gradient divergence, especially in deep networks where gradient vanishing or exploding are common training challenges. Batch Normalization normalizes the input of each layer, making the model more stable during training and accelerating the convergence of initial features. The activation layer uses the SeLU (Scaled Exponential Linear Unit) activation function to perform a non-linear transformation on the batch-normalized output. The SeLU activation function has self-normalization properties, ensuring that the output distribution remains within a certain range even in the early stages of training, avoiding overfitting and gradient vanishing problems. Furthermore, the SeLU activation function introduces non-linear characteristics into the model, enhancing its expressive power. The output features of each convolutional path are superimposed along the vertical channel dimension using the Concat function, achieving feature fusion. This fusion approach fully utilizes the feature information extracted by convolutional kernels of different scales, generating richer and more comprehensive local feature representations. This is crucial for subsequent global feature extraction and final control signal prediction.

[0079] In specific implementation, the local feature extraction unit includes three convolutional paths. The kernel sizes of the convolutional layers in each convolutional path are (3,3,1), (3,4,1), and (3,4,1), respectively. The three values ​​in parentheses correspond to the number of channels, width, and height, respectively. That is, in the three convolutional paths of the local feature extraction unit, the kernel of the convolutional layer in the first convolutional path has 3 channels, 3 widths, and 1 height; the kernel of the convolutional layer in the second convolutional path has 3 channels, 4 widths, and 1 height; and the kernel of the convolutional layer in the third convolutional path has 3 channels, 4 widths, and 1 height.

[0080] By using three convolutional paths with different kernel sizes, the local feature extraction unit can capture features of the input signal at different scales, enhancing the model's feature representation capabilities. Simultaneously, this design balances computational efficiency with model complexity and performance. A (3,3,1) kernel is suitable for capturing more detailed and local features, while a (3,4,1) kernel can capture a wider range of feature information. Although the third kernel has the same size as the second, this may indicate that the path is designed to capture slightly different features through different weight initializations or subsequent processing steps, or it could be a redundant design to enhance the model's robustness. This innovative design allows the local feature extraction unit to more effectively provide rich feature information for subsequent global feature extraction and intelligent adjustment stages.

[0081] In other embodiments, those skilled in the art can also set the number of convolutional paths and the size of each convolutional kernel according to the actual application scenario and requirements, which will not be elaborated here.

[0082] The global feature extraction unit is used to extract forward-backward sequence-dependent global features of the dynamic performance of the MRE vibration isolator based on the output signal of the local feature extraction unit. The global feature extraction unit includes a two-layer Bi-LSTM model, which includes two LSTMs for forward and backward propagation, respectively, to obtain feature values ​​in the forward and backward propagation directions.

[0083] The structure of the LSTM in the two-layer Bi-LSTM model is as follows: Figure 5 As shown, the data flow is regulated through three gating mechanisms: forget gate, input gate, and output gate.

[0084] For the time series output features of the local feature extraction unit; the forget gate allows the LSTM to forget previously unused information, based on the current input x. t Previous state C t-1 and output h t-1The system determines the memory portion that needs to be forgotten; after the LSTM forgets the portion from the previous state, the input gate replenishes the most recent memory unit from the candidate memory units. It is based on x t C t-1 and h t-1 Decide which part will enter the current state C t The output gate generates an output for the LSTM after calculating the new state, based on C. t h t-1 and x t Determine the current output h t The calculation process is as follows:

[0085]

[0086] h t =o t tanh(C t );

[0087] In the formula, W f W i W o and W c b is the weight parameter. f b i b o and b c Here, σ and tanh are the bias parameters, representing the sigmoid and hyperbolic tangent activation functions, respectively.

[0088] Combining the forward and backward propagation LSTMs simultaneously yields the global output features H of a two-layer Bi-LSTM model. t :

[0089]

[0090] in and These are the outputs of the forward and backward LSTM, respectively. and These are the weights for the forward and backward LSTMs, respectively; b H These are the bias parameters for the Bi-LSTM model.

[0091] By introducing three gating mechanisms—forget gate, input gate, and output gate—the LSTM units in the two-layer Bi-LSTM model can more effectively handle noise and outliers in time series data. These gating mechanisms enhance the model's memory capacity, flexibility, and robustness by dynamically adjusting the information flow; based on this gating mechanism, the vanishing and exploding gradient problems are effectively mitigated. Simultaneously, the bidirectional structure design enables the model to capture forward and backward dependencies in the time series, further improving the model's accuracy and generalization ability.

[0092] This technology provides strong support for the inverse dynamic modeling of MRE vibration isolators, enabling the model to predict control signals more accurately and achieve intelligent regulation. Combining forward and backward propagation LSTMs to obtain the global output features of a two-layer Bi-LSTM model demonstrates significant effects in enhancing feature representation capabilities, improving model accuracy, robustness and generalization ability, providing flexibility and scalability, and maintaining computational efficiency. These advantages make Bi-LSTM models promising for applications in natural language processing, time series analysis, and other fields. Although Bi-LSTM models increase computational cost compared to unidirectional LSTMs, their ability to capture bidirectional dependencies typically allows for convergence within fewer iterations, thus improving overall training efficiency. Furthermore, with advancements in hardware computing power and optimization of deep learning frameworks, the computational efficiency of Bi-LSTM models continues to improve.

[0093] In practice, the attention mechanism unit uses a weighted approach to differentiate the importance of temporal information features extracted by the Bi-LSTM model, thereby reducing the impact of long-term dependent redundant information on the current output result. Specifically, the weights of all feature information are calculated for the obtained one-dimensional sequence signal, the feature vector is processed by the Softmax function to obtain the attention score, each component of the weight sequence is multiplied by the corresponding original channel data to obtain the feature vector after the attention mechanism, and finally the weighted sum is used as the output feature of the feature extraction unit.

[0094] S2. Perform dynamic mechanical performance tests on the MRE vibration isolator, collect and record the raw data of the device; and preprocess the raw data to obtain training data.

[0095] In practice, the equipment used for dynamic mechanical performance testing of MRE vibration isolators includes an excitation system, displacement sensors, force sensors, a data acquisition instrument, a computer, and double-end clamping fixtures. The dynamic mechanical performance testing process involves applying different excitation conditions to the MRE vibration isolators, simultaneously acquiring and recording the device's current, displacement, velocity, and force signals to construct the initial dataset. This technical approach to dynamic mechanical performance testing of MRE vibration isolators, through high-precision testing equipment and a comprehensive testing process, can accurately evaluate the dynamic mechanical performance of the isolators, providing a reliable foundation for subsequent data processing and model building. This helps optimize the design and performance of the vibration isolators, improving their stability and reliability in practical applications.

[0096] When preprocessing the raw data, the preprocessing includes filtering and noise reduction. These filtering and noise reduction techniques significantly improve data quality, optimize subsequent analysis processes, and enhance the performance and robustness of the model. This is of great significance for improving the accuracy and reliability of the inverse dynamics model of MRE vibration isolators.

[0097] In practice, the training data is divided into training, validation, and test sets according to a preset ratio, and the training set undergoes sliding window data augmentation and input matrix construction. In this embodiment, 60% is allocated to the training set, 20% to the validation set, and 20% to the test set. In other embodiments, those skilled in the art can also set the division ratio according to specific usage scenarios and requirements, which will not be elaborated here.

[0098] To facilitate better understanding, step S2 will be explained using an MRE vibration isolator designed for low-frequency vibration isolation applications.

[0099] First, raw experimental data of the MRE vibration isolator was obtained by building a dynamic performance testing module. Sinusoidal excitation with amplitudes of 1mm, 2mm, and 3mm and frequencies of 3Hz, 4Hz, 5Hz, 7Hz, and 9Hz was used. Continuous rectangular wave signals of 1A, 2A, and 3A were used for control current to ensure continuity and complete coverage. Second, the data was filtered and denoised using a dynamic signal preprocessing module to obtain the dynamic performance dataset of the MRE vibration isolator, as shown below. Figure 6 As shown in the diagram. Then, the training data preparation module divides the preprocessed data: 60% as the training set, 20% as the validation set, and an additional 20% as the test set for generalization. Sliding window data augmentation and input matrix construction are also performed to avoid model overfitting. Furthermore, the deep fusion neural network inverse model construction module is responsible for constructing the inverse dynamic model of the MRE vibration isolator. This module is mainly implemented using the CBi-AM fusion network inverse model; see Example 2 for details. Finally, the model training and parameter tuning update are completed through the model training and testing module, and performance testing is performed using the test set to obtain the device's predicted output.

[0100] When performing sliding window data augmentation on the training set, for the preprocessed dataset: displacement s = {s1, s2, ..., s} n}, velocity v = {v1, v2, ..., v n Damping force f = {f1, f2, ..., f n} and control current i={i1,i2,…,i n}; Set the sliding window size to T and the step size to stp; The constructed sample sequence is represented as:

[0101]

[0102] The above formula represents the displacement S constructed after data augmentation. t Speed ​​V t Execution F t Control current sample I t The set of the t-th sequence is set N = (nT) / stp+1;

[0103] Smaller sliding windows hinder the characterization of the hysteresis characteristics of MRE isolators, while longer windows increase training time and data redundancy.

[0104] This embodiment has undergone thorough testing, and the parameters were ultimately set to T=10 and stp=1. This method effectively increases the capacity of the dataset without affecting the feature extraction effect. Several signals of size 10*3 obtained after data augmentation are expanded to a dimension of 1*10*3 to construct a three-dimensional matrix, which will be subsequently input into the deep fusion neural network inverse model construction module.

[0105] In this way, the sliding window data augmentation technique effectively increases the amount of training data by truncating fixed-length subsequences at different positions as training samples. This helps the model learn more features and improves its generalization ability. It also enhances the model's robustness. Through sliding window data augmentation, the model can access more subsequences of different positions and lengths, thereby enhancing its adaptability to different input data. This helps improve the model's robustness, enabling it to maintain stable performance when facing noisy data or outliers. The sliding window technique can generate a large number of new samples from the preprocessed dataset. These new samples have some temporal continuity but different start and end points, thus increasing data diversity. This diversity helps the model learn more features and improves its generalization ability. Because the samples generated by the sliding window contain various variations from the original dataset, the model is exposed to more situations during training. This helps the model maintain stable performance when facing noisy data or outliers, thereby improving the model's robustness.

[0106] Constructing the enhanced data into a three-dimensional matrix makes it easier to input into neural network models for processing. This structured data format helps the model better understand and process the data, improving training efficiency and prediction accuracy. Each row of the three-dimensional matrix represents data at a time step, and each column represents a feature dimension (displacement, velocity, execution force). This representation fully utilizes the information in the original dataset, enabling the model to learn more comprehensive features. Using a three-dimensional matrix as input supports more complex neural network models, such as Convolutional Neural Networks (CNNs) or Recurrent Neural Networks (RNNs). These models can handle long-term dependencies in time series data, further improving model performance.

[0107] S3. Use the obtained training data to train the constructed MRE vibration isolator inverse dynamics model.

[0108] In this embodiment, the flowchart of the MRE vibration isolator fusion network inverse model training is as follows: Figure 7 As shown, a total of 500 epochs were trained, with each epoch containing 280 iteration cycles. In each iteration cycle, the training set was divided into several batches of size 32. Each batch was sequentially input into the CBi-AM fusion network inverse model (i.e., the MRE vibration isolator inverse dynamic model) to predict the device current, and the prediction was compared with the actual current label. After the model output, the loss function was calculated (mean squared error MSE was used as the loss function in this embodiment). If the iteration termination condition was not met, iterative optimization was performed. The Adam optimizer was used for backpropagation to update the trainable parameters in the network, with an initial learning rate of 0.0008, and the network was continuously trained until the epoch was completed. Finally, after all the training data was trained, the trained CBi-AM fusion model was saved, and the test set was input into the CBi-AM fusion network to obtain the final current prediction result, thus verifying the model's effectiveness. The final control current test results of the MRE vibration isolator are as follows: Figure 8 As shown.

[0109] S4. Use the trained MRE isolator inverse dynamics model to control the MRE isolator.

[0110] In practical implementation, the trained MRE vibration isolator inverse dynamics model is used. The three-dimensional signal matrix (displacement s, velocity v, and actuation force f) working condition data of the MRE vibration isolator to be controlled are used as the model input. The control current corresponding to the required control condition is obtained from the output of the trained model. Then, the MRE vibration isolator is controlled by the obtained control current, thereby achieving precise vibration control of the MRE vibration isolator.

[0111] Steps S1 and S2 can be interchanged.

[0112] This method, through a local feature extraction unit employing multi-scale convolution technology, can accurately capture the local dynamic characteristics of MRE isolators from input multivariate time series. This not only improves network training efficiency to a certain extent but also reduces the risk of model overfitting, while enhancing the extraction of local features from signals within the nonlinear time series neighborhood. Compared to traditional methods, this approach can analyze time series data more meticulously and improve feature extraction accuracy. Furthermore, the global feature extraction unit utilizes a two-layer Bi-LSTM model, considering not only forward dependencies but also backward dependencies in the time series, thus comprehensively capturing the global features of the MRE isolator's dynamic performance. By leveraging the bidirectional unit structure of the Bi-LSTM to associate contextual information, effective data features are extracted from long-term series, obtaining the forward and backward dependencies of the sequence, thereby emphasizing the learning of the nonlinear hysteresis global features of the MRE isolator's time series data. This design has a greater advantage in capturing sequence dependencies compared to unidirectional LSTMs or traditional RNNs.

[0113] Furthermore, this method introduces an attention mechanism unit to weight the output features of the global feature extraction unit, enabling the model to focus on more important feature channels and further improving its predictive ability for the dynamic performance of MRE isolators. Moreover, by combining the attention mechanism to calculate weights, the correlation between the prediction target and the input features is obtained. This combination of structures adapts to predictions at multiple time steps, thereby improving the algorithm's convergence and generalization capabilities. Compared to models without an attention mechanism, this method is more intelligent and efficient in feature selection. In addition, this method organically combines MRE vibration reduction and isolation technology with cutting-edge deep learning techniques to construct a mapping relationship between the displacement, velocity, force, and control current of the MRE isolator. This makes it highly suitable for reverse modeling of MRE isolators where expert experience is lacking.

[0114] This method constructs an inverse dynamic model capable of accurately and efficiently predicting the control signal of MRE isolators. Through effective extraction of local and global features, the introduction of an attention mechanism, flexible and efficient model training, and the realization of intelligent control, this method overcomes the difficulties of inverting traditional parametric phenomenological models and the limited research and low accuracy of non-parametric neural network models. This innovative technical solution provides strong support for the intelligent control of MRE isolators, promoting the application and development of MRE isolator technology in the field of intelligent control.

[0115] Example 2

[0116] To verify the efficiency of this method in inverse modeling the nonlinear and hysteretic behavior of MRE vibration isolators, this embodiment compares the model with traditional machine learning or deep learning models on the same dataset. Simultaneously, ablation experiments were conducted using different combinations of the fusion network of this invention. Mean squared error (MSE), mean absolute error (MAE), and goodness of fit (R²) were used as the metrics. 2 The prediction performance of the current is evaluated using three indicators, and the calculation process is as follows:

[0117]

[0118] Where y i and These represent the model's predicted output and the true label data, respectively, with n being the length of the test set data samples.

[0119] The comparison results are shown in Table 1 and Table 2.

[0120] Table 1 Performance comparison with traditional methods

[0121]

[0122] Table 2 Performance Comparison with Different Deep Learning Models and Methods

[0123]

[0124]

[0125] As shown in Table 1, compared with traditional machine learning and deep learning methods, the inverse model of our method (i.e., CBi-AM in the table) achieves the best results in all three evaluation metrics: MSE, MAE, and R. 2 The values ​​are 0.04157, 0.10665, and 0.97802, respectively. As shown in Table 2, the inverse model of this method still exhibits excellent prediction performance in the comparison of various deep learning methods, particularly in MAE and R... 2 The evaluation metrics were optimal, and while the MSE was slightly higher than that of CNN-Bi-LSTM, the difference was negligible. This indicates that in the MRE vibration isolator dynamics inverse modeling of this embodiment, the system and method proposed in this invention outperform other benchmark models, significantly improving prediction accuracy.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks, characterized in that, Includes the following steps: S1. Construct an inverse dynamics model for the MRE isolator based on a deep fusion network; the inverse dynamics model for the MRE isolator includes: The local feature extraction unit is used to extract local features from the input multivariate time series using multi-scale convolution; The global feature extraction unit is used to extract the forward-backward sequence-dependent global features of the dynamic performance of the MRE vibration isolator based on the output signal of the local feature extraction unit. The global feature extraction unit includes a two-layer Bi-LSTM model, which includes two LSTMs for forward and backward propagation, respectively, to obtain feature values ​​in the forward and backward propagation directions. The attention mechanism unit is used to assign weights to each channel of the output features of the global feature extraction unit. The fully connected layer is used to receive the output signal of the attention mechanism and output the control current signal of the device. S2. Perform dynamic mechanical performance tests on the MRE vibration isolator, collect and record the raw data of the device; and preprocess the raw data to obtain training data. S3. Use the obtained training data to train the constructed MRE vibration isolator inverse dynamics model; S4. Use the trained MRE isolator inverse dynamics model to control the MRE isolator; Steps S1 and S2 can be swapped in order.

2. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 1, characterized in that: The local feature extraction unit includes multiple parallel convolutional paths; each convolutional path includes a convolutional layer, a normalization layer, and an activation layer, and the convolutional layers in each convolutional path use convolutional kernels of different sizes; in any convolutional path, the convolutional layer is used to extract features from the input signal matrix, the normalization layer is used to process the features extracted by the convolutional layer using the Batch Normalization method, and the activation layer is used to perform a nonlinear transformation on the batch normalized output using the SeLU activation function; The output features of each convolutional path are superimposed in the vertical channel dimension using the Concat function to obtain the output features of the local feature extraction unit.

3. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 2, characterized in that: The local feature extraction unit includes three convolutional paths; in the first convolutional path, the convolutional kernel of the convolutional layer has 3 channels, 3 widths, and 1 height; in the second convolutional path, the convolutional kernel of the convolutional layer has 3 channels, 4 widths, and 1 height; and in the third convolutional path, the convolutional kernel of the convolutional layer has 3 channels, 4 widths, and 1 height.

4. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 1, characterized in that: The LSTM in the two-layer Bi-LSTM model regulates the data flow through three gating mechanisms: forget gate, input gate, and output gate. For the time series output features of the local feature extraction unit; the forget gate allows the LSTM to forget previously unused information, based on the current input x. t Previous state C t-1 and output h t-1 The system determines the memory portion that needs to be forgotten; after the LSTM forgets the portion from the previous state, the input gate replenishes the most recent memory unit from the candidate memory units. It is based on x t C t-1 and h t-1 Decide which part will enter the current state C t ; The output gate generates an output for the LSTM after calculating the new state, based on C. t h t-1 and x t Determine the current output h t The calculation process is as follows: h t =o t fishy(C) t ); In the formula, W f W i W o and W c b is the weight parameter. f b i b o and b c Here, σ and tanh are the bias parameters, representing the sigmoid and hyperbolic tangent activation functions, respectively.

5. The MRE vibration isolator inverse dynamic modeling method based on deep fusion network as described in claim 4, characterized in that: Combining the forward and backward propagation LSTMs simultaneously yields the global output features H of a two-layer Bi-LSTM model. t : in and These are the outputs of the forward and backward LSTM, respectively. and These are the weights for the forward and backward LSTMs, respectively; b H These are the bias parameters for the Bi-LSTM model.

6. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 1, characterized in that: The input to the inverse dynamic model of the MRE isolator is a three-dimensional signal matrix consisting of the displacement, velocity, and actuation force of the MRE isolator, and the output is the device control current.

7. The MRE vibration isolator inverse dynamic modeling method based on deep fusion network as described in claim 6, characterized in that: In S2, the training data is divided into training set, validation set and test set according to a preset ratio, and the training set is augmented with sliding window data and the input matrix is ​​constructed.

8. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 7, characterized in that: In S2, when performing sliding window data augmentation on the training set, for the preprocessed dataset: displacement s = {s1, s2, ..., s...} n }, velocity v = {v1, v2, ..., v n Damping force f = {f1, f2, ..., f n } and control current i={i1,i2,…,i n }; Set the sliding window size to T and the step size to stp; The constructed sample sequence is represented as: The above formula represents the displacement S constructed after data augmentation. t Speed ​​V t Execution F t Control current sample I t The set of the t-th sequence is set N = (nT) / stp+1; The N*3 signals obtained after data augmentation are expanded to a dimension of 1*N*3 to construct a three-dimensional matrix, which serves as the three-dimensional signal matrix for inputting the inverse dynamic model of the MRE vibration isolator.

9. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 1, characterized in that: In S2, the equipment used for dynamic mechanical performance testing of MRE vibration isolators includes a vibration excitation system, displacement sensor, force sensor, data acquisition instrument, computer, and double-end clamping fixture. The process of conducting dynamic mechanical performance testing includes: applying different excitation conditions to perform dynamic mechanical performance testing on the MRE vibration isolator, and simultaneously acquiring and recording the device current, displacement, velocity and force signals to construct the original dataset.

10. The method for inverse dynamic modeling of MRE vibration isolators based on deep fusion networks as described in claim 1, characterized in that: In S2, when preprocessing the raw data, the preprocessing includes filtering and noise reduction.

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