A method for modeling a magneto-rheological damper based on a Gaussian process regression model

Abstract

A kind of magnetorheological damper modeling method based on Gaussian process regression model, comprising the following steps: step 1: based on the data acquisition and preprocessing of magnetorheological damper mechanical property test;Step 2: determine the Gaussian process regression prior distribution of magnetorheological damper;Step 3: calculate the posterior mean and posterior covariance of Gaussian process regression model;Step 4: magnetorheological damper Gaussian process regression model evaluation;Step 5: hyperparameter optimization calculation;Step 6: final evaluation and application of magnetorheological damper Gaussian process regression model.The present application overcomes the problems of insufficient computing resources and increased training time cost that may be caused by non-parametric models represented by neural network models when facing large-scale data sets while ensuring the accuracy of the model;At the same time, in view of the problem that noise interference in training data may cause model overfitting, a kernel function with noise interference suppression effect is proposed to improve the modeling accuracy of the model.

Description

Technical Field

[0001] This invention relates to the field of magnetorheological vibration damper technology, and in particular to a magnetorheological vibration damper modeling method based on a Gaussian process regression model. Background Technology

[0002] Magnetorheological suspension systems have attracted widespread attention in the automotive suspension technology field and have gained market recognition and application due to their characteristics such as rapid response, controllable high damping force, and low energy consumption. The mechanical properties of magnetorheological dampers are crucial to suspension performance. Given the significant nonlinearity and uncertainty of the mechanical properties of magnetorheological dampers, establishing an accurate and practical mechanical property model is particularly important. Therefore, in-depth research and development of a model that can accurately describe the mechanical behavior of magnetorheological dampers is a prerequisite for achieving efficient and intelligent suspension system design and control, and plays a decisive role in improving system dynamic response and ride comfort.

[0003] Currently, modeling methods for the mechanical characteristics of magnetorheological dampers mainly include parametric and non-parametric modeling. Parametric models, represented by the Bingham and Bouc-Wen models, primarily utilize series and parallel combinations of physical components and hysteresis modules to simulate the mechanical behavior of the damper, offering advantages such as simple structure and ease of analysis. While parametric models can accurately describe the mechanical behavior of magnetorheological dampers within a certain range, the optimization and identification of their multiple parameters inevitably faces difficulties due to factors such as initial values, constraints, and convergence. In practical control applications, numerical processing of strongly nonlinear equations may cause control lag, affecting the control effect.

[0004] Traditional parametric models struggle to describe nonlinear or highly complex systems, such as magnetorheological dampers. Their mathematical expressions are often difficult to construct, and parameter identification may require complex optimization algorithms. Nonparametric models, on the other hand, are more flexible, typically using data and expert knowledge to characterize the modeling process. They better describe the complex nonlinear mechanical characteristics of magnetorheological dampers and therefore have greater research and application potential. Nonparametric models can be further divided into data-driven and non-data-driven models. Non-data-driven models include fuzzy logic and empirical models, primarily based on expert knowledge, system theory, or physical laws. In practical applications, they require extensive empirical knowledge for adjustment, making them difficult to implement. Data-driven models include neural networks and vector machines. These methods establish nonlinear mappings between the input and output of magnetorheological dampers based on sufficiently rich experimental data to characterize their dynamic behavior. Neural networks, as a typical data-driven model, can accurately approximate any continuous function, making them particularly suitable for describing complex nonlinear systems like magnetorheological dampers. Patent CN202211361602.0 proposes a calculation method for the inverse mapping model of magnetorheological vibration dampers based on LSTM. This method utilizes LSTM, a neural network model, to construct the inverse dynamic model of the magnetorheological vibration damper, improving the fitting speed and accuracy of the inverse dynamic model. Patent CN202210561440.9 proposes an intelligent simulation neural network algorithm with fast optimization speed and strong adaptability, capable of accurately and quickly identifying the dynamic damping characteristics of the vibration damper and shortening the development cycle. However, in practical applications, on the one hand, neural network models typically require a large amount of training data to ensure the model's accuracy and generalization ability, leading to the consumption of significant computational resources and increased training time costs. On the other hand, the experimental data used for neural network training inevitably contains noise. If the network structure has redundancy, it may cause noise interference during training, thus affecting the network's final convergence performance, causing the training to deviate from the global optimum, and resulting in overfitting due to memorizing noise details, thereby reducing generalization ability. Therefore, in the process of studying the mechanical model of magnetorheological vibration dampers, overcoming the shortcomings of non-parametric models represented by neural network models, in order to achieve the high-precision modeling requirements of magnetorheological vibration dampers, is of great research significance. Summary of the Invention

[0005] To address the challenges of large training data requirements, long training times, and the need for additional noise removal to ensure model accuracy when using non-parametric models, such as neural network models, to model magnetorheological dampers, this invention proposes a modeling method for magnetorheological dampers based on a Gaussian process regression model. This method overcomes the problems of insufficient computational resources and increased training time costs that may arise with non-parametric models, such as neural network models, when dealing with large datasets, while maintaining model accuracy. Furthermore, to address the issue of overfitting caused by noise interference in the training data, a kernel function with noise suppression capabilities is proposed to improve the modeling accuracy.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] A modeling method for magnetorheological vibration dampers based on a Gaussian process regression model includes the following steps:

[0008] Step 1: Data acquisition and preprocessing based on the mechanical property test of magnetorheological vibration damper;

[0009] Step 2: Determine the prior distribution of the Gaussian process regression for the magnetorheological vibration damper;

[0010] Step 3: Calculate the posterior mean and posterior covariance of the Gaussian process regression model;

[0011] Step 4: Evaluation of the Gaussian process regression model for the magnetorheological vibration damper;

[0012] If the root mean square error (RMSE) is less than the set value, the model is considered to be a Gaussian process regression model for the magnetorheological damper that meets the performance conditions, and the process proceeds to step 6. If the RMSE is greater than or equal to the set value, the process proceeds to step 5 to further perform hyperparameter optimization calculations and readjust the relevant parameters of the Gaussian process model for the magnetorheological damper.

[0013] Step 5: Hyperparameter optimization calculation;

[0014] Step 6: Final evaluation and application of the Gaussian process regression model for magnetorheological vibration dampers:

[0015] After step 4, which satisfies the accuracy requirements of the Gaussian process regression model evaluation process, the test set data is used to conduct a final evaluation test on all the Gaussian process regression models of magnetorheological vibration dampers that meet the performance conditions. The model with the lowest root mean square error value is selected as the optimal Gaussian process regression model for magnetorheological vibration dampers and applied to actual engineering.

[0016] Furthermore, step 1 also includes the following steps:

[0017] The mechanical performance of the magnetorheological vibration damper was tested using a mechanical testing platform system. Sample data of the magnetorheological vibration damper during operation was collected using sensors. All sample data were normalized and scaled to the [-1,1] interval to enhance the convergence efficiency and prediction accuracy of the model training.

[0018] The preprocessed data is divided into training set, validation set and test set. The training set is used to train and adjust the Gaussian process regression model of the magnetorheological vibration damper. The validation set is used to check whether the Gaussian process regression model of the magnetorheological vibration damper meets the set performance requirements. The test set is used to select the optimal Gaussian process regression model of the magnetorheological vibration damper for practical application.

[0019] The Gaussian process regression model for magnetorheological dampers uses operating current, piston displacement and velocity as input variables and predicted damping force as output variable. By training and adjusting the Gaussian process regression model for magnetorheological dampers, the complex mapping relationship between input and output variables can be captured, with the aim of accurately predicting the output damping force of the magnetorheological damper.

[0020] Furthermore, step 2 also includes the following steps:

[0021] Let the mean function and kernel function of a Gaussian process be defined as the prior distributions, where the Gaussian process... Defined as:

[0022]

[0023] In the formula: f(x) is the regression function; m(x) is the mean function; k(x) is the mean function. i ,x j ) is the kernel function; x i x j Let i and j be the i-th and j-th data points in the dataset;

[0024] By setting the mean function m(x) to zero, we construct the dot product kernel function, the Matern5 / 2 kernel function, and the white noise kernel function to characterize the complex linear and nonlinear mechanical properties and noise characteristics present in step 1:

[0025] The set dot product kernel function k Linear (x i ,x j )satisfy:

[0026]

[0027] In the formula: is the variance parameter of the dot product kernel;

[0028] The set Matern5 / 2 kernel function k Mat52(x i ,x j )satisfy:

[0029]

[0030] In the formula: Let |x| be the variance parameter of the Matern5 / 2 kernel, and l be the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space. i -x j || is data point x i and x j The Euclidean distance between them;

[0031] Define the white noise kernel function k Noise (x i ,x j )satisfy:

[0032]

[0033] In the formula: δ(x) is the variance parameter of the white noise kernel, used to simulate the level of random noise in the observed data. i -x j ) is the Dirac function, which represents 1 when i and j are equal, and 0 otherwise;

[0034] Based on the three kernel functions in equation (2-4), a composite kernel function k is constructed. total (x i ,x j )satisfy:

[0035] k total (x i ,x j )=k Linear (x i ,x j )+k Mat52 (x i ,x j )+k Noise (x i ,x j (5)

[0036] By constructing the aforementioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper, as well as the noise during the data acquisition process, are captured, ensuring that the model learns the above three types of characteristics from the data to the greatest extent possible, thereby effectively improving the prediction accuracy of the damping force value of the magnetorheological damper.

[0037] Furthermore, step 3 also includes the following steps:

[0038] To find the optimal hyperparameter θ of the Gaussian process model of the magnetorheological vibration damper opt Set initial hyperparameters As a starting point for searching for optimal hyperparameters; The initial value of l is set to 1. The initial value is set within the range of [0.1, 10], allowing the Bayesian optimization algorithm described in step 5 to find the optimal noise variance value within this range;

[0039] Given the input training set and initial values ​​for the hyperparameters, calculate the posterior mean and posterior covariance, where the posterior mean m * and posterior covariance C * They respectively satisfy:

[0040] m * =K X*X (K+∈I) -1 y (6)

[0041]

[0042] In the formula: K represents the kernel matrix of the training set x and itself; K X*X Represents the validation set x * The kernel matrix of the training set x; K XX* Represents the training set x and the validation set x * The kernel matrix; Represents the validation set x * The kernel matrix of itself; I is the identity matrix; y is the observed data of the training set; ∈ is the regularization coefficient;

[0043] The calculation process of the kernel matrix is ​​shown in equation (8):

[0044]

[0045] In the formula: n is the total number of samples in the training set; m is the total number of samples in the validation set; x n This is the last data point in the training set; This is the last data point in the validation set;

[0046] The calculated Gaussian process expression satisfies:

[0047]

[0048] Where: m * C is the posterior mean; * For posterior covariance; y * For the validation set x * The predicted output value satisfies:

[0049]

[0050] In the formula: It is the i-th predicted value in the validation set, that is, the damping force value predicted by the Gaussian process regression model of the magnetorheological damper.

[0051] Furthermore, step 4 also includes the following steps:

[0052] A Gaussian process regression model was used to predict the validation set data. The difference between the actual and predicted values ​​was calculated, and the root mean square error (RMSE) was used to evaluate the prediction accuracy.

[0053]

[0054] In the formula: y i It is the i-th observation in the verification set, that is, the output damping force value obtained from the actual magnetorheological damper.

[0055] Furthermore, step 5 also includes the following steps:

[0056] If the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements after step 4, the hyperparameters need to be recalculated. The calculation process is as follows:

[0057] First, the marginal log-likelihood function L(θ) is used as the objective function to adjust the hyperparameters, thereby measuring the goodness of fit of the model. The marginal log-likelihood function L(θ) is set as follows:

[0058]

[0059] In the formula: θ is a hyperparameter;

[0060] A higher value for the marginal log-likelihood function L(θ) indicates a better fit to the data; conversely, a lower value indicates a worse fit.

[0061] Secondly, a Bayesian optimization algorithm is used to iteratively adjust the marginal log-likelihood function, and the optimal hyperparameter θ is obtained by finding the value of the maximum marginal log-likelihood function. opt Its expression satisfies:

[0062] θ opt =argmax θ L(θ) (13)

[0063] The optimal hyperparameter θ obtained through iterative optimization opt The Gaussian process regression model of the magnetorheological damper will be replaced by the initial hyperparameters and updated cyclically to accurately adjust the model and achieve continuous improvement in predictive performance.

[0064] The beneficial effects of this invention are mainly reflected in:

[0065] 1) This invention trains and constructs a mechanical model of a magnetorheological damper using training data, thereby predicting its output damping force, effectively reducing the model's dependence on a large-scale training set.

[0066] 2) This invention proposes a kernel function for the modeling process of magnetorheological vibration dampers based on a Gaussian process regression model. The kernel function is constructed taking into account the linearity, nonlinearity and noise characteristics of the data collected by the magnetorheological vibration damper, which can effectively suppress the noise interference problem generated in the training data of the Gaussian process regression model and improve the overall modeling accuracy. Attached Figure Description

[0067] Figure 1 This is a flowchart of the present invention.

[0068] Figure 2 This is a comparison chart of the predicted and actual values ​​output by the Gaussian process regression model in this embodiment of the invention.

[0069] Figure 3 It is a set of fitting characteristic curves of the model for final application.

[0070] Figure 4 It is a set of speed characteristic curves of the model for final application. Detailed Implementation

[0071] The present invention will now be further described with reference to the accompanying drawings.

[0072] Reference Figures 1-4 A modeling method for magnetorheological vibration dampers based on a Gaussian process regression model, such as... Figure 1 As shown, this method mainly includes six steps: data acquisition and preprocessing based on the mechanical characteristic test of magnetorheological dampers; determining the prior distribution of the Gaussian process regression of the magnetorheological damper; calculating the posterior mean and posterior covariance of the Gaussian process regression model; evaluating the Gaussian process regression model of the magnetorheological damper; hyperparameter optimization calculation; and the final evaluation and application of the Gaussian process regression model of the magnetorheological damper. The specific implementation methods for each step are as follows:

[0073] Step 1: Data acquisition and preprocessing based on the mechanical property test of magnetorheological vibration damper

[0074] In this embodiment, a magnetorheological damper mechanical testing platform system is used to test the mechanical performance of a certain magnetorheological damper. Sensors are used to collect sample data such as piston displacement, velocity, operating current, and damping force generated by the magnetorheological damper during operation. During data acquisition, the input signal is set to a sine wave, the amplitude of the magnetorheological damper is 40mm, the operating control current is between 0.5 and 3A, increasing by 0.5A each time, and the test frequency is between 1 and 5Hz, increasing by 1Hz each time. The total amount of sample data collected is 1236. All sample data are normalized and scaled to the [-1,1] interval to enhance the convergence efficiency and prediction accuracy of model training. The preprocessed data was divided into a training set (70%), a validation set (15%), and a test set (15%). The training set was used to train and adjust the Gaussian process regression model for magnetorheological dampers. The validation set was used to verify whether the Gaussian process regression model for magnetorheological dampers met the set performance requirements. The test set was used to select the optimal Gaussian process regression model for magnetorheological dampers for practical applications.

[0075] In this embodiment, the Gaussian process regression model of the magnetorheological damper uses the operating current, piston displacement, and velocity as input variables, and the predicted damping force as the output variable. The operating current directly affects the magnetization of the magnetorheological fluid, determining the damping characteristics of the damper; the piston displacement and velocity parameters characterize the static and dynamic response characteristics of the magnetorheological damper, respectively. By training and adjusting the Gaussian process regression model of the magnetorheological damper, the complex mapping relationship between the input and output variables is captured, aiming to accurately predict the output damping force of the magnetorheological damper.

[0076] Step 2: Determine the prior distribution of the Gaussian process regression for the magnetorheological vibration damper

[0077] The mean function and kernel function of a Gaussian process are defined as prior distributions. The Gaussian process... Defined as:

[0078]

[0079] In the formula: f(x) is the regression function; m(x) is the mean function; k(x) is the mean function. i ,x j ) is the kernel function; x i x j Let i and j be the i-th and j-th data points in the dataset.

[0080] In this embodiment, the mean function m(x) is set to zero, that is, m(x) = 0.

[0081] Since the magnetorheological damper piston displacement, velocity, working current and damping force data collected in step 1 contain various complex linear and nonlinear mechanical characteristics and noise features, the dot product kernel function, Matern5 / 2 kernel function and white noise kernel function as shown in equation (2-4) are constructed to characterize the above three features.

[0082] The set dot product kernel function k Linear (x i ,x j )satisfy:

[0083]

[0084] In the formula: is the variance parameter of the dot product kernel.

[0085] The set Matern5 / 2 kernel function k Mat52 (x i ,x j )satisfy:

[0086]

[0087] In the formula: Let |x| be the variance parameter of the Matern5 / 2 kernel, and l be the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space. i -x j || is data point x i and x j The Euclidean distance between them.

[0088] Define the white noise kernel function k Noise (x i ,x j )satisfy:

[0089]

[0090] In the formula: δ(x) is the variance parameter of the white noise kernel, used to simulate the level of random noise in the observed data. i -x j ) is the Dirac function, which means that 1 is true when i and j are equal, and 0 is true otherwise.

[0091] Based on the three kernel functions in equations (2-4), the composite kernel function k shown in equation (5) is constructed. total (x i ,x j )satisfy:

[0092] k total (x i ,x j )=kLinear (x i ,x j )+k Mat52 (x i ,x j )+k Noise (x i ,x j (5)

[0093] By constructing the aforementioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper, as well as the noise during the data acquisition process, are captured, ensuring that the model learns the above three types of characteristics from the data to the greatest extent possible, thereby effectively improving the prediction accuracy of the damping force value of the magnetorheological damper.

[0094] Step 3: Calculate the posterior mean and posterior covariance of the Gaussian process regression model.

[0095] To find the optimal hyperparameter θ of the Gaussian process model of the magnetorheological vibration damper opt Set initial hyperparameters This serves as the starting point for searching for the optimal hyperparameters. In this embodiment... The initial value of l is set to 1. The initial values ​​are set within the range of [0.1, 10], allowing the Bayesian optimization algorithm described in step 5 to find the optimal noise variance value within this range.

[0096] Given the input training set and initial values ​​for the hyperparameters, calculate the posterior mean and posterior covariance, where the posterior mean m * and posterior covariance C * They respectively satisfy:

[0097] m * =K X*X (K+∈I) -1 y (6)

[0098]

[0099] In the formula: K represents the kernel matrix of the training set x and itself; K X*X Represents the validation set x * The kernel matrix of the training set x; K XX* Represents the training set x and the validation set x * The kernel matrix; Represents the validation set x * The kernel matrix is ​​itself; I is the identity matrix; y is the observed data in the training set; ∈ is the regularization coefficient.

[0100] The calculation process of the kernel matrix is ​​shown in equation (8):

[0101]

[0102] In the formula: n is the total number of samples in the training set; m is the total number of samples in the validation set; x n This is the last data point in the training set; This is the last data point in the validation set.

[0103] The calculated Gaussian process expression satisfies:

[0104]

[0105] Where: m * C is the posterior mean; * For posterior covariance; y * For the validation set x * The predicted output value satisfies:

[0106]

[0107] In the formula: It is the i-th predicted value in the validation set, that is, the damping force value predicted by the Gaussian process regression model of the magnetorheological damper.

[0108] The Gaussian process model is adjusted by calculating the posterior mean and posterior covariance. Compared to the initial model, the model predicted by the continuously optimized hyperparameter model more accurately approximates the true value of the magnetorheological damper's output damping force.

[0109] Step 4: Evaluation of the Gaussian process regression model for magnetorheological vibration dampers

[0110] A Gaussian process regression model was used to predict the validation set data. The difference between the actual and predicted values ​​was calculated, and the root mean square error (RMSE) was used to evaluate the prediction accuracy.

[0111]

[0112] In the formula: y i It is the i-th observation in the verification set, that is, the output damping force value obtained from the actual magnetorheological damper.

[0113] Based on the requirements of actual engineering applications of magnetorheological vibration dampers, this invention sets a model that can achieve an RMSE value of less than 100 as the Gaussian process regression model of magnetorheological vibration dampers that meets the performance conditions, and proceeds to step 6; if the RMSE is greater than or equal to the set value, then proceeds to step 5 to further carry out hyperparameter optimization calculations and readjust the relevant parameters of the Gaussian process model of the magnetorheological vibration damper.

[0114] Step 5: Hyperparameter optimization calculation

[0115] If the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements after step 4, the hyperparameters need to be recalculated. The calculation process is as follows:

[0116] First, the marginal log-likelihood function L(θ) is used as the objective function to adjust the hyperparameters, thereby measuring the goodness of fit of the model. The marginal log-likelihood function L(θ) is set as follows:

[0117]

[0118] In the formula: θ is a hyperparameter.

[0119] A higher value for the marginal log-likelihood function L(θ) indicates a better fit to the data; conversely, a lower value indicates a worse fit.

[0120] Secondly, a Bayesian optimization algorithm is used to iteratively adjust the marginal log-likelihood function, and the optimal hyperparameter θ is obtained by finding the value of the maximum marginal log-likelihood function. opt Its expression satisfies:

[0121] θ opt =argmax θ L(θ) (13)

[0122] The optimal hyperparameter θ obtained through iterative optimization opt The Gaussian process regression model of the magnetorheological damper will be replaced by the initial hyperparameters and updated cyclically to accurately adjust the model and achieve continuous improvement in predictive performance.

[0123] Step 6: Final evaluation and application of the Gaussian process regression model for magnetorheological vibration dampers

[0124] After step 4, which satisfies the accuracy requirements of the Gaussian process regression model evaluation process, the test set data is used to conduct a final evaluation test on all the Gaussian process regression models of magnetorheological vibration dampers that meet the performance conditions. The model with the lowest root mean square error value is selected as the optimal Gaussian process regression model for magnetorheological vibration dampers and applied to actual engineering.

[0125] Figure 2 The image comparison between the predicted value and the actual value in this embodiment is provided. The predicted value and its confidence interval output by the Gaussian process regression model of the magnetorheological vibration damper in this embodiment are shown. The predicted value of each sample is within the 95% confidence interval. Figure 3 , Figure 4 The model finally applied in this embodiment is shown to have a set of fitted performance characteristic curves and velocity characteristic curves, which are almost completely consistent with the actual results obtained by the magnetorheological vibration damper through the mechanical testing platform system, indicating that the Gaussian process regression model of the magnetorheological vibration damper has accurate predictive effect.

[0126] Gaussian process regression is a data-driven, non-parametric machine learning method that maps input data to a Gaussian process by constructing covariance relationships between data points, thereby predicting the output for any new input point. Gaussian process regression possesses powerful nonlinear modeling capabilities. Applying it to the construction of mechanical characteristic models for magnetorheological dampers, leveraging the flexibility of its kernel function construction, effectively reduces the impact of various complex linear and nonlinear mechanical characteristics of magnetorheological dampers, as well as unavoidable noise interference during data acquisition, on model accuracy.

[0127] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. The scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A modeling method for magnetorheological vibration dampers based on a Gaussian process regression model, characterized in that: The modeling method includes the following steps: Step 1: Data acquisition and preprocessing based on the mechanical property test of magnetorheological vibration damper: The mechanical performance of the magnetorheological vibration damper was tested using a mechanical testing platform system. Sample data of the magnetorheological vibration damper during operation was collected using sensors. All sample data were normalized and scaled to the [-1,1] interval to enhance the convergence efficiency and prediction accuracy of the model training. The preprocessed data is divided into training set, validation set and test set. The training set is used to train and adjust the Gaussian process regression model of the magnetorheological vibration damper. The validation set is used to check whether the Gaussian process regression model of the magnetorheological vibration damper meets the set performance requirements. The test set is used to select the optimal Gaussian process regression model of the magnetorheological vibration damper for practical application. The Gaussian process regression model of the magnetorheological damper uses the operating current, piston displacement and velocity as model input variables, and the predicted damping force as model output variable. By training and adjusting the Gaussian process regression model of the magnetorheological damper, the complex mapping relationship between the input and output variables is captured, in order to accurately predict the output damping force of the magnetorheological damper. Step 2: Determine the prior distribution of the Gaussian process regression for the magnetorheological vibration damper; Step 3: Calculate the posterior mean and posterior covariance of the Gaussian process regression model; Step 4: Evaluation of the Gaussian process regression model for the magnetorheological vibration damper: If the root mean square error (RMSE) is less than the set value, the model is considered to be a Gaussian process regression model for the magnetorheological damper that meets the performance conditions, and the process proceeds to step 6. If the RMSE is greater than or equal to the set value, the process proceeds to step 5 to further perform hyperparameter optimization calculations and readjust the relevant parameters of the Gaussian process model for the magnetorheological damper. Step 5: Hyperparameter optimization calculation; Step 6: Final evaluation and application of the Gaussian process regression model for magnetorheological vibration dampers: After step 4, which satisfies the accuracy requirements of the Gaussian process regression model evaluation process, the test set data is used to conduct a final evaluation test on all the Gaussian process regression models of magnetorheological vibration dampers that meet the performance conditions. The model with the lowest root mean square error value is selected as the optimal Gaussian process regression model for magnetorheological vibration dampers and applied to actual engineering.

2. The magnetorheological vibration damper modeling method based on a Gaussian process regression model as described in claim 1, characterized in that: Step 2 also includes the following steps: Let the mean function and kernel function of a Gaussian process be defined as the prior distributions, where the Gaussian process... Defined as: In the formula: f(x) is the regression function; m(x) is the mean function; k(x) is the mean function. i ,x j ) is the kernel function; x i x j Let i and j be the i-th and j-th data points in the dataset; By setting the mean function m(x) to zero, we construct the dot product kernel function, the Matern5 / 2 kernel function, and the white noise kernel function to characterize the complex linear and nonlinear mechanical properties and noise characteristics present in step 1: The set dot product kernel function k Linear (x i ,x j )satisfy: In the formula: is the variance parameter of the dot product kernel; The set Matern5 / 2 kernel function k Mat52 (x i ,x j )satisfy: In the formula: Let |x| be the variance parameter of the Matern5 / 2 kernel, and l be the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space. i -x j || is data point x i and x j The Euclidean distance between them; Define the white noise kernel function k Noise (x i ,x j )satisfy: In the formula: δ(x) is the variance parameter of the white noise kernel, used to simulate the level of random noise in the observed data. i -x j ) is the Dirac function, which represents 1 when i and j are equal, and 0 otherwise; Based on the three kernel functions in equation (2-4), a composite kernel function k is constructed. total (x i ,x j )satisfy: k total (x i ,x j )=k Linear (x i ,x j )+k Mat52 (x i ,x j )+k Noise (x i ,x j ) (5) By constructing the aforementioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper, as well as the noise during the data acquisition process, are captured, ensuring that the model learns the above three types of characteristics from the data to the greatest extent possible, thereby effectively improving the prediction accuracy of the damping force value of the magnetorheological damper.

3. The magnetorheological vibration damper modeling method based on a Gaussian process regression model as described in claim 2, characterized in that: Step 3 also includes the following steps: To find the optimal hyperparameter θ of the Gaussian process model of the magnetorheological vibration damper opt Set initial hyperparameters As a starting point for searching for optimal hyperparameters; Given the input training set and initial values ​​for the hyperparameters, calculate the posterior mean and posterior covariance, where the posterior mean m * and posterior covariance C * They respectively satisfy: In the formula: K represents the kernel matrix of the training set x and itself; Represents the validation set x * The kernel matrix of the training set x; Represents the training set x and the validation set x * The kernel matrix; Represents the validation set x * The kernel matrix of itself; I is the identity matrix; y is the observed data of the training set; ∈ is the regularization coefficient; The calculation process of the kernel matrix is ​​shown in equation (8): In the formula: n is the total number of samples in the training set; m is the total number of samples in the validation set; x n This is the last data point in the training set; This is the last data point in the validation set; The calculated Gaussian process expression satisfies: Where: m * C is the posterior mean; * For posterior covariance; y * For the validation set x * The predicted output value satisfies: In the formula: It is the i-th predicted value in the validation set, that is, the damping force value predicted by the Gaussian process regression model of the magnetorheological damper.

4. The magnetorheological vibration damper modeling method based on a Gaussian process regression model as described in claim 3, characterized in that: Step 4 also includes the following steps: A Gaussian process regression model was used to predict the validation set data. The difference between the actual and predicted values ​​was calculated, and the root mean square error (RMSE) was used to evaluate the prediction accuracy. In the formula: y i It is the i-th observation in the verification set, that is, the output damping force value obtained from the actual magnetorheological damper.

5. The magnetorheological vibration damper modeling method based on a Gaussian process regression model as described in claim 4, characterized in that: Step 5 also includes the following steps: If the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements after step 4, the hyperparameters need to be recalculated. The calculation process is as follows: First, the marginal log-likelihood function L(θ) is used as the objective function to adjust the hyperparameters, thereby measuring the goodness of fit of the model. The marginal log-likelihood function L(θ) is set as follows: In the formula: θ is a hyperparameter; A higher value for the marginal log-likelihood function L(θ) indicates a better fit to the data; conversely, a lower value indicates a worse fit. Secondly, a Bayesian optimization algorithm is used to iteratively adjust the marginal log-likelihood function, and the optimal hyperparameter θ is obtained by finding the value of the maximum marginal log-likelihood function. opt Its expression satisfies: i opt =argmax θ L(θ) (13) The optimal hyperparameter θ obtained through iterative optimization opt The Gaussian process regression model of the magnetorheological damper will be replaced by the initial hyperparameters and updated cyclically to accurately adjust the model and achieve continuous improvement in predictive performance.

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