Magnetorheological damper modeling method based on Gaussian process regression model

Abstract

The invention discloses a magneto-rheological damper modeling method based on a Gaussian process regression model. The magneto-rheological damper modeling method comprises the following steps: step 1, acquiring and preprocessing data based on a mechanical property test of a magneto-rheological damper; 2, determining Gaussian process regression prior distribution of the magnetorheological damper; 3, calculating a posteriori mean value and a posteriori covariance of the Gaussian process regression model; 4, evaluating the Gaussian process regression model of the magnetorheological damper; 5, performing hyper-parameter optimization calculation; and step 6, final evaluation and application of the Gaussian process regression model of the magnetorheological damper. On the premise of ensuring the model precision, the problems of insufficient computing resources, increased training time cost and the like possibly caused when a non-parameterized model represented by a neural network model faces a large-scale data set are solved; meanwhile, for the problem of model overfitting possibly caused by noise interference in training data, a kernel function with a noise interference suppression effect is provided so as to improve the modeling precision of the model.

Description

Technical Field

[0001] The invention relates to the technical field of magnetorheological dampers, and in particular to a magnetorheological damper modeling method based on a Gaussian process regression model. Background Art

[0002] Magnetorheological suspension systems have attracted widespread attention in the field of automotive suspension technology due to their fast response, high damping force controllability, and low energy consumption, and have been recognized and applied in the market. The mechanical properties of magnetorheological shock absorbers are crucial to suspension performance. Given that the mechanical properties of magnetorheological shock absorbers have significant nonlinearity and uncertainty, it is particularly important to establish an accurate and practical mechanical property model. Therefore, in-depth research and development of a model that can accurately describe the mechanical behavior of magnetorheological shock absorbers is a prerequisite for the design and control of efficient and intelligent suspension systems, and plays a decisive role in improving the system's dynamic response and ride comfort.

[0003] At present, the modeling methods for the mechanical characteristics of magnetorheological dampers mainly include parametric modeling and non-parametric modeling. Parametric models represented by the Bingham model and the Bouc-Wen model mainly use the series-parallel combination of physical elements and hysteresis modules to simulate the mechanical behavior of the damper, which has the advantages of simple structure and easy analysis. Although the parametric model can accurately describe the mechanical behavior of the magnetorheological damper within a certain range, its multi-parameter optimization and identification are inevitably subject to factors such as initial values, constraints, and convergence, which makes it difficult. In actual control applications, the numerical processing of strong nonlinear equations may cause control lag and affect the control effect.

[0004] Traditional parametric models are difficult to describe nonlinear or highly complex systems represented by magnetorheological dampers. Their mathematical expressions are usually difficult to construct and parameter identification may require complex optimization algorithms. Non-parametric models are more flexible and usually use data and expert knowledge to characterize the modeling process. They can better describe the complex nonlinear mechanical characteristics of magnetorheological dampers and therefore have greater research and application potential. Non-parametric models can be subdivided into data-driven models and non-data-driven models. Non-data-driven models include fuzzy logic, empirical models, etc., which are mainly based on expert knowledge, system theory or physical laws. In practical applications, they require rich empirical knowledge to adjust and are difficult to implement. Data-driven models include neural networks, vector machines, etc. This type of method establishes a nonlinear mapping relationship between the input and output of magnetorheological dampers based on sufficiently rich test data to characterize their dynamic behavior. As a typical data-driven model, neural networks can accurately approximate any continuous function and are particularly suitable for describing complex nonlinear systems such as magnetorheological dampers. Patent CN202211361602.0 proposes a LSTM-based calculation method for the reverse mapping model of a magnetorheological damper, and uses the LSTM neural network model to construct the reverse dynamics model of the magnetorheological damper, thereby improving the fitting speed and accuracy of the reverse dynamics model of the magnetorheological damper; Patent CN202210561440.9 proposes an intelligent simulation neural network algorithm with fast optimization speed and strong adaptability, which can accurately and quickly identify the dynamic damping characteristics of the shock absorber and shorten the development cycle of the shock absorber. However, in actual application, on the one hand, the neural network model usually requires a large amount of training data to ensure the accuracy and generalization ability of the model, resulting in the consumption of a large amount of computing resources and increased training time costs; on the other hand, the experimental data used by the neural network model for neural network training inevitably contains noise. If the network structure is redundant, it may cause noise interference during the training process, thereby affecting the final convergence performance of the network, causing the training to deviate from the global optimal point, and causing overfitting due to the memory of noise details, thereby reducing the generalization ability. Therefore, in the process of studying the mechanical model of magnetorheological shock absorbers, it is of great research significance to overcome the defects of non-parametric models represented by neural network models in order to meet the high-precision modeling requirements of magnetorheological shock absorbers. Summary of the invention

[0005] In view of the problems that a large amount of training data is required, the training time is long, and additional external noise removal is required to ensure the accuracy of the model in the process of modeling magnetorheological dampers using non-parametric models represented by neural network models, the present invention proposes a magnetorheological damper modeling method based on a Gaussian process regression model. Under the premise of ensuring the accuracy of the model, the non-parametric models represented by neural network models overcome the problems of insufficient computing resources and increased training time costs when facing large-scale data sets; at the same time, in view of the problem that noise interference in the training data may cause model overfitting, a kernel function with the effect of suppressing noise interference is proposed to improve the modeling accuracy of the model.

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

[0007] A magnetorheological damper modeling method based on a Gaussian process regression model comprises the following steps:

[0008] Step 1: Data collection and preprocessing based on the mechanical properties test of magnetorheological damper;

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

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

[0011] Step 4: Gaussian process regression model evaluation of magnetorheological damper;

[0012] The model that can achieve a root mean square error RMSE value less than the set value is set as the magnetorheological damper Gaussian process regression model that meets the performance conditions, and then proceed to step 6; if the root mean square error RMSE is greater than or equal to the set value, then proceed to step 5 to further carry out hyperparameter optimization calculations and readjust the relevant parameters of the magnetorheological damper Gaussian process model;

[0013] Step 5: Hyperparameter optimization calculation;

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

[0015] After step 4, when the model accuracy requirements in the Gaussian process regression model evaluation process are met, the test set data is used to conduct a final evaluation test on all magnetorheological damper Gaussian process regression models that meet the performance conditions, and the model with the lowest root mean square error value is selected as the optimal magnetorheological damper Gaussian process regression model for application in actual engineering.

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

[0017] The mechanical properties of the magnetorheological damper are tested using the magnetorheological damper mechanical test platform system. The sample data of the magnetorheological damper during its operation are collected using sensors. All sample data are normalized and scaled to the [-1,1] range to enhance the convergence efficiency and prediction accuracy of model training.

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

[0019] The Gaussian process regression model of magnetorheological shock absorber takes working current, piston motion displacement and speed as model input variables, and predicts damping force as model output variable; by training and adjusting the Gaussian process regression model of magnetorheological shock absorber, the complex mapping relationship between input variables and output variables is captured in order to accurately predict the output damping force of the magnetorheological shock absorber.

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

[0021] Set the mean function and kernel function of the Gaussian process as the prior distribution, where the Gaussian process Defined as:

[0022]

[0023] Where: f(x) is the regression function; m(x) is the mean function; k(x i ,x j ) is the kernel function; x i 、x j are the i-th and j-th data points of the data set;

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

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

[0026]

[0027] Where: The variance parameter of the dot product kernel;

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

[0029]

[0030] Where: is the variance parameter of the Mater5 / 2 kernel, l is the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space, ||x i -x j || is the data point x i and x j The Euclidean distance between

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

[0032]

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

[0034] Based on the three kernel functions in formula (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 above-mentioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper and the noise in the data acquisition process are captured to ensure that the model learns the above three types of characteristics from the data to the greatest extent, thereby effectively improving the prediction accuracy of the damping force value of the magnetorheological damper.

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

[0038] To find the optimal hyperparameter θ of the Gaussian process model of magnetorheological damper opt , set the 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 interval [0.1, 10], and the Bayesian optimization algorithm described in step 5 is allowed to find the optimal noise variance value within this range;

[0039] By giving the input training set and setting the initial value of the hyperparameter, the posterior mean and posterior covariance are calculated, where the posterior mean m * and the posterior covariance C * Respectively meet:

[0040]

[0041]

[0042] Where: K represents the kernel matrix of the training set x and itself; Represents the validation set x * and the kernel matrix of the training set x; Represents the training set x and the validation set x * The kernel matrix of Represents the validation set x * and its own kernel matrix; I is the unit matrix; y is the observed data of the training set; ∈ is the regularization coefficient;

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

[0044]

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

[0046] The calculated Gaussian process expression satisfies:

[0047]

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

[0049]

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

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

[0052] Use the Gaussian process regression model to predict the validation set data, calculate the difference between the true value and the predicted value, and use the root mean square error (RMSE) to evaluate the prediction accuracy:

[0053]

[0054] Where: y i is the i-th observation value in the validation set, i.e., the output damping force value observed by the actual magnetorheological damper.

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

[0056] After step 4, if the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements, 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 for adjusting the hyperparameters to measure the quality of the model fitting effect. The marginal log-likelihood function L(θ) is set as follows:

[0058]

[0059] Where: θ is a hyperparameter;

[0060] The higher the value of the marginal log-likelihood function L(θ), the better the fit to the data; otherwise, the worse it is.

[0061] Secondly, the 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 , whose expression satisfies:

[0062] θ opt = argmax θ L(θ) (13)

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

[0064] The beneficial effects of the present invention are mainly manifested in:

[0065] 1) The present invention trains and constructs a mechanical model of the magnetorheological damper through training data, and then predicts its output damping force, which effectively reduces the model's dependence on large-scale training sets.

[0066] 2) The present invention proposes a kernel function in the modeling process of magnetorheological damper based on Gaussian process regression model. The construction of the kernel function takes into account the linear, nonlinear and noise characteristics of the magnetorheological damper acquisition data, 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the present invention.

[0068] Figure 2 It is a comparison chart of the predicted value and the actual value output by the Gaussian process regression model in the embodiment of the present invention.

[0069] Figure 3 It is a set of fitting characteristic curves of the model finally applied.

[0070] Figure 4 It is a set of speed characteristic curves of the model finally applied. DETAILED DESCRIPTION

[0071] The present invention will be further described below in conjunction with the accompanying drawings.

[0072] Reference Figure 1 to Figure 4 , a modeling method for magnetorheological dampers based on Gaussian process regression model, such as Figure 1 As shown, the method mainly includes six steps: data collection and preprocessing based on the mechanical property test of magnetorheological damper, determining the Gaussian process regression prior distribution of magnetorheological damper, calculating the posterior mean and posterior covariance of the Gaussian process regression model, evaluating the Gaussian process regression model of magnetorheological damper, optimizing the calculation of hyperparameters, and finally evaluating and applying the Gaussian process regression model of magnetorheological damper. The specific implementation methods of each step are as follows:

[0073] Step 1: Data collection and preprocessing based on the mechanical properties test of magnetorheological damper

[0074] In this embodiment, the magnetorheological damper mechanical test platform system is used to test the mechanical properties of a magnetorheological damper, and the sensor is used to collect sample data such as piston movement displacement, speed, working current, and damping force generated by the magnetorheological damper during the working process of the magnetorheological damper. During the data collection process, the input signal is set to a sine wave signal, the amplitude of the magnetorheological damper is 40mm, the working control current is between 0.5 and 3A, and increases by 0.5A each time. The test frequency is between 1 and 5Hz, and increases by 1Hz each time. The total amount of measured and collected sample data is 1236. All sample data are normalized and standardized to the [-1,1] interval to enhance the convergence efficiency and prediction accuracy of model training. The preprocessed data are divided into a training set (70%), a validation set (15%) and a test set (15%). The training set is used to train and adjust the Gaussian process regression model of the magnetorheological damper, the validation set is used to test whether the Gaussian process regression model of the magnetorheological damper meets the set performance requirements, and the test set is used to screen out the optimal Gaussian process regression model of the magnetorheological damper for practical applications.

[0075] In this embodiment, the Gaussian process regression model of the magnetorheological shock absorber uses the working current, piston movement displacement and speed as model input variables, and predicts the damping force as the model output variable. The working current directly affects the magnetization of the magnetorheological fluid and determines the damping characteristics of the shock absorber; the piston movement displacement and speed parameters respectively characterize the static / dynamic response characteristics of the magnetorheological shock absorber. By training and adjusting the Gaussian process regression model of the magnetorheological shock absorber, the complex mapping relationship between the input variables and the output variables is captured, in order to accurately predict the output damping force of the magnetorheological shock absorber.

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

[0077] Set the mean function and kernel function of the Gaussian process as the prior distribution. Defined as:

[0078]

[0079] Where: f(x) is the regression function; m(x) is the mean function; k(x i ,x j ) is the kernel function; x i 、x j are the i-th and j-th data points in the data set.

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

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

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

[0083]

[0084] Where: Variance parameter of the dot product kernel.

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

[0086]

[0087] Where: is the variance parameter of the Mater5 / 2 kernel, l is the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space, ||x i -x j || is the data point x i and x j The Euclidean distance between .

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

[0089]

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

[0091] Based on the three kernel functions in formula (2-4), the composite kernel function k shown in formula (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 above-mentioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper and the noise in the data acquisition process are captured to ensure that the model learns the above three types of characteristics from the data to the greatest extent, 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 magnetorheological damper opt , set the initial hyperparameters As the starting point for searching for the optimal hyperparameters. The initial value of l is set to 1. The initial value is set within the interval [0.1, 10], and the Bayesian optimization algorithm described in step 5 is allowed to find the optimal noise variance value within this range.

[0096] By giving the input training set and setting the initial value of the hyperparameter, the posterior mean and posterior covariance are calculated, where the posterior mean m * and the posterior covariance C * Respectively meet:

[0097]

[0098]

[0099] Where: K represents the kernel matrix of the training set x and itself; Represents the validation set x * and the kernel matrix of the training set x; Represents the training set x and the validation set x * The kernel matrix of Represents the validation set x * and its own kernel matrix; I is the unit matrix; y is the observation data of the training set; ∈ is the regularization coefficient.

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

[0101]

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

[0103] The calculated Gaussian process expression satisfies:

[0104]

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

[0106]

[0107] Where: is the i-th predicted value in the validation set, i.e., 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 with the initial model, the damping force of the magnetorheological damper predicted by the model after continuous optimization and adjustment of the hyperparameters can more accurately approach the true value of the output damping force of the magnetorheological damper.

[0109] Step 4: Magnetorheological damper Gaussian process regression model evaluation

[0110] Use the Gaussian process regression model to predict the validation set data, calculate the difference between the true value and the predicted value, and use the root mean square error (RMSE) to evaluate the prediction accuracy:

[0111]

[0112] Where: y i is the i-th observation value in the validation set, i.e., the output damping force value observed by the actual magnetorheological damper.

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

[0114] Step 5: Hyperparameter optimization calculation

[0115] After step 4, if the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements, 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 for adjusting the hyperparameters to measure the quality of the model fitting effect. The marginal log-likelihood function L(θ) is set as follows:

[0117]

[0118] Where: θ is a hyperparameter.

[0119] The higher the value of the marginal log-likelihood function L(θ), the better the fit to the data; otherwise, the worse it is.

[0120] Secondly, the 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 , whose expression satisfies:

[0121] θ opt = argmax θ L(θ) (13)

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

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

[0124] After step 4, when the model accuracy requirements in the Gaussian process regression model evaluation process are met, the test set data is used to conduct a final evaluation test on all magnetorheological damper Gaussian process regression models that meet the performance conditions, and the model with the lowest root mean square error value is selected as the optimal magnetorheological damper Gaussian process regression model for application in actual engineering.

[0125] Figure 2 A graphic 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 damper in the embodiment are provided. The predicted value of each sample is within the 95% confidence interval. Figure 3 , Figure 4 A set of fitting demonstration characteristic curves and speed characteristic curves of the model finally applied in this embodiment are shown, which are almost completely consistent with the actual results obtained by the magnetorheological damper through the mechanical testing platform system, indicating that the Gaussian process regression model of the magnetorheological damper has an accurate prediction effect.

[0126] Gaussian process regression is a data-driven, non-parametric machine learning method that maps input data to a Gaussian process by building a covariance relationship between data points, thereby predicting the output of any new input point. The Gaussian process regression method has a powerful nonlinear modeling capability. It is applied to the construction of the mechanical characteristic model of the magnetorheological damper. With the flexibility of its kernel function construction, it can effectively reduce the various complex linear and nonlinear mechanical characteristics of the magnetorheological damper, as well as the influence of the inevitable noise interference in the data acquisition process on the model accuracy.

[0127] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. The scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but also should cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A magnetorheological damper modeling method based on a Gaussian process regression model, characterized in that: The modeling method comprises the following steps: Step 1: Data collection and preprocessing based on the mechanical properties test of magnetorheological damper; Step 2: Determine the Gaussian process regression prior distribution of the magnetorheological damper; Step 3: Calculate the posterior mean and posterior covariance of the Gaussian process regression model; Step 4: Gaussian process regression model evaluation of magnetorheological damper; The model that can achieve a root mean square error RMSE value less than the set value is set as the magnetorheological damper Gaussian process regression model that meets the performance conditions, and then proceed to step 6; if the root mean square error RMSE is greater than or equal to the set value, then proceed to step 5 to further carry out hyperparameter optimization calculations and readjust the relevant parameters of the magnetorheological damper Gaussian process model; Step 5: Hyperparameter optimization calculation; Step 6: Final evaluation and application of the Gaussian process regression model for MR dampers: After step 4, when the model accuracy requirements in the Gaussian process regression model evaluation process are met, the test set data is used to conduct a final evaluation test on all magnetorheological damper Gaussian process regression models that meet the performance conditions, and the model with the lowest root mean square error value is selected as the optimal magnetorheological damper Gaussian process regression model for application in actual engineering.

2. The magnetorheological damper modeling method based on the Gaussian process regression model according to claim 1, characterized in that: The step 1 also includes the following steps: The mechanical properties of the magnetorheological damper are tested using the magnetorheological damper mechanical test platform system. The sample data of the magnetorheological damper during its operation are collected using sensors. All sample data are normalized and scaled to the [-1,1] range to enhance the convergence efficiency and prediction accuracy of model training. The preprocessed data is divided into a training set, a validation set and a test set. The training set is used to train and adjust the Gaussian process regression model of the magnetorheological damper, the validation set is used to test whether the Gaussian process regression model of the magnetorheological damper meets the set performance requirements, and the test set is used to screen out the optimal Gaussian process regression model of the magnetorheological damper for practical application. The Gaussian process regression model of magnetorheological shock absorber takes working current, piston motion displacement and speed as model input variables, and predicts damping force as model output variable; by training and adjusting the Gaussian process regression model of magnetorheological shock absorber, the complex mapping relationship between input variables and output variables is captured in order to accurately predict the output damping force of the magnetorheological shock absorber.

3. A magnetorheological damper modeling method based on a Gaussian process regression model as claimed in claim 1 or 2, characterized in that: The step 2 also includes the following steps: Set the mean function and kernel function of the Gaussian process as the prior distribution, where the Gaussian process Defined as: Where: f(x) is the regression function; m(x) is the mean function; k(x i ,x j ) is the kernel function; x i 、x j are the i-th and j-th data points of the data set; Set the mean function m(x) to zero, and construct the dot product kernel function, Matern5 / 2 kernel function, and white noise kernel function to characterize the three characteristics of complex linear and nonlinear mechanical properties and noise characteristics in step 1: Set the dot product kernel function k Linear (x i ,x j )satisfy: Where: The variance parameter of the dot product kernel; Matern5 / 2 kernel function k is set Mat52 (x i ,x j )satisfy: Where: is the variance parameter of the Mater5 / 2 kernel, l is the length scale parameter, which controls the sensitivity of the Matern5 / 2 kernel to changes in the input space, ||x i -x j || is the data point x i and x j The Euclidean distance between Set the white noise kernel function k Noise (x i ,x j )satisfy: Where: is the variance parameter of the white noise kernel, which is used to simulate the random noise level in the observed data, δ(x i -x j ) is the Dirac function, which means it is 1 when i and j are equal, otherwise it is 0; Based on the three kernel functions in formula (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 above-mentioned composite kernel function, the complex linear and nonlinear mechanical characteristics of the magnetorheological damper and the noise in the data acquisition process are captured to ensure that the model learns the above three types of characteristics from the data to the greatest extent, thereby effectively improving the prediction accuracy of the damping force value of the magnetorheological damper.

4. A magnetorheological damper modeling method based on a Gaussian process regression model as claimed in claim 1 or 2, characterized in that: The step 3 also includes the following steps: To find the optimal hyperparameter θ of the Gaussian process model of magnetorheological damper opt , set the initial hyperparameters As a starting point for searching for optimal hyperparameters; By giving the input training set and setting the initial value of the hyperparameter, the posterior mean and posterior covariance are calculated, where the posterior mean m * and the posterior covariance C * Respectively meet: m * =K X*X (K+∈I) -1 y (6) Where: K represents the core matrix of the training set x and itself; K X*X Represents the validation set x * and the kernel matrix of the training set x; Represents the training set x and the validation set x * The kernel matrix of Represents the validation set x * and its own kernel matrix; I is the unit matrix; y is the observed data of the training set; ∈ is the regularization coefficient; The calculation process of the above kernel matrix is ​​shown in formula (8): Where: n is the total number of samples in the training set; m is the total number of samples in the validation set; x n It is the last data point of the training set; It is the last data point of the validation set; The calculated Gaussian process expression satisfies: Where: m * is the posterior mean; C * is the posterior covariance; y * is the validation set x * The predicted output value satisfies: Where: is the i-th predicted value in the validation set, i.e., the damping force value predicted by the Gaussian process regression model of the magnetorheological damper.

5. A magnetorheological damper modeling method based on a Gaussian process regression model as claimed in claim 1 or 2, characterized in that: The step 4 also includes the following steps: Use the Gaussian process regression model to predict the validation set data, calculate the difference between the true value and the predicted value, and use the root mean square error (RMSE) to evaluate the prediction accuracy: Where: y i is the i-th observation value in the validation set, i.e., the output damping force value observed by the actual magnetorheological damper.

6. A magnetorheological damper modeling method based on a Gaussian process regression model as claimed in claim 1 or 2, characterized in that: The step 5 also includes the following steps: After step 4, if the Gaussian process regression model of the magnetorheological damper fails to meet the model performance requirements, 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 for adjusting the hyperparameters to measure the quality of the model fitting effect. The marginal log-likelihood function L(θ) is set as follows: Where: θ is a hyperparameter; The higher the value of the marginal log-likelihood function L(θ), the better the fit to the data; otherwise, the worse it is. Secondly, the 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 , whose expression satisfies: i opt =argmax θ L(θ) (13) The optimal hyperparameter θ obtained after iterative optimization opt The initial hyperparameters will be replaced and cyclically updated to accurately adjust the Gaussian process regression model of the magnetorheological damper and achieve continuous improvement in the prediction performance.

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