CN112632705B - Road feel simulation method based on GMM and Gaussian process regression - Google Patents
Road feel simulation method based on GMM and Gaussian process regression Download PDFInfo
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Abstract
The invention discloses a road feel simulation method based on GMM and Gaussian process regression, which comprises the following steps: performing a real vehicle test and collecting data; preprocessing test data; clustering normalized test data by using a Gaussian mixture model classification algorithm; dividing a training data set and a test data set; training a road feel simulation model based on GMM and Gaussian process regression, wherein the input variables of the Gaussian process regression model are longitudinal speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle and steering wheel angular velocity, and the output variables are steering wheel moment; testing a road feel simulation model based on GMM and Gaussian process regression; and performing road feel simulation according to the obtained road feel simulation model based on GMM and Gaussian process regression. According to the invention, the GMM classification algorithm is used for clustering, and the road sense simulation model modeling is performed based on the Gaussian process regression algorithm, so that the obtained model has stable performance, high precision, high operation speed and good instantaneity.
Description
Technical Field
The invention relates to the technical field of vehicles, in particular to a road feel simulation method based on GMM and Gaussian process regression.
Background
The steering road sense, also called steering force sense and steering wheel feedback torque, refers to the reverse resistance torque sensed by the driver through the steering wheel feedback torque. The steering force sense can enable the driver to acquire key vehicle running state and running environment information to a certain extent, so that the driver makes a decision in a mode most suitable for the current running working condition, and running safety is guaranteed. When the vehicle uses the steer-by-wire system, if the real road feel is simulated without using any method, the driver can be caused to carry out irrational driving, and the driving safety of the real vehicle is threatened. The same situation occurs for a simulated driver without road feel simulation capability, which in turn leads to severe distortion of the simulated driving. At present, a main road feel modeling method is a mechanism modeling method, and parameters required to be adjusted by the method are numerous, and high accuracy is difficult to achieve.
The Chinese patent with publication number of CN110606121A and name of a drive-by-wire steering road feel simulation control method relates to a steering wheel feedback force control system, a steering load model is constructed through dynamics to calculate steering resistance moment, the model belongs to mechanism modeling, a plurality of parameters needing to be regulated are needed, and the precision is difficult to guarantee.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a road feel simulation method based on GMM and Gaussian process regression, which is used for modeling by using real vehicle test data, a Gaussian Mixture Model (GMM) classification algorithm and a Gaussian process regression algorithm to obtain a road feel simulation model based on the GMM and Gaussian process regression, and solves the problems of complex model structure, low precision and the like in the traditional mechanism modeling.
In order to achieve the above object, the present invention provides a road feel simulation method based on GMM and gaussian process regression, comprising the steps of:
step one, performing a real vehicle test and collecting data: selecting a driver to perform a real vehicle test, wherein the vehicle runs on a test road, and the collected test data comprise longitudinal vehicle speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, steering wheel angular speed and steering wheel moment;
step two, test data pretreatment: carrying out normalization treatment on the test data after abnormal points are removed, and obtaining a normalized test data set;
step three, clustering normalized test data: clustering the normalized test data by using a Gaussian mixture model classification algorithm, and obtaining a plurality of data classes with the same quantity as the clustered communities after clustering;
step four, dividing a training data set and a test data set: dividing the normalized test data set into a training data set and a test data set;
training a road feel model based on GMM and Gaussian process regression: training to obtain a plurality of road feel simulation models which have the same number as data classes and are based on GMM and Gaussian process regression by using a training data set and Gaussian process regression algorithm; when the model is trained, the input variables of the model are longitudinal speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel corner and steering wheel angular velocity, and the output variables are steering wheel moment;
step six, testing a road feel model based on GMM and Gaussian process regression: testing the obtained road feel simulation model based on GMM and Gaussian process regression by using a test data set;
step seven, judging whether the model is acceptable or not: if the model is acceptable, the modeling is successful, otherwise, the real vehicle road mining test is carried out again;
and step eight, road sense simulation is carried out according to the obtained plurality of road sense simulation models based on GMM and Gaussian process regression.
Further, in the real vehicle test of step one: test road types include expressways, urban roads, suburban roads, rural roads, and off-road roads.
Further, in the real vehicle test of step one: the driving conditions of the vehicle comprise ascending and descending slopes, straight running, reversing, turning and in-situ steering.
Further, in the second step, the removed abnormal points include data points out of the normal value range and data points with severely deviated distribution.
The data points beyond the normal value range are defined as: points that are clearly outside the normal range. Data points for which the speed is negative, such as when forward driving is performed; for another example, when the steering wheel is significantly right, the measured steering wheel angle value is a negative data point.
The data points for which the distribution deviates significantly are defined as: the data are distributed at points outside the range of standard deviation of a plurality of times of the whole related variable data. The multiple may be, but is not limited to, 3 times, i.e., a data point with a severely deviated distribution if one or more variables of the data point have a value greater than 3 times the standard deviation of the corresponding variable or less than minus 3 times the standard deviation of the corresponding variable.
Further, in the second step, the test data is normalized according to the following formula, so as to obtain normalized test data:
wherein i is the data number, j is the variable number, x i,j Represents the j-th variable, X in the unnormalized i-th set of data j And (3) representing a set formed by variable data values corresponding to all j, wherein min represents the minimum value of the related variable in the test data after the abnormal point is removed, and max represents the maximum value of the related variable in the test data after the abnormal point is removed.
Preferably, in the third step, when the gaussian mixture model classification algorithm is used for clustering, variables involved in clustering include, but are not limited to, longitudinal vehicle speed, vehicle lateral acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle and steering wheel angular velocity, and the number of communities is 4.
Further, the step of training the Gaussian mixture model is as follows:
1) Determining the population number k=1
2) Randomly setting Gaussian distribution function parameters corresponding to each class group, namely probability omega w Mean mu w Variance sigma w 。
3) E, step E: calculate each sample data x q (q is more than or equal to 1 and less than or equal to n) belongs to each community C w (1<w<k) Hidden variables of (i.e. probability z) q 。
Wherein,is a hybrid weighting coefficient.
Calculating posterior probability
4) M step: the parameter values for each cluster are recalculated.
5) Repeating the steps 3) and 4), and iteratively calculating to guide parameter value convergence or iteration times to reach an upper limit value.
6) And calculating a Bayesian index BIC value corresponding to the k value.
BIC＝-2log(L)+klog(n)
7) k=k+1, iterating steps 2) to 6) until the BIC value is smaller than the threshold value or the iteration number reaches the upper limit value.
8) And taking the condition of minimum BIC value as the optimal cluster setting.
When predicting new data, calculating to obtain the corresponding post of each classProbability value of testThe class corresponding to the maximum posterior probability value can be considered as the group to which the new data belongs.
Preferably, in the step four, when the training data set and the test data set are divided, a certain number of data points with a certain proportion are randomly selected from the normalized test data set as the training data set, and the others are all used as the test data set. In a preferred embodiment, this proportion is 70%.
Preferably, in the fifth step, modeling is performed by using a training dataset and a gaussian process regression algorithm, and the training is performed to obtain the road feel simulation models based on GMM and gaussian process regression, which are the same as the number of data classes, and the embodiment obtains 4 road feel simulation models. When the model is trained, the input variables of the Gaussian process regression model comprise vehicle longitudinal speed, vehicle transverse acceleration, vehicle yaw rate acceleration, vehicle vertical load, steering wheel corner and steering wheel angular velocity; the output variable is steering wheel torque. The model obtained by training the training data points of the same type is related to the type of the data points, namely, a road feel simulation model corresponding to a certain type of training data points can only be used for predicting the moment of the steering wheel of the data points of the type. Training the plurality of types of training data points results in a corresponding plurality of road feel simulation models.
When training a road feel simulation model based on GMM and Gaussian process regression, the method comprises the following specific steps:
for the gaussian process regression algorithm, the training dataset is represented as:
D＝(X,y)
wherein:
X＝{x i }，y＝{y i }，x i represents the ith input data, y i Representing an i-th output value;
y＝f(x n )+ξ n
mean value u, kernel function k (x i ,x j ) The method comprises the steps of carrying out a first treatment on the surface of the The noise matrix isThen
y～N[0,K(X,X)+σ 2 I]
Wherein K (X, X) is the corresponding kernel function, I is the corresponding identity matrix, given a new data input X * The corresponding output is y * The method comprises the steps of carrying out a first treatment on the surface of the According to the Bayesian principle, the output value y * The joint distribution with training data is:
calculating corresponding posterior distribution y; the predicted output y can be expressed as:
y*|X,y,x * ～N(μ,∑)
wherein,
the mean of the predicted distribution in the equation is actually an estimate of the test output.
Using the square-index covariance function (squared exponential covariance function, SE) to solve for the super-parameters of the kernel function, including sigma, by maximum likelihood estimation n 、σ f And l. The SE kernel function may be expressed as:
further, in testing a road feel simulation model based on GMM and gaussian process regression, a mean square error, or MSE, value may be used, but is not limited to, as a criterion for model quality. When the road feel simulation model based on GMM and Gaussian process regression is tested by using a test data set, the steps are as follows:
sequentially inputting the numerical values of input variables corresponding to the test data points in the test data set into a road feel simulation model to obtain a predicted steering wheel moment value; calculating to obtain MSE values between the steering wheel moment values obtained by predicting the test data points of the whole test data set and the real steering wheel moment values; if the MSE value is smaller than the preset threshold value alpha, the training-obtained road feel simulation model based on data driving is considered to be acceptable, and the modeling is successful. Otherwise, the model is not acceptable, and a supplementary road mining test is needed. The threshold α is empirically determined by an expert and in a preferred embodiment, the threshold α is set to 0.15.
After modeling is completed, the method further comprises a model application step, and road sense simulation is carried out according to the obtained plurality of road sense simulation models based on GMM and Gaussian process regression. Collecting real-time running data of a vehicle as new data, wherein the real-time running data comprises longitudinal speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel corner and steering wheel angular velocity, and calculating a posterior probability value corresponding to each class through a Gaussian mixture model according to the running dataThe class corresponding to the maximum posterior probability value can be considered as the group to which the new data belongs. And then, inputting the driving data into a road feel simulation model corresponding to the belonging group and based on GMM and Gaussian process regression, obtaining a predicted steering wheel moment value through model calculation, and controlling the steering wheel according to the steering wheel moment value so as to simulate vivid road feel.
By adopting the technical scheme, the invention achieves the following technical effects: the invention uses the real vehicle road acquisition data as the basis, adopts a Gaussian mixture model classification algorithm (GMM) to carry out clustering, and carries out modeling based on a Gaussian process regression algorithm, thus establishing a road feel simulation model with good robustness, high precision, high operation speed and good real-time performance; the road feel simulation is carried out according to the obtained road feel simulation model, so that the problems that the model accuracy of the traditional mechanism modeling is not high, the real-time performance in the application process is difficult to ensure and the like are solved.
Drawings
FIG. 1 is a flowchart of modeling steps in a road feel simulation method based on GMM and Gaussian process regression according to the present invention.
FIG. 2 is a graph (partial) of steering wheel torque for suburban operating conditions collected in an embodiment in accordance with the invention.
Fig. 3 is model test data (local) in an embodiment according to the invention.
Detailed Description
In order that the present invention may be better understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, in which it is to be understood that the invention is illustrated in the appended drawings. All other embodiments obtained under the premise of equivalent changes and modifications made by those skilled in the art based on the embodiments of the present invention shall fall within the scope of the present invention.
Referring to fig. 1 to 3, the present embodiment provides a road feel simulation method based on GMM and gaussian process regression, which includes modeling steps S1 to S7, and a model application step. Steps S1-S7 of the modeling process are described in detail below in conjunction with fig. 1.
S1, performing a real vehicle test and collecting data:
selecting a driver to perform a real-vehicle test, wherein the vehicle runs on test roads, and the types of the test roads include, but are not limited to, expressways, urban roads, suburban roads, rural roads and off-road roads; the related running conditions of the vehicle comprise ascending and descending slopes, straight running, reversing, turning and in-situ steering.
The collected test data comprise longitudinal vehicle speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, steering wheel angular velocity, steering wheel moment and the like. Steering wheel angle, steering wheel angular velocity, and steering wheel torque are measured using an angle torque sensor, model KISTLER MSW DTI sensors. The longitudinal speed, the lateral acceleration and the yaw rate of the vehicle are measured by an inertial navigation system, and the model is OxTs RT3002.
The data acquisition frequency in this embodiment is 100Hz. As shown in fig. 2, the steering wheel torque curve (local) for suburban operation collected in the test of this example is represented by the actual steering wheel torque-data numbering curve.
S2, preprocessing test data:
processing the test data includes outlier removal and data normalization. The outliers that are removed include data points that are outside of the normal range of values and data points that have a severely deviated distribution. The manner of removing outliers from the test data may be manual removal or filtering with a low pass filter.
In this embodiment, the collected test data is normalized according to the following formula, so as to obtain normalized test data. The normalization formula may take, but is not limited to, the following:
wherein i is the data number, j is the variable number, x i,j Represents the j-th variable, X in the unnormalized i-th set of data j And (3) representing a set formed by variable data values corresponding to all j, wherein min represents the minimum value of the related variable in the test data after the abnormal point is removed, and max represents the maximum value of the related variable in the test data after the abnormal point is removed.
After pretreatment, a normalized test dataset was obtained.
S3, clustering normalization test data
Clustering the normalized test data by using a Gaussian mixture model classification algorithm, and obtaining 4 data classes with the same quantity as the clustered communities after clustering in the embodiment.
When clustering is performed using a gaussian mixture model classification algorithm, variables involved in clustering include, but are not limited to, longitudinal vehicle speed, vehicle lateral acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, and steering wheel angular velocity.
The step of training the Gaussian mixture model is as follows:
1) Determining the population number k=1
2) Randomly setting Gaussian distribution function parameters corresponding to each class group, namely probability omega w Mean mu w Variance sigma w 。
3) E, step E: calculate each sample data x q (q is more than or equal to 1 and less than or equal to n) belongs to each community C w (1<w<k) Hidden variables of (i.e. probability z) q . The sample data in this example includes normalized longitudinal vehicle speed, vehicle lateral acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, and steering wheel angular velocity.
Wherein,is a hybrid weighting coefficient.
Calculating posterior probability
4) M step: the parameter values for each cluster are recalculated.
5) Repeating the steps 3) and 4), and iteratively calculating to guide parameter value convergence or iteration times to reach an upper limit value.
6) And calculating a Bayesian index BIC value corresponding to the k value.
BIC＝-2log(L)+klog(n)
7) k=k+1, iterating steps 2) to 6) until the BIC value is smaller than the threshold value or the iteration number reaches the upper limit value.
8) And taking the condition of minimum BIC value as the optimal cluster setting. In this example, the number of colonies was 4.
Calculating to obtain posterior probability value corresponding to each class when predicting new dataThe class corresponding to the maximum posterior probability value can be considered as the group to which the new data belongs.
S4, dividing a training data set test data set
When dividing the training data set and the test data set, 70% of the data points from the normalized test data set are randomly selected as the training data set, and the others are all used as the test data set. The ratio of the number of data points in the training data set to the number of data points in the test data set is 7:3.
S5, training a road feel model based on GMM and Gaussian process regression:
modeling is carried out by using a training data set and a Gaussian process regression algorithm, the road sense simulation model with the same quantity as the data classes and based on GMM and Gaussian process regression is obtained through training, and 4 road sense simulation models are obtained in the embodiment. When the model is trained, the input variables of the Gaussian process regression model comprise vehicle longitudinal speed, vehicle transverse acceleration, vehicle yaw rate acceleration, vehicle vertical load, steering wheel corner and steering wheel angular velocity; the output variable is steering wheel torque. The model obtained by training the training data points of the same type is related to the type of the data points, namely, a road feel simulation model corresponding to a certain type of training data points can only be used for predicting the moment of the steering wheel of the data points of the type. The present embodiment will yield corresponding 4 road feel simulation models after training with 4 types of training data points.
When training a road feel simulation model based on GMM and Gaussian process regression, the method comprises the following specific steps:
the training dataset is represented as:
D＝(X,y)
wherein:
X＝{x i }，y＝{y i }，x i represents the ith input data, y i Representing an i-th output value;
y＝f(x n )+ξ n
mean value u, kernel function k (x i ,x j ) The method comprises the steps of carrying out a first treatment on the surface of the Noise matrix is xi n ～N(0,σ n 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Then
y～N[0,K(X,X)+σ 2 I]
Wherein K (X, X) is the corresponding kernel function, I is the corresponding identity matrix, given a new data input X * The corresponding output is y * The method comprises the steps of carrying out a first treatment on the surface of the According to the Bayesian principle, the output value y * The joint distribution with training data is:
calculating corresponding posterior distribution y; the predicted output y can be expressed as:
y*|X,y,x * ～N(μ,∑)
wherein,
the mean of the predicted distribution in the equation is actually an estimate of the test output.
Selecting square index covariance function SE for solving super-parameters of kernel function by maximum likelihood estimation, including sigma n 、σ f And l. The SE kernel function may be expressed as:
s6, testing a road feel model based on GMM and Gaussian process regression:
when testing the road feel model based on GMM and Gaussian process regression, the steps of using the test data set to test the obtained road feel simulation model based on GMM and Gaussian process regression are as follows: sequentially inputting the numerical values of input variables corresponding to the test data points in the test data set into a road feel simulation model to obtain a predicted steering wheel moment value; calculating to obtain MSE values between the steering wheel moment values obtained by predicting the test data points of the whole test data set and the real steering wheel moment values; if the MSE value is smaller than the preset threshold value alpha, the training-obtained road feel simulation model based on data driving is considered to be acceptable, and the modeling is successful. In this embodiment, as shown in fig. 3, which shows a model test curve (local), it can be seen from the graph that the simulated steering wheel moment-time curve (sim) substantially coincides with the actual steering wheel moment-time curve (real) in the period of 0-400s, and the MSE value is 0.11.
S7, judging whether the model is acceptable
The MSE value=0.11 obtained by the test is far smaller than the threshold value alpha=0.15 preset by an expert, and the obtained model is acceptable and does not need to carry out a supplementary road mining test.
Model application step:
after modeling, the road feel simulation method according to the invention further comprises a model application step: and performing road feel simulation according to the obtained road feel simulation model based on GMM and Gaussian process regression. Inputting the obtained 4 road feel simulation models based on GMM and Gaussian process regression into a driving simulator, collecting running state parameters such as vehicle longitudinal speed, vehicle transverse acceleration, vehicle yaw rate acceleration, vehicle vertical load, steering wheel angle, steering wheel angular velocity and the like of a simulated vehicle in real time when a simulated driving test is carried out on the driving simulator, and calculating according to a Gaussian mixture model classification algorithm to obtain each road feel simulation modelPosterior probability value corresponding to individual classAnd taking the class corresponding to the maximum posterior probability value as the class group to which the new data belongs. And then, inputting the corresponding variable of the driving state parameter as an input variable into a road feel simulation model corresponding to the belonging group, calculating to obtain a steering wheel moment value through the road feel simulation model based on GMM and Gaussian process regression, and controlling the steering wheel in real time according to the steering wheel moment value, so that more lifelike road feel is simulated. Experiments prove that the road feel simulation model established by the invention has stable performance, high precision and high operation speed, and overcomes the defects of the prior art to a certain extent.
The foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention; it will be apparent to those skilled in the relevant art and it is intended to implement the invention in light of the foregoing disclosure without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. A road feel simulation method based on GMM and Gaussian process regression is characterized by comprising the following steps:
step one, performing a real vehicle test and collecting data: selecting a driver to perform a real vehicle test, wherein the vehicle runs on a test road, and the collected test data comprise longitudinal vehicle speed, vehicle transverse acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, steering wheel angular speed and steering wheel moment;
step two, test data pretreatment: carrying out normalization treatment on the test data after abnormal points are removed, and obtaining a normalized test data set;
step three, clustering normalized test data: clustering the normalized test data by using a Gaussian mixture model classification algorithm, and obtaining a plurality of data classes with the same quantity as the clustered communities after clustering; specifically, when a Gaussian mixture model classification algorithm is used for clustering, variables involved in clustering include longitudinal vehicle speed, vehicle lateral acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle and steering wheel angular velocity; the step of training the Gaussian mixture model is as follows:
1) Determining the community number k=1;
2) Randomly setting Gaussian distribution function parameters corresponding to each class group, namely probability omega w Mean mu w Variance sigma w ；
3) E, step E: calculate each sample data x q (q is more than or equal to 1 and less than or equal to n) belongs to each community C w (1<w<k) Hidden variables of (i.e. probability z) q The method comprises the steps of carrying out a first treatment on the surface of the Sample data includes normalized longitudinal vehicle speed, vehicle lateral acceleration, vehicle yaw rate, vehicle vertical load, steering wheel angle, and steering wheel angular velocity;
wherein,is a mixed weighting coefficient;
calculating posterior probability
4) M step: recalculating parameter values of each cluster;
5) Repeating the steps 3) and 4), and iteratively calculating to guide parameter value convergence or iteration times to reach an upper limit value;
6) Calculating a Bayesian index BIC value corresponding to the k value;
BIC＝-2log(L)+klog(n)
7) k=k+1, iterating steps 2) to 6) until the BIC value is smaller than the threshold value or the iteration number reaches the upper limit value;
8) Taking the condition of minimum BIC value as the optimal clustering setting;
calculating to obtain posterior probability value corresponding to each class when predicting new dataThe class corresponding to the maximum posterior probability value can be considered as the class group to which the new data belongs;
step four, dividing a training data set and a test data set: dividing the normalized test data set into a training data set and a test data set;
training a road feel model based on GMM and Gaussian process regression: training to obtain a plurality of road feel simulation models which have the same number as data classes and are based on GMM and Gaussian process regression by using a training data set and Gaussian process regression algorithm; when the model is trained, the input variables of the model comprise vehicle longitudinal speed, vehicle transverse acceleration, vehicle yaw rate acceleration, vehicle vertical load, steering wheel rotation angle and steering wheel angular velocity; the output variable is steering wheel torque;
step six, testing a road feel model based on GMM and Gaussian process regression: testing the obtained road feel simulation model based on GMM and Gaussian process regression by using a test data set;
step seven, judging whether the model is acceptable or not: if the model is acceptable, the modeling is successful, otherwise, the real vehicle road mining test is carried out again;
and step eight, road sense simulation is carried out according to the obtained plurality of road sense simulation models based on GMM and Gaussian process regression.
2. The road feel simulation method based on GMM and gaussian process regression according to claim 1, wherein in the real vehicle test of step one: test road types include expressways, urban roads, suburban roads, rural roads, and off-road roads.
3. The road feel simulation method based on GMM and gaussian process regression according to claim 1, wherein in the real vehicle test of step one: the driving conditions of the vehicle comprise ascending and descending slopes, straight running, reversing, turning and in-situ steering.
4. The method of claim 1, wherein in the second step, the outliers that are removed include data points that are outside the normal range and data points that have a severely deviated distribution.
5. The road feel simulation method based on GMM and Gaussian process regression according to claim 1, wherein in the second step, the test data is normalized according to the following formula to obtain normalized test data:
wherein i is the data number, j is the variable number, x i,j Represents the j-th variable, X in the unnormalized i-th set of data j And (3) representing a set formed by variable data values corresponding to all j, wherein min represents the minimum value of the related variable in the test data after the abnormal point is removed, and max represents the maximum value of the related variable in the test data after the abnormal point is removed.
6. The road feel simulation method based on GMM and gaussian process regression according to claim 1, wherein in the fourth step, when the training data set and the test data set are divided, a certain number of data points in proportion are randomly selected from the normalized test data set as the training data set, and the other data points are all used as the test data set.
7. The method according to any one of claims 1 to 6, wherein in the fifth step, when training the model of road feel simulation based on GMM and gaussian process regression, the square index covariance function SE is selected to be used, and the super-parameters of the kernel function are solved by maximum likelihood estimation.
8. The road feel simulation method based on GMM and Gaussian process regression according to claim 1, wherein the specific steps of testing the road feel simulation model based on GMM and Gaussian process regression and judging whether the model is acceptable according to the test result are as follows:
sequentially inputting the numerical values of input variables corresponding to the test data points in the test data set into a road feel simulation model to obtain a predicted steering wheel moment value; calculating to obtain MSE values between the steering wheel moment values obtained by predicting the test data points of the whole test data set and the real steering wheel moment values; if the MSE value is smaller than the preset threshold value alpha, the training-obtained road feel simulation model based on data driving is considered to be acceptable, and the modeling is successful.
9. The method of road feel simulation based on GMM and gaussian process regression according to claim 8, wherein the threshold α is 0.15.
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