Physical information neural network rack force estimation method considering friction compensation

Abstract

The invention relates to the technical field of steer-by-wire vehicles, and particularly discloses a physical information neural network rack force estimation method considering friction compensation, and the method comprises the steps: constructing a physical information neural network model; establishing an adaptive Kalman filter based on a state space model, wherein the state space model is based on a kinetic equation of a vehicle steering system; designing a composite loss function, training the physical information neural network model by using the composite loss function, taking the output of the trained physical information neural network model as the observed quantity input and parameter input of the adaptive Kalman filter, and outputting a final rack force estimated value; according to the method, the neural network is combined with the loss function of the steering kinetic equation, so that the network can estimate the friction torque which cannot be modeled in the state-space equation at the same time, and the modeling accuracy of the Kalman filter is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of steer-by-wire vehicles, and particularly relates to a rack force estimation method of a physical information neural network considering friction compensation. BACKGROUND

[0002] The rack force in a steering system can reflect the force of the road on the tire, so accurate estimation of the rack force is crucial in steer-by-wire systems and power steering systems. However, the traditional estimation method based on Kalman filtering has the following shortcomings: first, because the torque required to overcome friction is ignored in the modeling process, there is a large error in load estimation. Even if the friction torque is added, its nonlinear characteristics usually cause it to be simplified as a state variable equal to the previous state, rather than accurately modeled. This results in a large estimation error when the steering wheel is reversed. Second, the effectiveness of the filter depends largely on the accuracy of the noise covariance matrix. An inaccurate covariance matrix can greatly reduce the estimation accuracy and even cause the filter to diverge. Therefore, the traditional model-based method has unavoidable errors when estimating the rack force. SUMMARY

[0003] The present application aims to provide a rack force estimation method of a physical information neural network considering friction compensation to solve the problems raised in the background.

[0004] To achieve the above-mentioned purpose, the present application provides the following technical solutions: A rack force estimation method of a physical information neural network considering friction compensation, the method comprising: constructing a physical information neural network model for simultaneously outputting a preliminary estimation value of the rack force, a system friction compensation torque, and an observation noise covariance based on vehicle sensor data; establishing an adaptive Kalman filter based on a state space model, the state space model being based on a dynamics equation of a vehicle steering system; designing a composite loss function, the composite loss function comprising a physical information loss term based on the dynamics equation and a Kalman loss term based on the final output result of the adaptive Kalman filter; training the physical information neural network model using the composite loss function to guide it to learn the friction compensation torque and the observation noise covariance; inputting the output of the trained physical information neural network model as the observation and parameter inputs of the adaptive Kalman filter, and outputting a final rack force estimation value.

[0005] As a further solution of the present application, the composite loss function further comprises a data loss term based on maximum likelihood estimation of observation data.

[0006] As a further scheme of the present application, the physical information loss term is: ; wherein, is the steering execution motor angle, i am is the reduction ratio of the reducer, r p is the pinion indexing circle radius in the rack-and-pinion steering mechanism, T am is the steering execution motor output torque, J is the system equivalent moment of inertia, C is the system equivalent damping coefficient, F ture is the rack force true value, is the initial estimated value of the rack force.

[0007] As a further scheme of the present application, the data loss term is: ; wherein, F net is the network output rack force estimated value, is the network output observation noise covariance, F ture is the rack force true value.

[0008] As a further scheme of the present application, the Kalman loss term is the mean square error between the rack force estimated value output by the adaptive Kalman filter and the rack force true value.

[0009] As a further scheme of the present application, the compound loss function is the sum of the Kalman loss term, the data loss term and the physical information loss term.

[0010] As a further scheme of the present application, the state quantity of the state space model of the adaptive Kalman filter comprises the steering execution motor angle, angular velocity and the rack force to be estimated.

[0011] Compared with the prior art, the present application has the beneficial effect that the neural network can autonomously estimate the filter parameters without true values, and the loss function combined with the steering dynamics equation enables the network to simultaneously estimate the friction torque that cannot be modeled in the state space equation, effectively improves the modeling accuracy of the Kalman filter and improves the rack force estimation accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application.

[0013] Figure 1 A flow chart of a physical information neural network rack force estimation method considering friction compensation is provided for the embodiments of the present application.

[0014] Figure 2 A structure block diagram of a physical information neural network rack force estimation method considering friction compensation is provided for the embodiments of the present application. DETAILED DESCRIPTION

[0015] In order to make the technical problems to be solved by the present application, technical solutions and beneficial effects more clearly understood, the following will further describe the present application in combination with the drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present application, and are not used to limit the present application.

[0016] Please refer to Figure 1 and Figure 2 , Figure 1 A flow chart of a physical information neural network rack force estimation method considering friction compensation, in the embodiments of the present application, a physical information neural network rack force estimation method considering friction compensation, the method comprises: Constructing a physical information neural network model, for synchronously outputting a preliminary estimation value of rack force, a system friction compensation torque and an observation noise covariance according to vehicle sensor data; Establishing an adaptive Kalman filter based on a state space model, the state space model is based on the dynamics equation of the vehicle steering system; Designing a composite loss function, the composite loss function includes a physical information loss term based on the dynamics equation, and a Kalman loss term based on the final output result of the adaptive Kalman filter; Training the physical information neural network model using the composite loss function to guide it to learn the friction compensation torque and the observation noise covariance; The output of the trained physical information neural network model is used as the observation quantity input and parameter input of the adaptive Kalman filter, and the final rack force estimation value is output.

[0017] In the present embodiment, the information provided by the IMU sensor, vehicle chassis CAN, steering wheel angle sensor, tension and compression force sensor, etc. is read, and a data set is established according to the read information; A neural network estimation model containing physical information is established, and the network output quantity is set as the initial estimation value of rack force , the observation noise covariance and the friction compensation torque a physical information loss term based on the steering dynamics equation is designed; an adaptive Kalman filter based on the state space equation is established, and the Kalman filter is compensated for friction and adaptively adjusted for parameters according to the network output; a data loss term based on data combined with the Kalman final estimate is designed; the network is trained, the network weight adjustment is realized through back propagation, and the trained network helps the Kalman filter to compensate for the friction torque and adaptively adjust the parameters; the final estimate of the rack force is output.

[0018] The neural network estimation model containing physical information is established, the preliminary estimate of the rack force is taken as one of the network output, the parameters of the Kalman filter, i.e. the observation noise covariance, is taken as another network output, and the internal friction torque of the system which cannot be modeled in the steering dynamics equation, i.e. the friction compensation torque, is taken as the third network output.

[0019] The preliminary estimate of the rack force and the friction compensation torque are taken as the observation of the Kalman filter, and the observation noise covariance matrix is taken as the adjustable parameter of the Kalman filter. The friction compensation torque corrects the nonlinear friction torque of the internal steering system which is simplified in the Kalman modeling process The structure of the physical information neural network model is designed as follows: First layer: input layer; Second layer: LSTM layer, consisting of 40 neurons; Third layer: fully connected layer, consisting of 30 neurons; Fourth layer: LSTM layer, consisting of 20 neurons; Fifth layer: fully connected layer, consisting of 10 neurons; Sixth layer: activation layer, using the hyperbolic tangent function as the activation function; Seventh layer: fully connected layer, mapping the features to a single output node; Eighth layer: regression layer, guiding the weight adjustment in the training process; Ninth layer: output layer, outputting the final prediction result of the model.

[0020] Hyperparameter setting: set the maximum training period, batch size, gradient threshold and initial learning rate to achieve higher prediction accuracy. The settings are as follows: Maximum training period: 30; Batch size: 20; Gradient threshold: 1; ​Initial learning rate: 0.01; The state quantity of the state space model of the adaptive Kalman filter includes the rotation angle of the steering execution motor, the angular velocity, and the rack force to be estimated.

[0021] As a preferred embodiment of the present application, the composite loss function further includes a data loss term based on the maximum likelihood estimation of the observation data, which mainly guides the network to learn the observation noise covariance matrix in the absence of true values.

[0022] As a preferred embodiment of the present application, a physical information loss term based on physical information combined with the steering dynamics equation is designed , which mainly guides the network to learn the friction compensation torque in the absence of true values. First, the steering dynamics equation is established as follows: ; ; Among them: J am、 C am、 K am J, B, K are the equivalent moment of inertia, damping coefficient and torsional stiffness of the steering execution motor to the reducer, respectively; m r , C r m, B are the rack mass and rack damping coefficient in the rack and pinion steering gear; is the steering execution motor rotation angle; i am is the reduction ratio of the reducer; r p is the pinion indexing circle radius in the rack and pinion steering mechanism; x r is the rack displacement in the rack and pinion steering mechanism; T am is the steering execution motor output torque; is the equivalent friction torque between the steering execution motor and the reducer; F r is the rack force of the steering tie rod acting on the rack; is the internal friction of the rack and pinion steering gear.

[0023] Combine the above formula, and consider the wheel end steering mechanism as a rigid transmission system, under this assumption, the inertia and damping of each component are equivalent to the axis of the lower steering column of the steering motor: ; Among them, J is the equivalent moment of inertia of the system,C The system equivalent damping coefficient is expressed as follows: ; ; The friction torque and friction force between each component are also equivalent to the friction torque on the steering column T f The expression is as follows: ; Established with T f The loss function of the loss term of the physical information directly related to the estimated value is fused and corrected to the state quantity, and the loss function is as follows: ; Wherein, The steering execution motor rotation angle is i am The reduction ratio of the reducer is r p The pinion indexing circle radius in the rack and pinion steering mechanism is T am The steering execution motor output torque is J The system equivalent moment of inertia is C The system equivalent damping coefficient is The initial estimated value of the rack force is F ture The true value of the rack force is measured by the tension and compression force sensor. The network can be autonomously learned without T f The true value of the friction torque T f The network quickly realizes gradient descent.

[0024] As a preferred embodiment of the present application, the data-based loss function considering the initial estimated value of the network, that is, the data loss term, is designed, and the data loss term is: ; Wherein, F net The rack force estimated value output by the network is The observation noise covariance output by the network is F ture The true value of the rack force is

[0025] In this embodiment, the data-based loss function maximizes the likelihood of the observed data by adjusting the network weights of the LSTM at each step, thus implementing negative log-likelihood minimization. The data-based loss function guides the LSTM network to learn both the rack force prediction and the variance simultaneously, which ensures that the LSTM provides rack force predictions and observed noise covariance even without the true values.

[0026] As a preferred embodiment of the present application, the Kalman loss term is the mean squared error between the rack force estimate output by the adaptive Kalman filter and the true rack force value.

[0027] In this embodiment, an adaptive Kalman filter based on the state space equation is established, and the Kalman filter is friction compensated and adaptively adjusted in terms of the network output quantity and the observation noise covariance; First, the state space equation is established based on the steering dynamics equation: ; ; wherein, ; ; ; ; ; ; ; .

[0028] The system is process predicted by the following formula to obtain the prior estimate: ; ; The prior estimate obtained by process prediction is updated by observation to obtain the optimal estimate: ; ; ; Design a Kalman-based loss function considering the final estimate value of the filter , i.e. the Kalman loss term, is as follows: ; wherein, T is the length of the time series sequence of each minibatch, N is the number of minibatches.

[0029] The Kalman-based loss function is the RMSE between the final estimate of the rack force and the true value of the rack force. Its main function is to treat the KF as a computational graph that unfolds over time and introduce it into the backpropagation process of the network. It is simultaneously affected by the three outputs of the network and the KF estimate, so it can achieve the effect of learning the three outputs at the same time during the backpropagation process.

[0030] In a preferred embodiment of the present invention, the composite loss function is the sum of the Kalman loss term, the data loss term, and the physical information loss term.

[0031] In this embodiment, the total loss function is obtained by adding the three loss functions together. The network is trained, and the network weights are adjusted through backpropagation. The trained network helps the Kalman filter compensate for friction torque and adaptively adjust parameters. The overall loss function formula is designed as follows: ; The first part of the loss function Part Two: Helping LSTM correctly estimate spurious measurements and their noise covariance matrix It is a friction torque loss function that incorporates physical information to achieve rapid gradient descent in the network, Part 3. It is the output of AKF. F AKF True value of rack force F ture The error is due to the fact that the network output directly affects the AKF output. It is simultaneously affected by the network's three outputs and the AKF output.

[0032] The network is trained using the overall loss function, and then recursively calculated from back to front using a typical backpropagation algorithm. t- 1 hour has arrived t The loss function at time step is calculated by taking the gradient of the spurious measurement uncertainty parameter and the filter output state, and then the loss function is calculated recursively. gradient with respect to network weights θ The calculation formula is as follows: ; ; Gradient calculation applies the chain rule to the above equation and moves forward, progressively calculating the weight of each network node.

[0033] Using the trained network, the initial estimate of the rack force is output in real time. Observation noise covariance and friction compensation torque The three output quantities are input to the Kalman filter, which provides an initial estimate of the rack force and friction compensated torque to the Kalman filter and adaptively adjusts the filter observation noise covariance.

[0034] The final output is a final estimate of the rack force.

[0035] The above description is merely preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A physical information neural network rack force estimation method considering friction compensation, characterized in that, The method comprises: constructing a physical information neural network model for synchronously outputting a preliminary estimation value of rack force, a system friction compensation torque and an observation noise covariance according to vehicle sensor data; establishing an adaptive Kalman filter based on a state space model based on a dynamics equation of a vehicle steering system; designing a composite loss function comprising a physical information loss term based on the dynamics equation and a Kalman loss term based on a final output result of the adaptive Kalman filter; training the physical information neural network model by using the composite loss function to guide learning of the friction compensation torque and the observation noise covariance; inputting an output of the trained physical information neural network model as an observation quantity input and a parameter input of the adaptive Kalman filter, and outputting a final rack force estimation value.

2. The physical information neural network rack force estimation method considering friction compensation according to claim 1, wherein, The composite loss function further comprises a data loss term based on maximum likelihood estimation of observation data.

3. The physical information neural network rack force estimation method considering friction compensation according to claim 2, characterized in that, the physical information loss term is: ； wherein, is the steering execution motor angle, i am is the reduction ratio of the reduction gear, r p is the pinion indexing circle radius in the rack and pinion steering mechanism, T am is the steering execution motor output torque, J C is the system equivalent moment of inertia, F ture is the rack force true value, is the initial estimate of the rack force.​ 4. The physical information neural network rack force estimation method considering friction compensation according to claim 3, characterized in that, The data loss term Is: ； wherein, F net is the network output rack force estimate, is the network output observation noise covariance, F ture is the rack force true value.

5. The physical information neural network rack force estimation method considering friction compensation according to claim 4, characterized in that, The Kalman loss term is a mean square error between the rack force estimation value output by the adaptive Kalman filter and a true value of the rack force.

6. The physical information neural network rack force estimation method considering friction compensation according to claim 5, wherein, The composite loss function is a sum of the Kalman loss term, the data loss term and the physical information loss term.

7. The physical information neural network rack force estimation method considering friction compensation according to claim 1, characterized in that, State quantities of the state space model of the adaptive Kalman filter comprise a rotation angle, an angular velocity of a steering execution motor and the rack force to be estimated.

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