A physical information neural network method for rack force estimation considering friction compensation

Abstract

This invention relates to the field of steer-by-wire vehicle technology, specifically disclosing a physical information neural network (PEN) method for estimating rack force considering friction compensation. The method includes constructing a PSN model; establishing an adaptive Kalman filter based on a state-space model, where the state-space model is based on the dynamic equations of the vehicle steering system; designing a composite loss function; training the PSN model using the composite loss function; and using the output of the trained PSN model as the observation input and parameter input of the adaptive Kalman filter to output the final rack force estimate. This invention, by combining a neural network with the loss function of the steering dynamics equations, enables the network to simultaneously estimate friction torques that cannot be modeled in the state-space equations, effectively improving the modeling accuracy of the Kalman filter.

Description

Technical Field

[0001] This invention relates to the field of steer-by-wire vehicle technology, specifically a physical information neural network method for rack force estimation that considers friction compensation. Background Technology

[0002] The rack force in a steering system reflects the force exerted by the road surface on the tires; therefore, accurate estimation of the rack force is crucial in both steer-by-wire and power steering systems. However, traditional Kalman filter-based estimation methods have the following drawbacks: First, because the torque required to overcome friction is ignored during modeling, load estimation has significant errors. Even when friction torque is included, its nonlinear characteristics often lead to simplification to a state variable equal to the previous state, rather than accurate modeling. This results in large estimation errors when the steering wheel reverses. Second, the effectiveness of the filter largely depends on the accuracy of the noise covariance matrix. An inaccurate covariance matrix significantly reduces estimation accuracy and may even cause the filter to diverge. Therefore, traditional model-based methods all suffer from unavoidable errors in estimating rack forces. Summary of the Invention

[0003] The purpose of this invention is to provide a physical information neural network method for rack force estimation that considers friction compensation, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A physical information neural network method for rack force estimation considering friction compensation, the method comprising:

[0006] A physical information neural network model is constructed to synchronously output preliminary estimates of rack force, system friction compensation torque, and observation noise covariance based on vehicle sensor data.

[0007] An adaptive Kalman filter based on a state-space model is established, wherein the state-space model is based on the dynamic equations of the vehicle steering system;

[0008] Design a composite loss function, which includes a physical information loss term based on the dynamic equation and a Kalman loss term based on the final output of the adaptive Kalman filter;

[0009] The physical information neural network model is trained using the composite loss function to guide it in learning the friction compensation torque and the observation noise covariance.

[0010] The output of the trained physical information neural network model is used as the observation input and parameter input of the adaptive Kalman filter to output the final rack force estimate.

[0011] As a further embodiment of the present invention, the composite loss function further includes a data loss term based on the maximum likelihood estimation of the observed data.

[0012] As a further embodiment of the present invention, the physical information loss term for:

[0013] ;

[0014] in, To adjust the steering angle of the motor, i am r is the reduction ratio of the reducer. p T is the pitch circle radius of the pinion in the rack and pinion steering mechanism. am The output torque of the steering actuator motor is J, the equivalent moment of inertia of the system is C, and the equivalent damping coefficient of the system is F. ture This represents the true value of the rack force. This is the friction compensation torque.

[0015] As a further embodiment of the present invention, the data loss item for:

[0016] ;

[0017] Among them, F net The rack force estimate is output by the network. F represents the observation noise covariance of the network output. ture This represents the true value of the rack force.

[0018] As a further embodiment of the present invention, the Kalman loss term is the mean square error between the rack force estimate output by the adaptive Kalman filter and the true rack force.

[0019] As a further 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.

[0020] As a further embodiment of the present invention, the state variables of the state space model of the adaptive Kalman filter include the steering angle, angular velocity and rack force to be estimated of the steering actuator motor.

[0021] Compared with the prior art, the beneficial effects of the present invention are: it enables the neural network to autonomously estimate filter parameters without the truth value, and at the same time, by combining the loss function of the steering dynamics equation, the network can simultaneously estimate the friction torque that cannot be modeled in the state space equation, effectively improving the modeling accuracy of the Kalman filter and enhancing the rack force estimation accuracy. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention.

[0023] Figure 1 This is a flowchart illustrating a physical information neural network-based rack force estimation method considering friction compensation, provided in an embodiment of the present invention.

[0024] Figure 2 The diagram below shows a structural block diagram of a physical information neural network rack force estimation method considering friction compensation, provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0026] Please see Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating a physical information neural network-based rack force estimation method considering friction compensation. In this embodiment of the invention, a physical information neural network-based rack force estimation method considering friction compensation includes:

[0027] A physical information neural network model is constructed to synchronously output preliminary estimates of rack force, system friction compensation torque, and observation noise covariance based on vehicle sensor data.

[0028] An adaptive Kalman filter based on a state-space model is established, wherein the state-space model is based on the dynamic equations of the vehicle steering system;

[0029] Design a composite loss function, which includes a physical information loss term based on the dynamic equation and a Kalman loss term based on the final output of the adaptive Kalman filter;

[0030] The physical information neural network model is trained using the composite loss function to guide it in learning the friction compensation torque and the observation noise covariance.

[0031] The output of the trained physical information neural network model is used as the observation input and parameter input of the adaptive Kalman filter to output the final rack force estimate.

[0032] In this embodiment, information from IMU sensors, vehicle chassis CAN, steering wheel angle sensor, tension and compression sensor, etc., is read, and a dataset is built based on the read information;

[0033] Establish a neural network estimation model incorporating physical information, and set the network output as the initial estimate of the rack force. Observation noise covariance and friction compensation torque ;

[0034] Design a physical information loss term based on physical information that incorporates the steering dynamics equations;

[0035] An adaptive Kalman filter based on state-space equations is established, and friction compensation and adaptive parameter adjustment of the Kalman filter are performed according to the network output.

[0036] Design a data-based loss term that incorporates the Kalman final estimate;

[0037] The network is trained, and the network weights are adjusted through backpropagation. The trained network helps the Kalman filter compensate for frictional torque and adaptively adjust parameters.

[0038] The final estimated value of the rack force at the final output.

[0039] The established neural network estimation model, which incorporates physical information, uses the preliminary estimate of the rack force as one output of the network, the parameters of the Kalman filter (i.e., the observation noise covariance) as another output, and the internal friction torque of the system (i.e., the friction compensation torque) that cannot be modeled in the steering dynamics equation as the third output.

[0040] The preliminary estimate of the rack force and the friction compensation torque are used as observations for the Kalman filter, and the observation noise covariance matrix is ​​used as an adjustable parameter of the Kalman filter. The friction compensation torque corrects the nonlinear friction torque inside the steering system that was simplified during the Kalman modeling process.

[0041] The physical information neural network model structure is designed as follows:

[0042] First layer: Input layer;

[0043] The second layer: the LSTM layer, which consists of 40 neurons;

[0044] The third layer: a fully connected layer, consisting of 30 neurons;

[0045] The fourth layer: the LSTM layer, consisting of 20 neurons;

[0046] The fifth layer: a fully connected layer, consisting of 10 neurons;

[0047] Sixth layer: Activation layer, using the hyperbolic tangent function as the activation function;

[0048] The seventh layer: a fully connected layer that maps features to a single output node;

[0049] Eighth layer: Regression layer, which guides weight adjustments during the training process;

[0050] Ninth layer: Output layer, outputs the final prediction result of the model.

[0051] Perform hyperparameter settings: Set the maximum training epochs, batch size, gradient threshold, and initial learning rate to achieve higher prediction accuracy. The settings are as follows:

[0052] Maximum training cycles: 30;

[0053] Batch size: 20;

[0054] Gradient threshold: 1;

[0055] Initial learning rate: 0.01;

[0056] The state variables of the state-space model of the adaptive Kalman filter include the steering angle, angular velocity, and rack force to be estimated of the steering actuator motor.

[0057] In a preferred embodiment of the present invention, the composite loss function further includes a data loss term based on the maximum likelihood estimation of the observed data, the main function of which is to guide the network to learn the observation noise covariance matrix in the absence of true values.

[0058] As a preferred embodiment of the present invention, a physical information loss term based on physical information is designed incorporating the steering dynamics equations. Its main function is to guide the network to learn the friction compensation torque when there is no truth value;

[0059] First, the steering dynamics equations are established as follows:

[0060] ;

[0061] ;

[0062] Among them: J am、 C am、 K am These are the equivalent moment of inertia, damping coefficient, and torsional stiffness from the steering actuator motor to the reducer, respectively; m r C r For rack and pinion steering gears, the rack mass and rack damping coefficient are given. The motor rotates to adjust the steering angle; i am The reduction ratio of the reducer; r px is the pitch circle radius of the pinion in the rack and pinion steering mechanism; r T represents the rack displacement in the rack and pinion steering mechanism. am The motor outputs torque to drive the steering mechanism; The equivalent frictional torque between the steering actuator motor and the reducer; F r The rack force exerted on the rack by the steering tie rod; This refers to the internal friction force of the rack and pinion steering gear.

[0063] Combining the above equations and considering 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:

[0064] ;

[0065] Where J is the equivalent moment of inertia of the system, and C is the equivalent damping coefficient of the system, expressed as follows:

[0066] ;

[0067] ;

[0068] At the same time, the frictional torque and frictional force between the various components are also equivalent to the frictional torque T on the steering column. f The expression is as follows:

[0069] ;

[0070] Establish with T f The loss function of the physical information loss term directly related to the estimated value is used as an observation to fuse and correct the state variables. The loss function is as follows:

[0071] ;

[0072] in, To adjust the steering angle of the motor, i am r is the reduction ratio of the reducer. p T is the pitch circle radius of the pinion in the rack and pinion steering mechanism. am The torque output by the steering motor is J, where J is the system's equivalent moment of inertia and C is the system's equivalent damping coefficient. For friction compensation torque, F ture The true value of the rack force is obtained by measuring the tension / compression sensor. Using the loss function described above, the network can be optimized even without T. f In the case of truth value, the friction torque T is learned autonomously. f This enables the network to quickly achieve gradient descent.

[0073] As a preferred embodiment of the present invention, a data-based loss function, i.e., a data loss term, is designed that considers the initial network estimate. for:

[0074] ;

[0075] Among them, F net The rack force estimate is output by the network. F represents the observation noise covariance of the network output. ture This represents the true value of the rack force.

[0076] In this embodiment, the data-based loss function maximizes the likelihood probability of the observed data by adjusting the LSTM network weights within each step, thereby minimizing the negative log-likelihood. During this process, the data-based loss function guides the LSTM network to simultaneously learn the predicted rack force and variance, ensuring that the LSTM operates without... Even in the case of true values, it still provides predicted rack force values ​​and observation noise covariance.

[0077] In a preferred embodiment of the present invention, the Kalman loss term is the mean square error between the estimated rack force output by the adaptive Kalman filter and the true rack force.

[0078] In this embodiment, an adaptive Kalman filter based on state-space equations is established, and friction compensation and adaptive adjustment of observation noise covariance are performed on the Kalman filter according to the network output.

[0079] First, the state-space equations are established based on the steering dynamics equations:

[0080] ;

[0081] ;

[0082] In the formula, ; ; ; ; ; ; ; .

[0083] The prior estimate is obtained by using the following formula to predict the process of the system:

[0084] ;

[0085] ;

[0086] The prior estimates obtained from the process prediction are updated using the following formula to obtain the optimal estimate:

[0087] ;

[0088] ;

[0089] ;

[0090] Design a Kalman-based loss function that considers the final estimate of the filter. That is, the Kalman loss term, which is formulated as follows:

[0091] ;

[0092] Where T is the length of the time series of each minibatch, and N is the number of minibatch.

[0093] 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.

[0094] 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.

[0095] 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.

[0096] The overall loss function formula is designed as follows:

[0097] ;

[0098] 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 With the 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.

[0099] The network is trained using the overall loss function. A typical backpropagation algorithm is used to recursively calculate the gradient of the loss function from time t-1 to time t with respect to the pseudo-measurement uncertainty parameter and the filter output state. Then, the loss function is further calculated recursively. gradient with respect to network weights θ The calculation formula is as follows:

[0100] ;

[0101] ;

[0102] Gradient calculation applies the chain rule to the above equation and moves forward, progressively calculating the weight of each network node.

[0103] 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 outputs are input to the Kalman filter, providing the Kalman filter with an initial estimate of the rack force and friction compensation torque, and adaptively adjusting the filter's observation noise covariance.

[0104] The final estimated value of the rack force at the final output.

[0105] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A physical information neural network method for rack force estimation considering friction compensation, characterized in that, The method includes: A physical information neural network model is constructed to synchronously output preliminary estimates of rack force, system friction compensation torque, and observation noise covariance based on vehicle sensor data. An adaptive Kalman filter based on a state-space model is established, wherein the state-space model is based on the dynamic equations of the vehicle steering system; Design a composite loss function, which includes a physical information loss term based on the dynamic equation and a Kalman loss term based on the final output of the adaptive Kalman filter. The physical information loss term is used to guide the network to learn the friction compensation torque in the absence of a truth value. The physical information neural network model is trained using the composite loss function to guide the learning of the friction compensation torque and the observation noise covariance; The output of the trained physical information neural network model is used as the observation input and parameter input of the adaptive Kalman filter to output the final rack force estimate.

2. The physical information neural network rack force estimation method considering friction compensation according to claim 1, characterized in that, The composite loss function also includes a data loss term based on the maximum likelihood estimation of the observed 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 item for: ； in, To adjust the steering angle of the motor, i am r is the reduction ratio of the reducer. p T is the pitch circle radius of the pinion in the rack and pinion steering mechanism. am The output torque of the steering actuator motor is J, the equivalent moment of inertia of the system is C, and the equivalent damping coefficient of the system is F. ture This represents the true value of the rack force. This is the friction compensation torque.

4. The physical information neural network rack force estimation method considering friction compensation according to claim 3, characterized in that, The data loss item for: ； Among them, F net The rack force estimate is output by the network. F represents the observation noise covariance of the network output. ture This represents the true value of the rack force.

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 the mean square error between the estimated rack force output by the adaptive Kalman filter and the true rack force.

6. The physical information neural network rack force estimation method considering friction compensation according to claim 5, characterized in that, The composite loss function is the 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, The state variables of the state-space model of the adaptive Kalman filter include the steering angle, angular velocity, and rack force to be estimated of the steering actuator motor.

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