Vehicle dynamics modeling method based on multi-order network hybrid model of digital-analog co-driving

Abstract

The application provides a special vehicle dynamics modeling method based on a digital-analog co-driving network hybrid model, which is based on the hybrid modeling idea of fusing a physical model and a network model, and is directed to a five-axle transport vehicle lateral dynamics model, and proposes a multi-level network hybrid model of digital-analog co-driving, and fuses the physical model and the multi-level network model through a residual block. In the process of training the neural network, the dynamics equation provides data input for the network model, and the mathematical model is input into the network model in the form of data. The final simulation result shows that the network model fused with the physical information has faster convergence speed and generalization in the training process, and the multi-level network model of digital-analog co-driving has better predictability.

Description

Technical Field

[0001] This invention belongs to the field of vehicle dynamics technology, specifically relating to a vehicle dynamics modeling method based on a multi-order network hybrid model with both numerical and analog driving. Background Technology

[0002] In autonomous driving, vehicle dynamics models should be able to reflect the real-world state of the vehicle during operation, playing a crucial role in vehicle control, trajectory planning, and behavioral decision-making. Modeling vehicle dynamics is a process of abstracting the vehicle's dynamic behavior into mathematical function equations. Depending on the perspective of understanding vehicle dynamics, models can be categorized into first-principles-based physical models and data-driven network models.

[0003] Most vehicle modeling is based on first-principles physical models. In first-principles models, vehicle dynamics are abstractly expressed within the Newtonian mechanics framework, and the modeling process strictly adheres to physical laws, thus providing sufficient interpretability. A complete vehicle dynamics system is a complex, strongly nonlinear system. Accurate model response implies higher model complexity. As model complexity increases, the vehicle physical model needs to calibrate more vehicle parameters, and the model itself becomes more complex. However, for objects like tires that are difficult to model accurately, model accuracy relies more heavily on experimental parameters from empirical models. This process requires dedicated experimental platforms under specific experimental conditions, making it very difficult and costly to obtain complete vehicle parameters. Therefore, vehicle dynamics modeling based on physical models must simplify the vehicle dynamics model according to application requirements and the limitations of known model parameters. Depending on the degree of simplification, vehicle dynamics modeling can be categorized into single-track models, dual-track models, and multi-body models, which makes it difficult for physical models to accurately reflect the true response of the vehicle dynamics system.

[0004] Deep learning has developed rapidly in recent years. Neural networks have the ability to discover patterns in data. Through offline training with large datasets, network models can fit arbitrary functions and have been widely applied in various fields such as image classification, semantic analysis, and pattern recognition. Data-driven network models rely on the large datasets generated by the modeling object, and the model optimizes network parameters from the data. During vehicle operation, onboard sensors can provide rich vehicle state information, providing a rich dataset for building vehicle dynamics neural network models. Therefore, some researchers have begun to combine network models with vehicle dynamics modeling.

[0005] Pan et al. proposed a neural network model for vehicle longitudinal dynamics, with longitudinal velocity and front wheel torsion as inputs and braking distance as output. Comparison with Carsim simulation results showed that the network model accurately predicted longitudinal velocity and travel distance, and could be applied to real-time vehicle simulation and control. Mauro et al. optimized the network model using a distributed network structure based on the different sources of longitudinal force components, proposing a physically inspired pre-connected network modeling method. Simulation results showed that the pre-connected network model had better generalization ability and improved performance. With further exploration of vehicle modeling, Simon et al. used a multilayer perceptron to establish a vehicle longitudinal dynamics model and analyzed in detail the impact of initial weights and network size on the model's generalization ability. Their research found that initial weights affect the final training result, and increasing the network size helps improve convergence. Leonhard et al. used a recurrent network model to establish a vehicle dynamics model with longitudinal and lateral coupling. Experimental data was collected under different road conditions through real-vehicle experiments to train the network. Simulation results showed that the network model outperformed the single-track model under highly dynamic vehicle conditions. However, when there is a significant difference between the test set conditions and the network model, the predictive ability of the network model decreases.

[0006] Vehicle dynamics models built using neural networks can also be applied to vehicle control. Mohammad et al. constructed a vehicle handling model using a fully connected neural network and designed a model predictor based on the neural network model. Simulation results showed that the neural network model can fully capture the nonlinear characteristics of the vehicle dynamics system, and the model predictive controller designed based on the network model has better control performance. As a data-driven model, neural networks can also represent the inverse model of the system by transforming the network input and output. Xu et al. addressed the coupling problem between the vehicle's active steering and the hydropneumatic suspension control system by constructing the inverse system of the vehicle chassis using a generalized regression neural network model and proposed a decoupling control strategy based on neural networks.

[0007] While data-driven network models offer rapid and accurate system dynamic responses, freeing vehicle dynamics models from dependence on physical parameters, their quality is entirely dependent on data quality, network size, optimizer, and activation function type. The model itself, as a black box, lacks physical interpretability, limiting the application of data modeling. Refined, strong physics models not only require parameter calibration but also involve complex modeling processes, resulting in high nonlinearity, computational load, and difficulties in parameter calibration, leading to high experimental costs. Therefore, they fail to achieve good results in high-fidelity vehicle dynamics modeling applications. Although network models trained on large datasets can produce good predictions, the lack of interpretability in the training process makes it difficult to guarantee the generalization ability of the network model itself. Summary of the Invention

[0008] To address the aforementioned problems, this invention fully leverages the interpretability of the physical model and the fitting ability of the network model, proposing a multi-level residual network hybrid modeling method that integrates physical and network models. This method uses a linearized vehicle lateral dynamics model as the physical baseline and employs a multi-level network progressive compensation approach to enhance the model. The linearized dynamics model serves as the baseline term for the hybrid model while also providing data input to the network model. A continuous residual block approach is used to fuse the physical and network models.

[0009] This invention utilizes the physical model of a special vehicle as input for data modeling, reducing the network model's requirement for input data. When refined physical modeling of vehicle dynamics is not feasible, the network model can compensate for errors and improve the accuracy of the hybrid model by using state data from the vehicle's driving process, while simplifying the physical model. Because the network is integrated into the multi-order network model using residual blocks, the multi-order network hybrid modeling based on simultaneous mathematical and model-based approaches can further improve model fidelity by expanding the residual blocks, thus solving the problem of refined vehicle dynamics modeling.

[0010] The technical solution to achieve the purpose of this invention is as follows:

[0011] A method for modeling the dynamics of special vehicles based on a multi-order network hybrid model with both numerical and analog driving is characterized by the following steps:

[0012] Step 1: Construct a lateral dynamics model of a five-axle vehicle using a single-track model as the physics term for hybrid modeling;

[0013] Step 2: Establish a model of tire lateral force based on the magic tire model, and obtain the tire slip angle and the steering angle of each wheel during vehicle movement;

[0014] Step 3: Linearize the tire lateral force model to obtain a lateral dynamics model of a five-axle vehicle based on the linearized tire model;

[0015] Step 4: Perform Euler forward expansion on the obtained lateral dynamics model of the five-axle vehicle based on the linearized tire model to obtain the discretized lateral dynamics model, thus obtaining the physical model of the five-axle vehicle.

[0016] Step 5: Perform multi-level network hybrid modeling on the fused physical model to obtain the final five-axle vehicle dynamics model.

[0017] Furthermore, the basic lateral dynamics model of the five-axle vehicle established in step 1 is as follows:

[0018] (1)

[0019] (2)

[0020] in, It refers to the overall vehicle quality; It is the first Lateral force of the tires on the axle; It is the moment of inertia; It is the longitudinal speed of the vehicle; It is the vehicle's yaw rate; It is the longitudinal distance from the axis to the center of mass; It is the vehicle's lateral speed.

[0021] Furthermore, the specific operational steps of step 2 include:

[0022] Step 21: Establish a model of the lateral force of the tire:

[0023] (3)

[0024] Where B, C, D, and E are the stiffness factor, shape factor, peak factor, and curvature factor, respectively; It is the tire slip angle;

[0025] Step 22: Calculate the tire slip angle based on vehicle dynamics:

[0026] (4)

[0027] (5)

[0028] in, It is the tire steering angle.

[0029] Step 23: Assuming the tires maintain pure rolling contact with the ground throughout the journey, and each wheel has only one steering center, the steering angles of each wheel during vehicle movement can be obtained as follows:

[0030] (6)

[0031] (7)

[0032] (8)

[0033] (9)

[0034] (10)

[0035] in, denoted by , where is the steering wheel angle and is the gear ratio.

[0036] Furthermore, the specific operational steps of step 3 include:

[0037] Step 31: Linearize equation (3) to obtain:

[0038] (11)

[0039] in, It is the lateral stiffness of the tire under a specific vertical load;

[0040] Step 32: Adjust the tire slip angle for each axle Linearization is performed to obtain the linearized tire slip angle:

[0041] (12)

[0042] (13)

[0043] Step 33: Substitute equations (3)-(13) into equations (1) and (2) to obtain the lateral dynamics model of the five-axle vehicle based on the linearized tire model:

[0044] (14)

[0045] (15)

[0046] in, This represents the tire lateral stiffness along the i-th axis.

[0047] Furthermore, the specific operational steps of step 4 include:

[0048] Step 41: Perform an Euler forward expansion on equations (14) and (15) to obtain the discretized transverse dynamic model within the time interval T:

[0049] (16)

[0050] in:

[0051] ,

[0052] ,

[0053] ,

[0054] ,

[0055] ;

[0056] Step 42: Based on the Ackermann steering relationship, adjust the steering angle of each axle wheel using the steering wheel angle. The physical model of the vehicle's lateral dynamics is calculated as follows:

[0057] (17)

[0058] in, yes Constantly control the steering wheel angle. and yes The lateral velocity and yaw rate predicted by the dynamic model at any given time. yes The longitudinal speed of the vehicle is collected at all times.

[0059] Furthermore, the specific operational steps of step 5 include:

[0060] Step 51: Establish a black-box error model by using a neural network to identify the systematic errors between the physical model and the real system. Then, fuse the physical model obtained in Step 4 with the black-box error model to obtain the real vehicle dynamics model. :

[0061] (18)

[0062] in, For vehicle dynamics physical model, A black-box error model built using a neural network;

[0063] Step 52: Perform discretization analysis on equation (18) to obtain:

[0064] (19)

[0065] in:

[0066] (20)

[0067] (twenty one)

[0068] In the formula, This represents the state variable updated by the physical model at time t. These are the system state variables that need to be collected when updating the physical model. These are the control variables input into the model. Representing discrete dynamic equations; express Time of the first The output of the level network, where N represents the highest level of the network model;

[0069] Step 53: When i is 1, the first-level network approximates the system based on the physical model, and we can obtain... The output expression of the first-level network at time step:

[0070] (twenty two)

[0071] in, The equations representing the first-order network model, express Network parameters in;

[0072] Step 54: The higher-order network model approximates the previous-order system's approximation results, thus yielding... The output expression of the Nth level network at time n:

[0073] (twenty three);

[0074] Step 55: Rewrite equation (21) according to equations (22) and (23) as follows:

[0075] (twenty four)

[0076] in, for The equations of the 1-order network model, for Network parameters in;

[0077] Step 56: Obtain the mathematical expression for hybrid modeling based on equations (18), (20), and (24):

[0078] (25);

[0079] Step 57: Using a residual network, the output of the physical model is fused with the fully connected network in the form of residual blocks within the network to obtain the PGRN1st model that conforms to expression (25), and its network output expression is:

[0080] (29);

[0081] in, yes Constantly control the steering wheel angle. yes The longitudinal speed of the vehicle is collected at all times. It is a network model. These are network parameters;

[0082] Step 58: Based on the PGRN1st model, input the output of the PGRN1st model and the acquired signal into the next-level network model, and add the output of the PGRN1st model to the next-level network model as a residual, to obtain the output expression of the 2nd-PGRN network model:

[0083] (30);

[0084] Step 59: Based on the 2nd-PGRN network model, construct the PGRN3rd network model, whose output expression is:

[0085] (31).

[0086] Compared with the prior art, the present invention has the following advantages:

[0087] This invention addresses the shortcomings of physical and network models by proposing a new modeling paradigm that integrates physical and network models. It constructs a multi-level network hybrid model based on a priori vehicle dynamics model and unifies the physical model and multi-layer network structure into a single network model through a multi-level residual network, thus achieving the fusion of network and physical models.

[0088] This invention establishes a hybrid model containing networks of different levels and compares it with the commercial software Trucksim. The simulation results show that the hybrid modeling established in this invention improves the predictive ability of the model based on the original physical model. Based on the physical model, the hybrid model converges faster during training, and the multi-level network model with both numerical and model-driven simulation has better predictive ability. Attached Figure Description

[0089] Figure 1 A monorail model for vehicles;

[0090] Figure 2For Bicycle Model;

[0091] Figure 3 for Physical Model Sensors Neural Networks;

[0092] Figure 4 It is a residual network structure;

[0093] Figure 5 For PGRN1st;

[0094] Figure 6 It is PGRN2nd;

[0095] Figure 7 It is PGRN3rd;

[0096] Figure 8 a- Figure 8 b represents the trend of the network loss function; where Figure 8 'a' is a graph showing the convergence analysis of the loss function. Figure 8 b is a graph showing the convergence rate analysis of the loss function;

[0097] Figure 9 This is a path planning graph for the test set;

[0098] Figure 10 a- Figure 10 f represents the result of the lateral velocity comparison analysis; where Figure 10 Figure a shows a comparison and analysis of lateral velocities. Figure 10 b represents the prediction result of PGRN1st. Figure 10 c represents the prediction result of PGRN2nd. Figure 10 d represents the PGRN3rd prediction result. Figure 10 e represents the PMSNN prediction result. Figure 10 f is the lateral velocity error analysis diagram;

[0099] Figure 11 a- Figure 11 f represents the comparison result of yaw rate, where Figure 11 a is a comparative analysis chart of yaw angular velocities. Figure 11 b represents the prediction result of PGRN1st. Figure 11 c represents the prediction result of PGRN2nd. Figure 11 d represents the PGRN3rd prediction result. Figure 11 e represents the PMSNN prediction result. Figure 11 f is the yaw rate error analysis diagram. Detailed Implementation

[0100] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0101] I. Lateral Dynamics Physical Model

[0102] The monorail model is a commonly used simplified vehicle dynamics model. During the modeling process, it does not require expensive experimental equipment to refine physical parameters. Therefore, the monorail model is used to establish the vehicle's lateral dynamics model as a physics component in the hybrid modeling. The vehicle's monorail model is as follows: Figure 1 As shown, after performing force analysis on the vehicle, the lateral dynamics model of the vehicle is established as shown in equations (1) and (2).

[0103] (1)

[0104] (2)

[0105] in, It refers to the overall vehicle quality; It is the first Lateral force of the tires on the axle; It is the moment of inertia; It is the longitudinal speed of the vehicle; It is the vehicle's yaw rate; It is the longitudinal distance from the axis to the center of mass; It is the vehicle's lateral speed;

[0106] Tires are the only part of a vehicle that comes into contact with the ground, therefore, tire models directly affect the accuracy of vehicle models. Tire models can be categorized into physical models, empirical models, and semi-empirical models. The magic tire model is one of the most widely used semi-empirical tire models, and the model of the tire's lateral force is shown in Equation 3:

[0107] (3)

[0108] Among them, B, C, D, and E are empirical parameters, namely stiffness factor, shape factor, peak factor, and curvature factor, respectively. It is the slip angle. According to vehicle dynamics, the tire slip angle can be calculated using the following formula:

[0109] (4)

[0110] (5)

[0111] in, It is the tire steering angle. When calculating the steering angle of each tire, it is generally assumed that the steering angle of each tire conforms to the Ackermann steering relationship when the vehicle is turning.

[0112] Assuming the tires maintain pure rolling contact with the ground throughout the journey, each wheel has only one center of rotation. The modeled vehicle has the third axle mechanically locked, with all three axle wheels having a constant steering angle of 0. The remaining tires can steer freely. Therefore, the steering angles of each wheel during vehicle movement are:

[0113] (6)

[0114] (7)

[0115] (8)

[0116] (9)

[0117] (10)

[0118] in, The steering wheel angle is represented by k, which represents the gear ratio.

[0119] However, because the magic tire model depends on multiple experimental parameters, and the complex nonlinear model itself is relatively complicated, linearization of the tire model is necessary in practical applications.

[0120] (11)

[0121] When the sideslip angle is small, the tire model has an approximately linear relationship with the sideslip angle. In the formula... This refers to the tire lateral stiffness under a specific vertical load. The wheel slip angles of each axle in equations (4) and (5) are... Linearized to:

[0122] (12)

[0123] (13)

[0124] Substituting equations (3) to (13) into equations (1) and (2), the lateral dynamics model based on the linearized tire model is shown in equations (14) and (15):

[0125] (14)

[0126] (15)

[0127] in, This represents the tire lateral stiffness along the i-th axis.

[0128] Combining equations (14) and (15) and performing an Euler forward expansion, we obtain a discretized transverse dynamic model:

[0129] (16)

[0130] In the formula ,

[0131] ,

[0132] ,

[0133] ,

[0134]

[0135] Based on the Ackermann steering relationship, the wheel steering angle of each axle can be expressed as the steering wheel angle. The calculation, therefore, can be viewed as follows for the physical model:

[0136] (17)

[0137] In the formula yes Constantly control the steering wheel angle. and yes The lateral velocity and yaw rate predicted by the dynamic model at any given time. yes The longitudinal speed of the vehicle is collected at all times.

[0138] II. Hybrid Modeling of Multi-Level Networks Integrating Physical Models

[0139] The linearized vehicle lateral dynamics model is based on many fundamental assumptions and involves significant simplification of the actual vehicle system, which reduces the model's accuracy and introduces systematic errors between the physical model and the real system. . The functional form of the vehicle system is difficult to determine under first-principles modeling conditions. Therefore, the physical model based on first-principles models, as a white-box model of the vehicle system, has a black-box error model that differs from the real system. Neural networks are better able to model black-box models. Therefore, the vehicle dynamics model is considered to consist of two parts: a physical model and a neural network model, as shown in Equation (18). The physical model is used to represent the model that can be interpreted for vehicle dynamics in the first principles, and the network model is used to compensate for the error between the physical model and the actual system response.

[0140] (18)

[0141] In the formula, A model representing the true dynamics of a vehicle. Representing the physical model of vehicle dynamics This represents a system error model built using a neural network;

[0142] Equation (18) is a continuous expression of the real vehicle dynamics system. After discretizing it, we can obtain Equation (19):

[0143] (19)

[0144] The discretization of continuous physics models often employs Euler forward expansion, therefore The generalized expression for can be shown in equation (20):

[0145] (20)

[0146] in, This represents the state variable updated by the physical model at time t. These are the system state variables that need to be collected when updating the physical model. These are the control variables input into the model. Representing discrete dynamic equations;

[0147] Network Model Physical model The compensation process is similar to Taylor expansion, which approximates the original function by summing the multi-level expansions of the original function. When modeling the network model, a progressive approximation modeling method based on the physical model is proposed. Its mathematical model is shown in Equation (21). The network model consists of a multi-level network model.

[0148] (twenty one)

[0149] in, express Time of the first The output of the level network, where N represents the highest level of the network model;

[0150] when When the value is 1, the first-level network approximates the system based on the physical model, and its functional form is shown in equation (22):

[0151] (twenty two)

[0152] In the formula, The equations representing the first-order network model, express Network parameters in;

[0153] The higher-order network model approximates the previous-order system based on the approximation results, as shown in equation (23):

[0154] (twenty three)

[0155] The entire network model is a summation of the multi-order network model, therefore the network model as the error term is shown in equation (24):

[0156] (twenty four)

[0157] in, express The equations of the 1-order network model, express Network parameters in;

[0158] Combining equations (18), (20), and (24), we obtain the general dynamic model expression for hybrid modeling, as shown in equation (25):

[0159] (25).

[0160] III. Constructing a general dynamic model based on multi-order residual networks using hybrid modeling

[0161] (1) Data fusion based on Physical Model Sensors Neural Networks

[0162] The physical model shown in equation (17) is a recursive update model, and the structure Figure 2 As shown, by initializing the model prediction variables, and inputting control signals and necessary system variables into the model, the model can continuously update the prediction variables. According to Equation (17), in the lateral dynamics model, the steering wheel angle and longitudinal velocity are the control signals and system state variables input to the model, while the lateral velocity and yaw rate are the predictable state variables of the model. In the data preprocessing stage, the physical model can continuously update the vehicle's lateral velocity and yaw rate based on the collected steering wheel angle and longitudinal velocity information. When training the network, the longitudinal velocity and steering wheel angle obtained from the test are used together as the network input data, with the structure as follows: Figure 3 As shown in the figure. This model, which uses a physical model as a pseudo-sensor to input data into the network, is called Physical Model Sensors Neural Networks (PMSNN).

[0163] PMSNN uses the output data of the physical model as the network input information, transforming the physical model into data for learning. At this time, the output of the network model is shown in equation (26), and the network model contains the physical model.

[0164] (26)

[0165] In the formula express The output of PMSNN at time 10:00 Representing the network model, and This represents the state variable predicted by the physical model at time k+1. These are network parameters. Therefore, equation (26) can also be expressed in a generalized way as:

[0166] (27)

[0167] In the formula, , , .

[0168] (2) Multi-order model fusion based on residual network

[0169] The residual network structure provides a paradigm that can be learned from for model fusion. A typical residual network architecture is as follows: Figure 4 As shown, the network output is:

[0170] (28)

[0171] To achieve the fusion of multi-level networks, residual blocks are introduced on top of PMSNN, with the following structure: Figure 4 As shown, the output of the physical model is fused with the fully connected network in the form of residual blocks within the network, realizing the fusion of the physical model and the network model. The network output is shown in Equation (29). When the network is being trained, since the data of the physical model is output to the network output in the form of residuals, the physical model and the fully connected module are added within the network. Therefore, during backpropagation training, the network module can continuously update its own parameters based on the discrete single-track model of the vehicle to capture the error between the physical model and the real system response. The network output is shown in Equation (29), and its mathematical expression is consistent with the first-level network hybrid model of the fused physical model proposed in this paper. This network model is called First-order Physics Guided Residual Networks (PGRN1st):

[0172] (29)

[0173] Further extending Fist-PGRN, a Second-order Physics Guided ResidualNetworks (2nd-PGRN) network model is constructed, such as... Figure 5As shown. Based on PGRN1st, the output of PGRN1st and the acquired signal are input into the next level network module. Similarly, the output of PGRN1st is added to the next level network model in the form of residuals. At this time, the output of the network is as shown in equation (30).

[0174] (30)

[0175] Similarly, using the same nesting method, Third-order Physics Guided Residual Networks (PGRN3rd) are constructed, and the network model structure is as follows: Figure 6 As shown, the model output is as follows:

[0176] (31)

[0177] By using hybrid modeling of multi-level networks, the system is continuously approximated to the real system through progressive compensation. However, neural networks themselves are a versatile fitting tool with powerful learning capabilities. Therefore, it is not necessary to expand the hybrid model of multi-level networks to more levels. Furthermore, an overly deep network architecture can even lead to gradient degradation and gradient vanishing problems. The hybrid model of this invention is only built up to three levels.

[0178] Example

[0179] 1. Dataset

[0180] The training set is used to train the network model offline. The generalization ability and accuracy of the network model are closely related to the dataset. When creating the dataset, it should include as many vehicle driving conditions as possible to comprehensively reflect the vehicle's state response under different driving conditions.

[0181] The training vehicles maintained a constant longitudinal speed of 30 km / h and 40 km / h for operational tests. Four commonly used test routes were employed: double lane change, figure-eight, circle, and straight line. The operational parameters are shown in Table 1.

[0182] Data on vehicle longitudinal velocity, steering wheel angle, yaw rate, and vehicle lateral velocity were acquired through joint simulation using Simulink and Trucksim, with a sampling frequency set to 100Hz. The physical model employed a linear two-degree-of-freedom lateral dynamics model derived from Equation 15 to provide the vehicle's lateral velocity and yaw rate. The simulation-acquired steering wheel angle, vehicle lateral velocity, and the lateral and yaw rates output from the linearized dynamics model were used as input variables to the network. The simulation-acquired yaw rate and longitudinal velocity served as labels for training the network model.

[0183] Table 1 Training Conditions

[0184]

[0185] 2. Loss Function Setting

[0186] The loss function is a standard for measuring the generalization ability of a network model. To avoid overfitting during training, which reduces the model's generalization ability, adding a network weight regularization function to the loss function is a common overfitting technique. This invention uses mean squared error as the loss function to measure the difference between the network output and the actual label, and adds an L2 regularization function to limit the weights to a small value range, thus improving the network's generalization ability. To facilitate adjusting the impact of the regularization function on the network weights, hyperparameters are introduced. Adjusting the impact of the L2 regularization term on the network. Simultaneously, to avoid the mean squared error being insensitive to small numerical labels and causing gradient vanishing, a penalty coefficient is set. Adjusting the mean square error scale, the loss function of the entire network is shown in equation (32):

[0187] (32)

[0188] Where loss represents the network loss function, and m is the number of data points input into the network in a single iteration. It is the output of the network model. These are the label values ​​output by the network. It is the penalty coefficient of the L2 regularization term. represents the size of the i-th weight, and N represents the total number of weights in the network.

[0189] 3. Dynamic optimization strategy for network parameters

[0190] During the backpropagation process of the network, the loss function is calculated with respect to each parameter using the chain rule. The network parameters are continuously adjusted along the gradient direction to minimize the loss function. The parameter update method is shown in equation (33):

[0191] (33)

[0192] In the formula Represents network parameters, Indicates the magnitude of the parameter update;

[0193] The method of parameter update affects the convergence speed during network training, and different types of optimizers have different strategies for updating network gradients. In this case, RMSprop is used as the network training optimizer. RMSprop is an adaptive learning rate optimizer that uses accumulated gradients to calculate the network parameter update size and introduces a hyperparameter decay rate when updating parameters. This approach weakens the influence of historical cumulative gradients, allowing the optimizer to shrink by using global cumulative gradients when updating parameters. This prevents parameter updates from becoming too small as the number of training iterations increases, thus accelerating network convergence. The update strategy is shown in Table 2.

[0194] Table 2 RMSprop optimizer update strategy

[0195]

[0196] During network training, continuously reducing the learning rate as the number of training iterations increases can lead to better training results. Therefore, based on RMSprop, a dynamic adjustment strategy is adopted for the global learning rate. Every 20 training iterations, the global learning rate is reduced to one-tenth of its original value. The pseudocode for the dynamic update of the global learning rate is shown in Table 3.

[0197] Table 3 Global Learning Rate Dynamic Update Strategy

[0198]

[0199] The network models compared are PMSNN, PFRN1st, PGRN2nd, and PGRN3rd. During network training, all models used the same hyperparameter structure, and the parameter settings are shown in Table 4: Table 4 Network Model Parameter Settings

[0200]

[0201] The trends of the loss functions of the four models are as follows: Figure 8 As shown, Figure 8 Figure a shows that after 100 training cycles, all four models converged to a stable state. Figure 8 b is the loss function log plot used to analyze the network's convergence speed. Figure 8 In b, the PGRN series networks converge faster than the PMSNN network model, and the loss function of the PGRN series networks converges to a lower range.

[0202] 4. Model generalization analysis

[0203] The test set should differ from the training set conditions as much as possible to test the generalization ability of the hybrid vehicle model under different conditions and to verify the dynamic characteristics learned by the network model. Therefore, the longitudinal speed of the vehicle in the test set is set to 35 km / h, and the driving path is randomly set, as shown in the example below. Figure 9 As shown.

[0204] The comparison results of the four network models, physical models, and actual test set values ​​are as follows: Figure 10As shown in Figure a, the four network models can predict vehicle state information more accurately than the physical model. The prediction results of the lateral velocity of the four network models are as follows: Figure 10 As shown in b, 10d, and 10f, PGRN1st, PGRN3nd, and PMSNN models exhibit significant prediction errors at vehicle turning points. In error analysis, this paper uses the mean absolute value of error and the maximum absolute value of error as standards to measure model accuracy. The comparison results are shown below. Figure 10 As shown in f, the maximum absolute error and the maximum mean absolute error of the PMSNN model are 0.03804 m / s and 0.01695 m / s, respectively. The PGRN2nd network model has the best prediction performance, as shown in f. Figure 10 As shown in c, the maximum absolute error and the maximum mean absolute error are 0.001721 m / s and 0.00281 m / s, respectively, which are 95.41% and 83.42% lower than the fully connected network model error.

[0205] For the PGRN model, which uses a network model to progressively compensate for the physical model, the generalization ability and predictive ability of the PGRN model decrease with the increase of network levels. For lateral velocity, the maximum absolute error and mean absolute error of PGRN1st are 0.03269 m / s and 0.01205 m / s, respectively. When the network level increases by 2, the maximum error of PGRN2nd model decreases by 61.12% and the mean error decreases by 76.68% compared to PGRN1st. Then, with the increase of network levels, the maximum error of PGRN3rd model increases by 81.20% and the mean error increases by 89.68% compared to PGRN2nd model. This indicates that as the network level increases and the network becomes deeper, deeper networks are more prone to model degradation during training, leading to a decrease in the overall predictive ability of the model.

[0206] The predicted yaw rate is as follows: Figure 11 As shown in Figure a, compared to the single-track model of the vehicle, the network model that incorporates physical information has better prediction performance. The prediction results of each group of models are as follows: Figure 11 b、 Figure 11 c. Figure 11 d Figure 11 As shown in e, the PGRN network model is consistent with the actual values, while PMSNN exhibits a significant prediction bias when the vehicle is turning. The error comparison results of the four models are shown below. Figure 11As shown in f, the PMSNN model has the largest error, with a maximum absolute error of 0.01285 deg / s and a mean absolute error of 0.00341 deg / s. Compared to PMSNN, the errors of the two prediction results from the PGRN1st network decreased by 26.25% and 45.45%, respectively. As the network level increases, the model error further decreases. Compared to PGRN1st, PGRN2nd saw a 26.50% decrease in maximum absolute error and a 23.12% decrease in mean absolute error. Compared to PGRN2nd, PGRN3rd saw a 1.15% decrease in maximum error and a 12.59% decrease in mean error. Although the percentage decrease in mean error is significant, the change in mean error for both models is only 0.00018 deg / s, within the ten-thousandths range. Therefore, for predicting vehicle yaw rate, PGRN2nd and PGRN3rd are at the same level.

[0207] 5. Results Analysis

[0208] Comparing four network models—PMSNN, PGRN1st, PGRN2nd, and PGRN3rd—the test results show that:

[0209] 1. The linearized vehicle lateral dynamics model provides prior information for network training, accelerating network convergence.

[0210] 2. The multi-level network hybrid model significantly improves the prediction accuracy of the model based on the physical model.

[0211] 3. For vehicle lateral dynamics modeling, the PGRN2nd proposed in this invention exhibits the best prediction performance, with mean absolute errors and maximum absolute errors of only 0.00281 m / s and 0.01271 m / s for lateral velocity and yaw rate, respectively, and 0.00143 deg / s and 0.00696 deg / s for yaw rate. Through the construction of a multi-level hybrid network model, the network modules can progressively compensate based on the physical model, achieving an accurate response of the hybrid model to the vehicle's lateral dynamics system.

[0212] Contents not described in detail in this specification are existing technologies known to those skilled in the art. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modeling the dynamics of special vehicles based on a multi-order network hybrid model with both numerical and analog driving, characterized in that, Includes the following steps: Step 1: Construct a lateral dynamics model of a five-axle vehicle using a single-track model as the physics term for hybrid modeling; Step 2: Establish a model of tire lateral force based on the magic tire model, and obtain the tire slip angle and the steering angle of each wheel during vehicle movement; Step 3: Linearize the tire lateral force model to obtain a lateral dynamics model of a five-axle vehicle based on the linearized tire model; Step 4: Perform Euler forward expansion on the obtained lateral dynamics model of the five-axle vehicle based on the linearized tire model to obtain the discretized lateral dynamics model, thus obtaining the physical model of the five-axle vehicle. Step 5: Perform multi-level network hybrid modeling on the fused physical model to obtain the final five-axle vehicle dynamics model; The specific steps in step 5 include: Step 51: Establish a black-box error model by using a neural network to identify the systematic errors between the physical model and the real system. Then, fuse the physical model obtained in Step 4 with the black-box error model to obtain the real vehicle dynamics model. : （18） in, For vehicle dynamics physical model, A black-box error model built using a neural network; Step 52: Perform discretization analysis on equation (18) to obtain: （19） in: （20） （21） In the formula, This represents the state variable updated by the physical model at time t. These are the system state variables that need to be collected when updating the physical model. These are the control variables input into the model. Representing discrete dynamic equations; express Time of the first The output of the level network, where N represents the highest level of the network model; Step 53: When i is 1, the first-level network approximates the system based on the physical model, and we can obtain... The output expression of the first-level network at time step: （22） in, The equations representing the first-order network model, express Network parameters in; Step 54: The higher-order network model approximates the previous-order system's approximation results, thus yielding... The output expression of the Nth level network at time n: （23）； Step 55: Rewrite equation (21) according to equations (22) and (23) as follows: （24） in, for The equations of the 1-order network model, for Network parameters in; Step 56: Obtain the mathematical expression for hybrid modeling based on equations (18), (20), and (24): （25）； Step 57: Using a residual network, the output of the physical model is fused with the fully connected network in the form of residual blocks within the network to obtain the PGRN1st model that conforms to expression (25). The network output expression is: （29）； in, yes Constantly control the steering wheel angle. yes The longitudinal speed of the vehicle is collected at all times. It is a network model. These are network parameters; Step 58: Based on the PGRN1st model, input the output of the PGRN1st model and the acquired signal into the next-level network model, and add the output of the PGRN1st model to the next-level network model as a residual, to obtain the output expression of the 2nd-PGRN network model: （30）； Step 59: Based on the 2nd-PGRN network model, construct the PGRN3rd network model, whose output expression is: （31）。 2. The special vehicle dynamics modeling method based on a multi-order network hybrid model with simultaneous numerical and analog driving as described in claim 1, characterized in that, The basic lateral dynamics model of the five-axle vehicle established in step 1 is as follows: （1） （2） in, It refers to the overall vehicle quality; It is the first Lateral force of the tires on the axle; It is the moment of inertia; It is the longitudinal speed of the vehicle; It is the vehicle's yaw rate; It is the longitudinal distance from the axis to the center of mass; It is the vehicle's lateral speed.

3. The special vehicle dynamics modeling method based on a multi-order network hybrid model with simultaneous numerical and analog driving as described in claim 2, characterized in that, Step 2 includes the following specific steps: Step 21: Establish a model of the lateral force of the tire: （3） Where B, C, D, and E are the stiffness factor, shape factor, peak factor, and curvature factor, respectively; It is the tire slip angle; Step 22: Calculate the tire slip angle based on vehicle dynamics: （4） （5） in, It is the tire steering angle. Step 23: Assuming the tires maintain pure rolling contact with the ground throughout the journey, and each wheel has only one steering center, the steering angles of each wheel during vehicle movement can be obtained as follows: （6） （7） （8） （9） （10） in, denoted by , where is the steering wheel angle and is the gear ratio.

4. The special vehicle dynamics modeling method based on a multi-order network hybrid model with simultaneous numerical and analog driving as described in claim 3, characterized in that, Step 3 includes the following specific steps: Step 31: Linearize equation (3) to obtain: （11） in, It is the lateral stiffness of the tire under a specific vertical load; Step 32: Adjust the tire slip angle for each axle Linearization is performed to obtain the linearized tire slip angle: （12） （13） Step 33: Substitute equations (3)-(13) into equations (1) and (2) to obtain the lateral dynamics model of the five-axle vehicle based on the linearized tire model: (14) (15) in, This represents the tire lateral stiffness along the i-th axis.

5. The special vehicle dynamics modeling method based on a multi-order network hybrid model with simultaneous numerical and analog driving as described in claim 4, characterized in that, Step 4 includes the following specific steps: Step 41: Perform an Euler forward expansion on equations (14) and (15) to obtain the discretized transverse dynamic model within the time interval T: （16） in: ， ， ， ， ； Step 42: Based on the Ackermann steering relationship, adjust the steering angle of each axle wheel using the steering wheel angle. The physical model of the vehicle's lateral dynamics is calculated as follows: （17） in, yes Constantly control the steering wheel angle. and yes The lateral velocity and yaw rate predicted by the dynamic model at any given time. yes The longitudinal speed of the vehicle is collected at all times.

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