Keywords

1 Introduction

Accurate suspension parameter identification of mining trucks is essential to its dynamic modeling and subsequent control strategy [1]. Existing models can be roughly divided into physics and data-driven models for the vertical dynamic modeling of vehicles and their coupling effects.

Existing models can be roughly divided into physics and data-driven models for the vertical dynamic modeling of vehicles and their coupling effects. Physical models are typically expressed using Newton's law or Lagrange equations to describe the vehicle's dynamic characteristics [2]. Dynamics modeling and parameter identification are then conducted using filtering methods or their combination [3]. Although the physical model has significant advantages in generalization, it is necessary to clarify all parameters and may fall short in transient conditions and extreme scenarios [4]. Data-driven models are superior to physical models in many fields and have a more comprehensive range of applications, but they still cannot escape the shortcomings of poor generalization and interpretability [5].

In recent years, physics-informed neural network has received widespread attention. Data-driven models can effectively compensate for parts that are challenging or impossible to model with physical models. Physical models can extend the applicability range of data-driven models, effectively expanding the applicable state space concerning vehicle dynamics [6]. In [7], a simplified vehicle model was integrated with a recurrent neural network to estimate the vehicle's lateral motion behavior, and results demonstrated that the hybrid architecture achieved excellent estimation quality while demonstrating generalization across various tires, surfaces, and driving scenarios. A novel car-following control model combining machine learning and kinematics models for automated vehicles was established in [8], the real vehicle trajectory data sets demonstrated better performance for controlling the longitudinal movements under a hybrid approach.

Considering the aforementioned limitations and challenges, this paper primarily focuses on establishing a longitudinal-vertical dynamic model for mining trucks during transportation. A hybrid-driven framework that combines data-driven and physical models to identify the suspension parameters of mining trucks is employed. At first, the nonlinear mapping relationship of the inertial measurement unit to the measured point is proposed for determining the vertical motion. Secondly, the mining truck longitudinal-vertical dynamics model is established considering the differences in parameters between the front and rear suspensions. Subsequently, the instrumental variable method derives baseline values for suspension parameter identification. The hybrid modeling architecture combining physics and learning methods is given for precise identification and prediction of the mining truck’s suspension parameters and dynamic characteristics.

2 PINN Architecture

The proposed method integrates a deep learning network into a physics model of the mining truck to establish an accurate mining truck longitudinal-vertical dynamic model and identify precise suspension parameters. Figure 1 shows the schematic diagram of the proposed algorithm. Firstly, the sequence states of the mining truck maneuver are collected by monitor sensors. The critical suspension parameters (such as stiffness and damping coefficients) are roughly determined by a linear dynamic model considering the longitudinal-vertical coupling effect. Meanwhile, the sequence states are the input of the deep learning network, which can calculate the parameter correlation factors. The modified parameters are fed into the mining truck dynamic model to estimate the state of the next time step. The state loss Lp between predicted and target states can be used as the loss error term of the neural network and update the neural network weights.

Fig. 1.
figure 1

Schematic diagram of the proposed PINN algorithm.

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The overall hybrid modeling architecture is shown in Fig. 2. According to the state of two consecutive moments as the input of the network and the physical model, the correction coefficients of the suspension parameters are calculated through the network and then input into the physical model to estimate the state of the next moment. The selected loss function is utilized to calculate the MSE after dimensional unification and perform backpropagation and weight training on the network. Since the parameters input to the network model in this article are time series signals, a recurrent neural network (RNN) is considered. The Long Short-Term Memory (LSTM) network is selected as the RNN network, with 3 layers and a hidden size of 128. The suspension correction parameters are calculated through a fully connected layer during output. In the network model, in order to avoid problems such as gradient disappearance or gradient explosion during the neural network training process, the Xavier initialization method is used to initialize the RNN network. The normal distribution initialization method is employed for the linear output layer to enhance the training stability and accelerate the convergence speed of the network.

Fig. 2.
figure 2

Hybrid modeling architecture and experimental platform TR100A mining truck.

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The mining truck longitudinal-vertical dynamic modeling and suspension parameter identification have been proposed by combining physics and deep learning methods. In order to verify the validity and accuracy of the proposed theory, the real test of the mining truck is carried out below.

3 Experiments and Results

In order to verify the accuracy and effectiveness of the proposed method, we conducted experiments on a real mining truck. The TR100A mining truck made by TEREX was selected as the experimental platform (Fig. 2). The experiments were conducted on a flat paved road, and the mining truck was in the unloaded state. For simplification, the ground’s excitation is neglected compared to the tire dimension during transportation. The experiments include longitudinal acceleration and deceleration tests, and specific tests are shown in Table 1.

Table 1. Mining Truck Experiment Conditions
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The hybrid model proposed in this article can give the suspension parameters of the mining truck, which is crucial to the structural design and performance prediction of the mining truck. Figure 3 and Fig. 4 show the change regulations of identified front and rear suspension stiffness, respectively.

Fig. 3.
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Change regulations of front and rear suspension stiffness.

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Fig. 4.
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Change regulations of front and rear suspension damping.

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Working conditions Part 1 and Part 5 are selected for display to verify the model effect during acceleration and deceleration. Figure 5 show the comparison results of the vertical acceleration of the center of gravity in the testing set of the two working conditions. It can be seen that the hybrid model proposed in this article has more robust applicability and accuracy than the physical model and data-driven model. In the physical model, the calculation of the unsprung position requires solving differential equations during the calculation process. This process will introduce errors and oscillations, leading to violent oscillations in the final state calculation at the next moment. The accuracy of the data-driven model is higher than that of the pure physical model, but it is affected by limited samples and a more significant number of iterations (about 10–15 epochs, depending on the size of samples), which limits its generalization ability. The model-based hybrid-driven model proposed in this article can effectively reflect the real motion state and converge within a limited number of iterations (about 2–3 epochs). It can also be seen from the comparison results that under some severe working conditions and sharp points, the hybrid model still has strong robustness.

Fig. 5.
figure 5

Comparison of the vertical acceleration at CoG (Part 1, 5).

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In order to give qualitative comparison results of the three models, this article uses the MSE of all testing sets as the measurement index. The smaller the value, the higher the accuracy of the model. The MSE comparison results for the vertical acceleration of the center of gravity ac, the sprung velocity of the front suspension vf and the sprung velocity of the rear suspension vr are shown in Table 2.

Table 2. The comparison of MSE in the experiment
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It can be seen that the hybrid model method proposed in this article has good performance in predicting different motion parameters. It is worth mentioning that the hybrid model method in this paper only relies on the sensor signals of the vehicle body and does not require unsprung information. This advantage makes it possible to directly predict the dynamic characteristics of the mining truck without building a complex mining truck sensor measurement system.

4 Conclusion

For precise prediction of mining truck vertical dynamic characteristics and accurate identification of the suspension parameters during the transportation process, a hybrid modeling architecture is proposed by combining physics and learning methods. Experimental results from real mining truck tests demonstrate enhanced accuracy and efficiency of the proposed hybrid model compared to traditional physical and data-driven models in estimating suspension nonlinear parameters and predicting the mining truck vertical dynamic characteristics under various working conditions.