Asphalt pavement construction flatness simulation method based on Kalman filtering technology

Abstract

The invention provides an asphalt pavement construction flatness simulation method based on a Kalman filtering technology, and the method comprises the following steps: building a white noise filtering pavement flatness simulation model through Matlab software, adding Kalman filtering into the model, and carrying out the optimization, thereby obtaining a new simulation model; operating the two models to obtain the vertical vibration acceleration of the quarter vehicle model and the road surface flatness profile; acquiring road surface flatness data on a specific road, acquiring vibration acceleration data above wheels through a driving test, and comparing the vibration acceleration data with the data obtained by the simulation model to verify the reliability of the new model; and substituting the road surface flatness simulation model data optimized by Kalman filtering into an international flatness index operation program to obtain a road surface flatness IRI value to verify the accuracy of the new model. According to the method, the problem that a road surface flatness model simulated by an existing filtering white noise model is greatly different from an actual road surface is solved.

Description

Technical Field

[0001] The invention provides a method for simulating the flatness of asphalt pavement construction based on Kalman filtering technology, belonging to the technical field of road construction. Background Art

[0002] The driving quality of a vehicle is related to the road surface roughness. Poor road surface roughness will lead to a decrease in transportation efficiency and directly affect the driving safety and comfort of the vehicle. The common road surface roughness measurement methods currently include: a dedicated ruler walking profiler, but this method has low measurement efficiency and is not suitable for long-mileage road surface measurement. The on-board laser roughness meter can automatically measure the road surface roughness. This method is expensive and greatly affected by the environment, and is not suitable for large-scale test promotion. The reaction-type road surface roughness measurement method, this method collects the vibration acceleration and other responses of the vehicle by installing an acceleration sensor at a specified position on the vehicle, and processes the response data to obtain the road surface roughness. This method is low-cost and simple to operate.

[0003] The road surface roughness response can be obtained through experimental measurement and model simulation. There are many experimental measurement methods. Some scholars have developed a longitudinal profile (LPA) profiler, which is an instrument used to generate a digital sequence related to the real road profile. The profile measurement method based on visual inspection is limited in use on rainy days. With the development of artificial intelligence methods, some scholars have used neural network models to identify road surface roughness, but neural network methods require a long calculation time due to the complexity of the model. The model-based sliding mode observer method, this method is aimed at complex models, resulting in a long calculation time. At the same time, the final reconstruction result depends largely on the quality of the model. For the simulation of the road surface roughness model, existing research shows that for the simulation of road surface roughness, the harmonic superposition method, the filtered white noise method, and the inverse Fourier transform method are relatively mature methods, among which the filtered white noise method is the most common, but some scholars believe that the road surface roughness model simulated by this method is not realistic and ideal, that is, the vehicle cannot travel according to each time domain state of the road surface roughness model.

[0004] In recent years, some methods combining determinism and randomness have been developed. These methods regard noise as a random process and assume that noise exists not only in the measured value but also in the state variable. Based on this method, some scholars have developed an enhanced Kalman filter, in which the unknown force is included in the state vector and identified together with the state. In order to obtain a cost-effective and easy-to-implement method, the proposed input force identification method is based on acceleration measurement. However, the method based on acceleration measurement is inherently unstable. Therefore, in order to make the road surface roughness response simulated by the filtered white noise model closer to the actual situation, it is necessary to use a filter to optimize the model, thereby obtaining a new road surface roughness simulation model. Summary of the invention

[0005] In order to solve the problem that the road surface roughness model simulated by the existing filtered white noise model is greatly different from the actual road surface, the present invention optimizes the existing model by adding Kalman filtering to obtain a new road surface roughness simulation model.

[0006] The Kalman filter algorithm can estimate discrete data very well with high efficiency and good accuracy. Its basic principle can be summarized into two steps: prediction and update. Prediction step: the state value and error covariance of the current moment are estimated for the state at the previous moment; update step: according to the measured value of the existing state, the value of the predicted state is corrected to obtain a more accurate state estimate. Therefore, the study uses the Kalman filter algorithm to process the road elevation data generated by the filtered white noise model, thereby reducing the noise impact of the road surface flatness model and making the established vehicle-road model closer to the actual situation.

[0007] The technical solution of the present invention is:

[0008] Asphalt pavement construction smoothness simulation method based on Kalman filtering technology. Since the smoothness can be inferred from the dynamic response of the vehicle, the specific principles and steps of the new model are as follows:

[0009] Step 1: Use Matlab software to establish a filtered white noise road surface roughness simulation model, and add Kalman filtering to the model for optimization to obtain a new simulation model. Run the two models to obtain the vertical vibration acceleration of the quarter-car model and the road surface roughness profile.

[0010] Step 2: Collect road surface roughness data on a specific road according to step 1, and obtain vibration acceleration data above the wheel through driving tests, and compare it with the data obtained by the simulation model in step 1 to verify the reliability of the new model.

[0011] Step 3: Substitute the road surface roughness simulation model data optimized by Kalman filtering in step 1 into the international roughness index calculation program to obtain the road surface roughness IRI value to verify the accuracy of the new model.

[0012] The present invention specifically comprises the following steps:

[0013] (1) Establishment of a quarter vehicle model, which only considers the vibration of the vehicle in the vertical direction on the sprung and unsprung directions, and simplifies the vehicle into a dynamic system consisting of springs, mass, and damping;

[0014] The 1 / 4 vehicle model is expressed as | after being derived from the D`Alembert principle:

[0015]

[0016] Where M is the mass matrix C is the damping matrix K is the stiffness matrix Z is the displacement array [z s z t ] T , P is the excitation array According to the above formula, the vertical displacement and vibration acceleration data of the quarter car model suspension are obtained through simulation software;

[0017] (2) Establishing the road surface roughness signal input for the quarter-car model, that is, adding Kalman filtering to the filtered white noise model for optimization. The iterative process of Kalman gain update includes calculating Kalman gain, state update, and error covariance update;

[0018] (3) The model is verified by conducting driving tests at designated test sites. The driving tests require the use of a small vibration acceleration sensor to collect vehicle vibration acceleration. The sensor is connected to a computer via a USB interface to set data transmission and acquisition frequency. During the driving test, the sensor is installed on the console directly above the wheels of the cab. The test site is a closed high-speed loop. The road surface of the test vehicle is in good condition. At the same time, the test road surface smoothness data is collected.

[0019] (4) The generated road roughness data is used to calculate the International Roughness Index (IRI) value. The calculation process uses a quarter-car model. The IRI value is equal to the sum of the absolute values ​​of the vertical displacements of the vehicle body and wheels when the quarter-car model is simulated driving at a speed of 80 km / h divided by the driving distance. The calculation is shown in the formula:

[0020]

[0021] Where L is the distance traveled by the car model; X1 is the vertical displacement of the car body; X2 is the vertical displacement of the wheel; substituting the data in the new model into the above formula can calculate the International Roughness Index IRI value. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a schematic diagram of a 1 / 4 car model of the present invention;

[0023] Figure 2 This is a 60km / h road surface flatness diagram of the embodiment;

[0024] Figure 3 This is a 100km / h road surface flatness diagram of the embodiment;

[0025] Figure 4 This is the 120km / h road surface flatness diagram of the embodiment;

[0026] Figure 5This is the 130km / h road surface flatness diagram of the embodiment;

[0027] Figure 6 This is a 60km / h vibration acceleration diagram of the embodiment;

[0028] Figure 7 100km / h vibration acceleration diagram of the embodiment;

[0029] Figure 8 This is a 120km / h vibration acceleration diagram of the embodiment;

[0030] Fig. 9 This is a 130km / h vibration acceleration diagram of the embodiment;

[0031] Fig.10 A diagram of a vibration acceleration sensor according to an embodiment;

[0032] Fig.11 A diagram showing the installation position of the sensor in the embodiment;

[0033] Fig.12 A diagram of a high-speed loop test site of an embodiment;

[0034] Fig.13 The figure is a comparative analysis diagram of 13 IRI values ​​obtained at the same speed in the embodiment and the measured values. DETAILED DESCRIPTION

[0035] The asphalt pavement construction smoothness simulation method based on Kalman filtering technology provided by the present invention comprises the following steps:

[0036] (1) The establishment of a quarter vehicle model, which only considers the vertical vibration of the vehicle's sprung (body) and unsprung (wheels), so according to this theory, the vehicle can be simplified into a dynamic system consisting of springs, mass, and damping. Figure 1 That is a 1 / 4 car model:

[0037] The 1 / 4 vehicle model can be expressed as shown in formula (1) after being derived from the D'Alembert principle:

[0038]

[0039] Arrange formula (2):

[0040]

[0041] Where M is the mass matrix C is the damping matrix K is the stiffness matrix Z is the displacement array [z s z t ] T, P is the excitation array According to the above formula, the vertical displacement, vibration acceleration and other data of the quarter car model suspension can be obtained through simulation software.

[0042] (2) The road surface roughness signal input is established for the quarter-car model, that is, Kalman filtering is added to optimize the filtered white noise model. The iterative process of Kalman gain update mainly includes calculating Kalman gain, state update and error covariance update. The calculation of Kalman gain involves the measurement matrix, the predicted value of the error covariance and the measurement noise covariance matrix. Its mathematical principle is as follows:

[0043] The principle of Kalman Filter state update equation derived from the Bayesian method is expressed as shown in formula (3):

[0044]

[0045] Where is the a priori state estimate, that is, the optimal estimate of the current system state after one correction; is the a priori estimate of the system state; is the measured sample value of the current state; is the a priori measurement value of the current state; represents the impact of random errors between the actual system and the estimated system; weighs the relationship between the prior model and the measured data on the posterior distribution, which is called the Kalman gain.

[0046] In order to make the algorithm correction effect optimal and the posterior state closer to the true value, the error vector needs to be defined as follows:

[0047]

[0048] Similarly, the posterior error covariance matrix is ​​defined as:

[0049]

[0050] Similarly, the prior error covariance matrix can also be defined. According to the minimum variance estimation principle, assuming the loss function is, the Kalman gain can be expressed as formula (5):

[0051] K k =argmin[tr(P k )] (5)

[0052] After recursively iterating equation (5), we can get the covariance update equation by inserting it into the posterior error covariance matrix expression:

[0053]

[0054] According to the above principle, the road surface roughness data generated by the filtered white noise method is optimized as the state quantity. In order to reflect the optimization effect of Kalman filtering, the mean filtering optimization group is added for comparison.

[0055] (3) The model of the present invention is verified by carrying out driving tests at a designated test site. The driving test requires the use of a small vibration acceleration sensor to collect the vehicle vibration acceleration. The sensor can be connected to a computer via a USB interface to set data transmission and acquisition frequency. Since the vibration data of the quarter-car model is closest to the vibration data collected directly above the vehicle suspension system, the sensor needs to be installed on the console directly above the wheels of the cab during the driving test. The test site is a closed high-speed loop, and the test vehicle is driving on a road surface with good smoothness. At the same time, the test road surface smoothness data is collected.

[0056] (4) The road surface roughness data generated by the present invention is used to calculate the International Roughness Index (IRI) value. The calculation process uses a quarter car model. The IRI value is equal to the sum of the absolute values ​​of the vertical displacements of the vehicle body and wheels when the quarter car model simulates driving at a speed of 80 km / h divided by the driving distance. The calculation is shown in formula (6):

[0057]

[0058] Where L is the distance traveled by the car model; X1 is the vertical displacement of the car body; X2 is the vertical displacement of the wheel. Substituting the data in the new model into the above formula, the International Roughness Index (IRI) value can be calculated.

[0059] The specific process of this embodiment is as follows:

[0060] Matlab software was used to establish a road surface roughness model optimized by filtering white noise method and Kalman filtering, and the B-level road surface roughness simulation was obtained at different vehicle speeds. In order to reflect the optimization effect, a road surface roughness simulation model optimized by mean filtering was also established. The simulation results are shown in Figures 2 to 5 .

[0061] from Figures 2 to 5 It can be seen that the road surface roughness generated by the white noise method has more peaks, and the road surface roughness simulated by the three models has the same change trend. As the vehicle speed increases, the "difference" in the simulation of road surface roughness by the three models becomes more obvious, and the optimization effect becomes better. This is because the higher the vehicle speed, the larger the peak of the road surface roughness elevation generated based on white noise, and the addition of filtering optimizes the peak value. After optimization by Kalman filtering and mean filtering, the peak effect of the road surface excitation signal is indeed reduced. It can be seen from the figure that Kalman wave has a better optimization effect on white noise than mean filtering, and the generated road surface roughness signal is more "smooth" and closer to the real road surface.

[0062] The obtained simulation results were verified, and the root mean square values ​​of the road surface elevations of the two filtering optimization simulation models were obtained and compared with the 8-level road roughness classification standard. The comparison results are shown in Table 1.

[0063] Table 1 Comparison of the RMS values ​​of road surface roughness elevation generated by the two optimization models

[0064]

[0065]

[0066] From Table 1, we can see that the root mean square value of the road surface roughness elevation after Kalman filter optimization is almost consistent with the standard value, indicating that the road surface excitation generated by the model is reasonable. Mean filter also has an optimization effect on road surface roughness, but the effect is not as good as Kalman filter, indicating that Kalman filter is better at predicting the "peak" of road surface roughness, and the minimum root mean square value of the Kalman filter optimization model meets the requirements. Figures 2 to 5 The generation law of the road surface roughness elevation is that the Kalman filter optimizes the road surface roughness generated by the white noise model, making the generated road surface roughness elevation closer to the actual road surface.

[0067] In Matlab, the three established road roughness models are used as road excitation signals of the quarter-car model for simulation. The simulation results are compared with the data collected from the driving test. The differences between the three road models and the real road surface are compared through driving data analysis.

[0068] According to formula (2), a quarter car model is established in the Matlab / Simulink environment. The model parameters are set as follows: suspension stiffness is 17000N / m, suspension damping coefficient is 1500N·s / m, sprung and unsprung masses are 345kg and 40.5kg respectively, and wheel equivalent stiffness is 192000N / m. The three models are used as road surface roughness input to calculate the vibration acceleration of the quarter car model. The simulation results are shown in Figure 2. Figures 6 to 9 .

[0069] From Figures 6 to 9The simulation results show that as the vehicle speed increases, the vibration acceleration of the vehicle suspension of the three models also increases. The vibration acceleration of the suspension will be transmitted to the seat. Excessive vibration acceleration will affect the riding comfort of the passengers, so controlling the vehicle speed can control the driving comfort. At the same speed, the vibration acceleration value of the Kalman filter model is the smallest, and the vibration acceleration of the white noise model is the largest. This is because the influence of the random road elevation model on the suspension vibration acceleration is caused by the change in the elevation of the road surface flatness. After the optimization of the Kalman and mean filters, the "peak" of the random road surface flatness elevation is also "optimized". In the actual driving process, the wheels do not drive according to the road surface flatness generated by white noise, but in the simulation, the excitation signal of the quarter-car model comes from white noise, resulting in a large difference between the vibration acceleration of the suspension and the vibration acceleration of the suspension when the actual vehicle is driving, and the "optimization" of the Kalman and mean filters can make the vibration acceleration value obtained by simulation closer to the true value.

[0070] Driving test:

[0071] In order to verify the model of the present invention, it is necessary to conduct a driving data collection test.

[0072] This study uses a small vibration acceleration sensor to collect vehicle vibration acceleration, such as Fig.10 As shown in the figure, the sensor can be connected to the computer through the USB interface to set the data transmission and acquisition frequency. Since the vibration data of the quarter car model is closest to the vibration data collected directly above the vehicle suspension system, the research test vehicle is: Haval H6 car, and the console position directly above the front tire of the car is as follows Fig.11 Install a small vibration acceleration sensor. The test site is: a closed high-speed loop test site such as Fig.12 , a 1300m straight section was selected for driving vibration acceleration collection test, and a straight section of 100m was set as an evaluation unit. The road surface comprehensive information collection system was used to carry out flatness detection, and 13 road surface flatness data were obtained (see Table 2).

[0073] Table 2 1300m road surface roughness data of the ring road

[0074]

[0075] Driving test method:

[0076] (1) First, determine the starting and ending locations. The driver is required to accurately identify the starting and ending locations and record the passing time.

[0077] (2) To ensure that the vehicle can travel at a constant speed set in advance on a straight section, there should be an acceleration section before entering the straight section.

[0078] (3) Set the acquisition frequency of the vibration acceleration sensor to 20 Hz and firmly fix it in the specified position to reduce the influence of other factors on the vibration acceleration data.

[0079] (4) During the test, ensure that the test vehicle is the only vehicle in the test site. The driver drives the test vehicle through the test section at speeds of 60 km / h, 80 km / h, 100 km / h, 120 km / h, 130 km / h, and 140 km / h respectively.

[0080] This embodiment uses a quarter car model to simulate the driving vibration acceleration at 60km / h, 80km / h, 100km / h, 120km / h, 130km / h, and 140km / h under Class B road conditions, and compares and analyzes the obtained vibration acceleration simulation data with the vibration acceleration data collected by the driving test. Since the simulated and collected vibration acceleration data is huge, the root mean square value (RMS) can characterize the effective value of a set of data. Therefore, the present invention uses the root mean square value of vibration acceleration as the vibration acceleration index at different vehicle speeds. The error results of the vibration acceleration data of the three simulation models and the driving test data are shown in Table 3.

[0081] Table 3 Error between RMS simulation value of vibration acceleration of Class B road surface and driving test data

[0082]

[0083] From Table 3, it can be seen that the root mean square value of the vibration acceleration generated by the quarter-car model with a single white noise as the excitation signal has a large error with the root mean square value of the vibration acceleration collected by the driving test, indicating that the road surface excitation generated by white noise cannot be used as the signal input of the driving vibration analysis model. The error between the root mean square value of the vibration acceleration obtained by the simulation with the addition of Kalman and mean filtering and the value collected by the driving test is reduced. The error of the quarter-car model with the mean filtering model as the road surface excitation is small when the vehicle speed is higher than 100km / h, and vice versa. The root mean square value error of the vibration acceleration generated by the Kalman filter optimization model as the road surface excitation is up to 16%, and when the vehicle speed is increased to 120km / h, 130km / h, and 140km / h, the error is only 0%, 2%, and 1%, which is almost consistent with the measured value, indicating that the road surface roughness excitation received by the quarter-car model at this time is very similar to the actual road surface roughness excitation received by the test vehicle, so the data obtained by driving simulation using the quarter-car model with the addition of Kalman filtering can be used as measured data for further analysis.

[0084] New model simulation data calculates IRI:

[0085] The International Roughness Index (IRI) was proposed by the World Bank. Its calculation process uses a two-degree-of-freedom quarter-car model. The IRI value is equal to the sum of the absolute values ​​of the vertical displacements of the vehicle body and wheels when the quarter-car model simulates driving at a speed of 80km / h divided by the distance traveled. The road surface roughness data generated by the model with Kalman filtering is used to calculate the IRI values ​​of 10km / h, 20km / h, 30km / h, 40km / h, 50km / h, 60km / h, 70km / h, and 80km / h for 1300m. The sampling interval of the calculation program defaults to 250mm. Since the interval of the IRI value output by the road comprehensive information acquisition system is 100m, 4000 points are set in the program to output an IRI value. 13 IRI values ​​are obtained at different speeds and compared with the measured values ​​as shown below. Fig.13 .

[0086] The results were analyzed and it was found that the IRI values ​​calculated by adding Kalman filter to obtain road surface roughness data at different speeds were somewhat different from the experimental collection values, but the IRI values ​​had the same change trend in the distances of 200m-400m, 500m-700m, 900m-1000m, and 1100m-1300m, with a similarity of 54%. This shows that the road surface roughness results calculated by adding Kalman filter model have high accuracy.

[0087] The average error of the calculated values ​​of IRI at different speeds is calculated, and the results are shown in Table 4:

[0088] Table 4 Average error between IRI measured and calculated values

[0089]

[0090] It can be seen from Table 4 that the error between the calculated and measured IRI values ​​is as large as 39.4% when the vehicle speed is 10 km / h, indicating that the road surface roughness simulation model with Kalman filtering is not suitable for calculating the roughness IRI value at low speeds. When the vehicle speed is 20 to 80 km / h, the average error of the IRI value does not exceed 20%, and the error fluctuation range of the IRI calculation is: 0.14 to 0.18 m / km. This shows that the present invention can simulate the actual road surface roughness very well and obtain the road surface roughness IRI value by calculation.

Claims

1. The asphalt pavement construction smoothness simulation method based on Kalman filtering technology is characterized by: The process includes: A filtered white noise road surface roughness simulation model was established using Matlab software, and a new simulation model was obtained by adding Kalman filtering to the model for optimization. The vertical vibration acceleration of the quarter-car model and the road surface roughness profile were obtained by running the two models. The reliability of the new model is verified by collecting road surface roughness data on a specific road and obtaining vibration acceleration data above the wheel through driving tests and comparing it with the data obtained by the simulation model; The road roughness simulation model data optimized by Kalman filtering is substituted into the international roughness index calculation program to obtain the road roughness IRI value to verify the accuracy of the new model.

2. The asphalt pavement construction smoothness simulation method based on Kalman filtering technology according to claim 1 is characterized in that: The specific steps include: (1) Establishment of a quarter vehicle model, which only considers the vibration of the vehicle in the vertical direction on the sprung and unsprung directions, and simplifies the vehicle into a dynamic system consisting of springs, mass, and damping; The 1 / 4 vehicle model is expressed as follows after being derived from the D'Alembert principle: Where M is the mass matrix C is the damping matrix K is the stiffness matrix Z is the displacement array [z s z t ] T , P is the excitation array According to the above formula, the vertical displacement and vibration acceleration data of the quarter car model suspension are obtained through simulation software; (2) Establishing the road surface roughness signal input for the quarter-car model, that is, adding Kalman filtering to the filtered white noise model for optimization. The iterative process of Kalman gain update includes calculating Kalman gain, state update, and error covariance update; (3) The model is verified by conducting driving tests at designated test sites. The driving tests require the use of a small vibration acceleration sensor to collect vehicle vibration acceleration. The sensor is connected to a computer via a USB interface to set data transmission and acquisition frequency. During the driving test, the sensor is installed on the console directly above the wheels of the cab. The test site is a closed high-speed loop. The road surface of the test vehicle is in good condition. At the same time, the test road surface smoothness data is collected. (4) The generated road roughness data is used to calculate the International Roughness Index (IRI) value. The calculation process uses a quarter-car model. The IRI value is equal to the sum of the absolute values ​​of the vertical displacements of the vehicle body and wheels when the quarter-car model is simulated driving at a speed of 80 km / h divided by the driving distance. The calculation is shown in the formula: Where L is the distance traveled by the car model; X1 is the vertical displacement of the car body; X2 is the vertical displacement of the wheel; substituting the data in the new model into the above formula can calculate the International Roughness Index IRI value.

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