# Error Correction of Measured Unstructured Road Profiles Based on Accelerometer and Gyroscope Data

Authors: Jinhua Han; Xiaoqiang Yang; Huanliang Li; Hongxin Cui
Journal: Mathematical Problems in Engineering
 (2017)

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## Abstract

This paper describes a noncontact acquisition system composed of several time synchronized laser height sensors, accelerometers, gyroscope, and so forth in order to collect the road profiles of vehicle riding on the unstructured roads. A method of correcting road profiles based on the accelerometer and gyroscope data is proposed to eliminate the adverse impacts of vehicle vibration and attitudes change. Because the power spectral density (PSD) of gyro attitudes concentrates in the low frequency band, a method called frequency division is presented to divide the road profiles into two parts: high frequency part and low frequency part. The vibration error of road profiles is corrected by displacement data obtained through two times integration of measured acceleration data. After building the mathematical model between gyro attitudes and road profiles, the gyro attitudes signals are separated from low frequency road profile by the method of sliding block overlap based on correlation analysis. The accuracy and limitations of the system have been analyzed, and its validity has been verified by implementing the system on wheeled equipment for road profiles’ measuring of vehicle testing ground. The paper offers an accurate and practical approach to obtaining unstructured road profiles for road simulation test.


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## Body

## 1. Introduction

Road profile is the most important external excitation of the ground vehicle, which influences vehicle ride comfort, operational stability, driving reliability, fatigue life of components, and so forth [1–3]. Therefore, providing accurate road profile for vehicle reliability testing and simulation has been an important research content in this field.The actual roads can be divided into structured and unstructured roads. The structured roads generally refer to the well-structured pavements with flat road surface and regular edge such as the expressway and urban roads. The unstructured roads generally refer to the less structured roads with high roughness, including the nonpaved roads such as gravel road and sand road, “bad road” whose road degree is E or below E and road cover is damaged, roadless road, and strengthened test pavement. Currently, road profile measuring concentrates on the structured roads mainly measured by the Highway Department. Moreover, lots of structured road profile models have been built up and can be simulated and reconstructed accurately [4, 5]. However, with regard to the unstructured roads, there is no standardized road profile to utilize because of the potential complexity. Furthermore, the unstructured road profile has evident non-Gaussian characteristics largely due to a large number of high amplitude excitations [6]. The characterization of the structured road profile based on the assumption of stationary, random, and Gaussian is difficult to be applied to the unstructured roads [7]. Therefore, an in situ acquisition operation of unstructured roads is always needed before performing any road simulation.Since the 1960s a lot of studies had been done for measuring road profiles, and many kinds of measuring devices had been invented [8–11], which contain Level and Rod, Multiwheel Profilograph, BPR Roughometer, Inertial Profiler, Laser Profiler, and so forth. But they are always difficult to simultaneously consider the measuring speed and accuracy. Nowadays, the most commonly used noncontact profilometers can measure the road profile with pretty high accuracy [12, 13]. Nonetheless, this system may not be applicable for the unstructured road profile measuring due to the following reasons [14]. The road profile mainly depends on the relative displacement between the sensor and the road surface measured by the sensor (laser, infrared, or ultrasonic) mounted on the vehicle. The obtained final displacement could represent the road profile only when the vehicle is not excessively interrupted and maintains steady while driving through the road. Obviously, this hypothesis is not true for unstructured roads because of the bumpiness of the unstructured road which result in severe vibration and attitudes’ change of the vehicle and the major variation in the vehicle speed [15, 16].To solve the problem, a laser measuring system for the unstructured road is proposed to realize the fast measurement of the road profiles, vibration acceleration, and gyro attitudes of the vehicle. To improve the accuracy of the measured road profiles, an error correction method based on measured acceleration and gyro attitudes data is discussed in detail. Aiming at the characteristic that the PSD of vehicle attitudes concentrates in the low frequency band, the measured road profile can be divided into high frequency part and low frequency part by the method of frequency division. Then the vibration error of the measured road profile is corrected by displacement data obtained through two times integration of measured acceleration data. The attitude error of the measured road profile is corrected by signal separation based on sliding block overlap and correlation analysis. The proposed acquisition system has been used in the unstructured road profile measurement of vehicle testing ground, and its validity has been evaluated in the paper.


## 2. Laser Road Profile Acquisition System

For the reliability simulation of the vehicle, the 2D profile curve in the direction of the vehicle wheels’ orbit is generally used as the research object. A road profile acquisition system is shown in Figure1 which integrates the gyro attitudes, GPS, vibration acceleration, and displacement measuring. The system can be used to measure road profiles of structured roads (asphalt road, expressway, etc.) and unstructured roads (gravel road, cross-country path, strengthen-road, etc.). The test vehicle is an 8 × 8 wheeled vehicle with independent suspension [17], which could reduce the impact of the road profiles to the vehicle and improve ride comfort. However, the vehicle’s attitude change is inevitable when driving on the unstructured roads. Generally, the frequencies of sensors are high enough for the acquisition. The sampling frequencies of acceleration and road profile data are 1 kHz, while the sampling frequency of gyro attitudes is 200 Hz.Figure 1
Road profile acquisition system of the vehicle.The road profile acquisition system consists of a HBM SoMat eDAQ System (data acquisition and record), a RMS Strapdown Platform System (mounted in the center of the vehicle and measuring vehicle’s attitudes change), two groups of Datron HF-500C laser height sensors (measuring the relative displacement between sensor and road surface, i.e., the road profile), ten groups of ENDEVCO 7596 accelerometers (measuring the vibration acceleration of laser sensors and the spindles of the vehicle), some groups of cable displacement sensors (measuring displacement of the spindles), an ordinary GPS module (measuring the longitude, latitude, altitude, and speed of the vehicle), an AXIS P1311 webcam (recording video information of testing roads), and so forth. As shown in Figure2, the laser height sensors and accelerometers are counted on the brackets that are fixed on both sides of the front of the vehicle.Figure 2
The mounted sensors of the acquisition system (left bracket).


## 3. Error Correction of Road Profiles

The road profile includes the large-scale signal that is from low frequency to high frequency; the laser height sensor could barely measure the signals of all frequency bands. In addition, the devices of the acquisition system are fixed on the vehicle; the road profiles measured by laser sensors are mostly high frequency and short wavelength signals (the wavelength is less than the wheelbase of testing vehicle). Therefore, the measuring frequency band is divided into several sections. For the low frequency and long wavelength part of road profile that the laser sensor cannot measure (the frequency is generally lower than 0.1 Hz), a Global Positioning System (GPS) receiver supplemented with Real Time Kinematics (RTK) technology can easily measure the road profile with centimeter level accuracy and has been widely used in road profile measurement [18, 19].For the short wavelength signals above 0.1 Hz that the laser sensor can measure, they are also divided into two parts due to the PSD of the vehicle attitudes [20]. To correct the errors of road profile caused by the vibration and attitudes change of the testing vehicle, the vibration acceleration and gyro attitudes are measured. For the road profile with frequency below 3 Hz (0.1 Hz~3 Hz), the error is corrected by the measured gyro attitudes. For the road profile with frequency above 3 Hz (>3 Hz), the error is corrected by displacement data obtained by two times integration of measured acceleration data. Finally, the final corrected road profile is obtained by combining the corrected low frequency part and the corrected high frequency part; its specific calculation process is shown in Figure 3. Each filtering frequency can be adjusted according to the actual need in the calculation process.Figure 3
The calculation flow chart of correcting road profile.


### 3.1. Division Frequency Determined

The division frequency of measured road profiles is mainly determined by the gyro attitudes frequency band and the road frequency band. The road frequency band depends on vehicle forward speedv and the wavelengths of road profile. The wavelengths of road profile are mainly concentrated within a certain range. It is hypothesized that λ1 and λ2 are the lower and upper of the wavelengths, respectively. Then the frequencies of road wavelengths measured by the laser sensor can be expressed as(1)fL=vλ2,fH=vλ1.Therefore, to divide the gyro attitudes frequency and road frequency of measured road profile, the division frequencyfd should be lower than the road frequency band fL,fH and higher than the gyro attitudes frequency band fa,fb, which can be expressed as(2)fb<fd<fL=vλ2.


### 3.2. Acceleration Integration

To correct the vibration error due to the movement of laser sensor along with the testing vehicle, the displacement is calculated by two times integration of measured acceleration data.As shown in Figure4, the measured acceleration signal should be preprocessed first, including singularity removed & detrend and band-pass filtering in order to improve measuring accuracy. Then the vibration velocity is obtained by acceleration integration. Finally, the vibration displacement is obtained by velocity integration after band-pass filtering. Scilicet, the vibration displacement is the vibration error of road profile. Therefore, the vibration error of road profile can be corrected by subtracting the vibration displacement.Figure 4
The flow chart of acceleration integration.


### 3.3. Mathematics Description of Gyro Attitude

To realize the error correction of measured road profile due to the vehicle’s attitudes change, the mathematical model between vehicle’s attitudes and road profile should be established first after analyzing the relation between them. Due to the relativity of motion, the corresponding coordinate system should be introduced in the gyro attitudes measurement. The gyro attitudes measured by strapdown gyroscope in this paper are the geometric angles of the body coordinate system (BCS)oxbybzb relative to the geographic coordinate system (GCS) oxtytzt. The BCS oxbybzb denotes the coordinate system fixed on the testing vehicle that its origin is located at the center of the vehicle, oxb points to forward along the longitudinal axis of the vehicle, oyb points to left along the horizontal axis of the vehicle, and ozb is perpendicular to the oxbyb plane and points to up along the vertical axis of the vehicle. The GCS oxtytzt denotes the coordinate system that its origin is also located at the center of the vehicle, oxt points to east, oyt points to north, and ozt points to sky along the vertical direction according to the right-hand rule.The gyro attitudes of the testing vehicle include three parameters [21], yaw angle γ, pitch angle θ, and roll angle φ. They denote the rotation angle of the vector around the x, y, and z axes, respectively. According to the right-hand rule, the inverse rotation is clockwise.As shown in Figure5, in the case of the invariant of the coordinate origin, the GCS oxtytzt is used as the reference coordinate system. Then the BCS oxbybzb is obtained after triple rotation according to the order of z-y-x. Its specific conversion process is as follows:(3)oxtytzt→oztγox′y′zt→oy′θoxby′z′→oxbφoxbybzb.Figure 5
Coordinate transformation diagram.Then the transformation relation from the BCSoxbybzb to the GCS oxtytzt is shown as follows:(4)xtytzt=Cbtxbybzb,where xtytztT and xbybzbT denote the coordinate of the laser sensor in the GCS oxtytzt and the BCS oxbybzb, respectively. Cbt denotes the rotational transformation matrix, also called the strapdown matrix.The emphasis of realizing the sensor coordinate transformation between different coordinate systems is the solution of the strapdown matrixCbt. Therefore, the obtained strapdown matrix Cbt according to the order of z-y-x can be expressed as(5)Cbt=Cz,γCy,θCx,φ=cos⁡γ-sin⁡γ0sin⁡γcos⁡γ0001cos⁡θ0sin⁡θ010-sin⁡θ0cos⁡θ1000cos⁡φ-sin⁡φ0sin⁡φcos⁡φ=cos⁡θcos⁡γsin⁡φsin⁡θcos⁡γ-cos⁡φsin⁡γcos⁡φsin⁡θcos⁡γ+sin⁡φsin⁡γcos⁡θsin⁡γsin⁡φsin⁡θsin⁡γ+cos⁡φcos⁡γcos⁡φsin⁡θsin⁡γ-sin⁡φcos⁡γ-sin⁡θsin⁡φcos⁡θcos⁡φcos⁡θ,where Cz,γ denotes the rotational transformation matrix around the z-axis with rotation angle γ. Cy,θ denotes the rotational transformation matrix around the y-axis with rotation angle θ. Cx,φ denotes the rotational transformation matrix around the x-axis with rotation angle φ.The research of road profile is concerned with the road roughness that is perpendicular to the ground. Scilicet, the main external excitation of the testing vehicle is the displacement of the road in thez-axis direction along the direction of the vehicle, rather than in the x-axis or y-axis direction. Thus, substituting (5) into (4) can be expressed as(6)zt=-sin⁡θsin⁡φcos⁡θcos⁡φcos⁡θxbybzb.When the change of the gyro attitudes anglesφ, θ, and γ is small, (6) can be simplified as(7)zt=-θ·xb+φ·yb+zb.Thus, the error of measured road profile caused by the gyro attitudes is given by(8)Δz=zt-zb=-θ·xb+φ·yb.As shown in (8), the measured road profiles are mainly affected by the pitch angle θ and roll angle φ; the yaw angle γ has almost no influence on them. Due to the relatively large values of xb and yb (up to several meters), the small changes of vehicle’s attitudes can cause large error of the measured road profiles. Therefore, the error of measured road profiles caused by vehicle’s attitudes must be corrected based on the calculation result of (8).


### 3.4. Error Correction Based on Signal Separation

According to (8), the relation between the vehicle’s attitudes and the error of road profile Δz can be approximately regarded as linear. Hence, the measured road profile can be regarded as the linear mixture of true road and vehicle’s attitude signals. The error correction of measured road profile due to vehicle’s attitudes change can be regarded as the signal separation of mixed signal [22]. The mixed and separation process of measured road profiles is shown in Figure 6. x1 denotes the true road profile, that is, unseparated signal. The additive mixed signal y=x1+x2 measured by the laser height sensor T1 consists of signals x1 and x2 that is obtained through the unknown transmission channel H1. x~2 denotes the vehicle’s attitudes measured by gyroscope T2 located in the center of the vehicle. Then the mixed signal y is separated to obtain the accurate road profile based on the observed signal y and the reference signal x~2.Figure 6
The mixed and separation process of measured road profiles.The signal separation algorithm in this paper is based on the assumption of linear mixture. However, the signal mixing has a certain nonlinearity in fact. To satisfy the assumption of linear mixture as much as possible, a method called sliding block overlap is proposed to correct the low frequency road profile. The correction steps are shown as follows.Step 1 (signals acquisition).
The low frequency road profiley and vehicle’s attitudes (pitch angle θ, roll angle φ, and yaw angle γ) are measured and calculated first. Then, according to (8), the reference signal x~2=-θ·xb+φ·yb is obtained.Step 2 (estimation of the time shiftm2 by cross-correlation function).
The cross-correlation function is a description of the correlation between random signalx~2 and y at different time. According to the properties of the cross-correlation function, when Ryx~2τ takes the maximum value at τ=τ1, the time shift m2=τ1 of the signals is determined.Step 3 (signal sliding segmentation and overlap).
The schematic diagram of the data segmentation is shown in Figure7. The testing data of the time length T is divided into N segments of the equal length t1. Then there are N-1 overlapping segments of the equal length t2. Data segment number N and length t can be adjusted according to the actual situation in order to achieve the best effect. The relation of the parameters is shown by(9)N·t1+N-1·t2=T.
After completing the time shift of Step2, the signal sliding segmentation and overlap of measured road profile y and reference attitudes x~2 are accomplished according to the above method. Then the i segment of measured road profile y and reference attitudes x~2 are recorded as yi and x~2i, respectively.Figure 7
The schematic diagram of the data segmentation.Step 4 (amplitude adjustment).
The amplitude of the vehicle’s attitude signal will change during the process of mixing into the road profile. Therefore, the amplitude adjustment is required to keep the reference signalx~2 in the same amplitude as the mixed signal y. To reduce the nonlinearity error, amplitude adjustment is performed for each data segment. The amplitude of reference signal x~2i after amplitude adjustment can be computed as(10)Axi′=Axi-mxidyidxi+mxi,where Axi denotes the amplitudes of references signal x~2i. mxi denotes the mean values of references signal x~2i. dxi and dyi denote the mean square errors (MSE) of references signal x~2i and mixed signal yi, respectively. Then the adjusted reference signal x~2i′ has the same amplitude and distribution as the mixed signal yi.Step 5 (segment error correction).
The true road profilex1i can be computed from(11)x1i=yi-x~2i′.Step 6 (smooth connection of segmental data).
The corrected segmented road profile is connected in a time sequence. For the data overlap part, the arithmetic mean is applied to reduce the difference within the data connection. Moreover, for the data connection, adaptive correction method based on local signal baseline adjustment is used to realize smooth connection of segmental data [23]. Then the low frequency road profile is corrected and obtained by the above steps.Step 7 (signal merging).
After correcting the low frequency and high frequency road profile, the final corrected road profile is obtained by combining the low frequency and high frequency corrected road profile.


## 3.1. Division Frequency Determined

The division frequency of measured road profiles is mainly determined by the gyro attitudes frequency band and the road frequency band. The road frequency band depends on vehicle forward speedv and the wavelengths of road profile. The wavelengths of road profile are mainly concentrated within a certain range. It is hypothesized that λ1 and λ2 are the lower and upper of the wavelengths, respectively. Then the frequencies of road wavelengths measured by the laser sensor can be expressed as(1)fL=vλ2,fH=vλ1.Therefore, to divide the gyro attitudes frequency and road frequency of measured road profile, the division frequencyfd should be lower than the road frequency band fL,fH and higher than the gyro attitudes frequency band fa,fb, which can be expressed as(2)fb<fd<fL=vλ2.


## 3.2. Acceleration Integration

To correct the vibration error due to the movement of laser sensor along with the testing vehicle, the displacement is calculated by two times integration of measured acceleration data.As shown in Figure4, the measured acceleration signal should be preprocessed first, including singularity removed & detrend and band-pass filtering in order to improve measuring accuracy. Then the vibration velocity is obtained by acceleration integration. Finally, the vibration displacement is obtained by velocity integration after band-pass filtering. Scilicet, the vibration displacement is the vibration error of road profile. Therefore, the vibration error of road profile can be corrected by subtracting the vibration displacement.Figure 4
The flow chart of acceleration integration.


## 3.3. Mathematics Description of Gyro Attitude

To realize the error correction of measured road profile due to the vehicle’s attitudes change, the mathematical model between vehicle’s attitudes and road profile should be established first after analyzing the relation between them. Due to the relativity of motion, the corresponding coordinate system should be introduced in the gyro attitudes measurement. The gyro attitudes measured by strapdown gyroscope in this paper are the geometric angles of the body coordinate system (BCS)oxbybzb relative to the geographic coordinate system (GCS) oxtytzt. The BCS oxbybzb denotes the coordinate system fixed on the testing vehicle that its origin is located at the center of the vehicle, oxb points to forward along the longitudinal axis of the vehicle, oyb points to left along the horizontal axis of the vehicle, and ozb is perpendicular to the oxbyb plane and points to up along the vertical axis of the vehicle. The GCS oxtytzt denotes the coordinate system that its origin is also located at the center of the vehicle, oxt points to east, oyt points to north, and ozt points to sky along the vertical direction according to the right-hand rule.The gyro attitudes of the testing vehicle include three parameters [21], yaw angle γ, pitch angle θ, and roll angle φ. They denote the rotation angle of the vector around the x, y, and z axes, respectively. According to the right-hand rule, the inverse rotation is clockwise.As shown in Figure5, in the case of the invariant of the coordinate origin, the GCS oxtytzt is used as the reference coordinate system. Then the BCS oxbybzb is obtained after triple rotation according to the order of z-y-x. Its specific conversion process is as follows:(3)oxtytzt→oztγox′y′zt→oy′θoxby′z′→oxbφoxbybzb.Figure 5
Coordinate transformation diagram.Then the transformation relation from the BCSoxbybzb to the GCS oxtytzt is shown as follows:(4)xtytzt=Cbtxbybzb,where xtytztT and xbybzbT denote the coordinate of the laser sensor in the GCS oxtytzt and the BCS oxbybzb, respectively. Cbt denotes the rotational transformation matrix, also called the strapdown matrix.The emphasis of realizing the sensor coordinate transformation between different coordinate systems is the solution of the strapdown matrixCbt. Therefore, the obtained strapdown matrix Cbt according to the order of z-y-x can be expressed as(5)Cbt=Cz,γCy,θCx,φ=cos⁡γ-sin⁡γ0sin⁡γcos⁡γ0001cos⁡θ0sin⁡θ010-sin⁡θ0cos⁡θ1000cos⁡φ-sin⁡φ0sin⁡φcos⁡φ=cos⁡θcos⁡γsin⁡φsin⁡θcos⁡γ-cos⁡φsin⁡γcos⁡φsin⁡θcos⁡γ+sin⁡φsin⁡γcos⁡θsin⁡γsin⁡φsin⁡θsin⁡γ+cos⁡φcos⁡γcos⁡φsin⁡θsin⁡γ-sin⁡φcos⁡γ-sin⁡θsin⁡φcos⁡θcos⁡φcos⁡θ,where Cz,γ denotes the rotational transformation matrix around the z-axis with rotation angle γ. Cy,θ denotes the rotational transformation matrix around the y-axis with rotation angle θ. Cx,φ denotes the rotational transformation matrix around the x-axis with rotation angle φ.The research of road profile is concerned with the road roughness that is perpendicular to the ground. Scilicet, the main external excitation of the testing vehicle is the displacement of the road in thez-axis direction along the direction of the vehicle, rather than in the x-axis or y-axis direction. Thus, substituting (5) into (4) can be expressed as(6)zt=-sin⁡θsin⁡φcos⁡θcos⁡φcos⁡θxbybzb.When the change of the gyro attitudes anglesφ, θ, and γ is small, (6) can be simplified as(7)zt=-θ·xb+φ·yb+zb.Thus, the error of measured road profile caused by the gyro attitudes is given by(8)Δz=zt-zb=-θ·xb+φ·yb.As shown in (8), the measured road profiles are mainly affected by the pitch angle θ and roll angle φ; the yaw angle γ has almost no influence on them. Due to the relatively large values of xb and yb (up to several meters), the small changes of vehicle’s attitudes can cause large error of the measured road profiles. Therefore, the error of measured road profiles caused by vehicle’s attitudes must be corrected based on the calculation result of (8).


## 3.4. Error Correction Based on Signal Separation

According to (8), the relation between the vehicle’s attitudes and the error of road profile Δz can be approximately regarded as linear. Hence, the measured road profile can be regarded as the linear mixture of true road and vehicle’s attitude signals. The error correction of measured road profile due to vehicle’s attitudes change can be regarded as the signal separation of mixed signal [22]. The mixed and separation process of measured road profiles is shown in Figure 6. x1 denotes the true road profile, that is, unseparated signal. The additive mixed signal y=x1+x2 measured by the laser height sensor T1 consists of signals x1 and x2 that is obtained through the unknown transmission channel H1. x~2 denotes the vehicle’s attitudes measured by gyroscope T2 located in the center of the vehicle. Then the mixed signal y is separated to obtain the accurate road profile based on the observed signal y and the reference signal x~2.Figure 6
The mixed and separation process of measured road profiles.The signal separation algorithm in this paper is based on the assumption of linear mixture. However, the signal mixing has a certain nonlinearity in fact. To satisfy the assumption of linear mixture as much as possible, a method called sliding block overlap is proposed to correct the low frequency road profile. The correction steps are shown as follows.Step 1 (signals acquisition).
The low frequency road profiley and vehicle’s attitudes (pitch angle θ, roll angle φ, and yaw angle γ) are measured and calculated first. Then, according to (8), the reference signal x~2=-θ·xb+φ·yb is obtained.Step 2 (estimation of the time shiftm2 by cross-correlation function).
The cross-correlation function is a description of the correlation between random signalx~2 and y at different time. According to the properties of the cross-correlation function, when Ryx~2τ takes the maximum value at τ=τ1, the time shift m2=τ1 of the signals is determined.Step 3 (signal sliding segmentation and overlap).
The schematic diagram of the data segmentation is shown in Figure7. The testing data of the time length T is divided into N segments of the equal length t1. Then there are N-1 overlapping segments of the equal length t2. Data segment number N and length t can be adjusted according to the actual situation in order to achieve the best effect. The relation of the parameters is shown by(9)N·t1+N-1·t2=T.
After completing the time shift of Step2, the signal sliding segmentation and overlap of measured road profile y and reference attitudes x~2 are accomplished according to the above method. Then the i segment of measured road profile y and reference attitudes x~2 are recorded as yi and x~2i, respectively.Figure 7
The schematic diagram of the data segmentation.Step 4 (amplitude adjustment).
The amplitude of the vehicle’s attitude signal will change during the process of mixing into the road profile. Therefore, the amplitude adjustment is required to keep the reference signalx~2 in the same amplitude as the mixed signal y. To reduce the nonlinearity error, amplitude adjustment is performed for each data segment. The amplitude of reference signal x~2i after amplitude adjustment can be computed as(10)Axi′=Axi-mxidyidxi+mxi,where Axi denotes the amplitudes of references signal x~2i. mxi denotes the mean values of references signal x~2i. dxi and dyi denote the mean square errors (MSE) of references signal x~2i and mixed signal yi, respectively. Then the adjusted reference signal x~2i′ has the same amplitude and distribution as the mixed signal yi.Step 5 (segment error correction).
The true road profilex1i can be computed from(11)x1i=yi-x~2i′.Step 6 (smooth connection of segmental data).
The corrected segmented road profile is connected in a time sequence. For the data overlap part, the arithmetic mean is applied to reduce the difference within the data connection. Moreover, for the data connection, adaptive correction method based on local signal baseline adjustment is used to realize smooth connection of segmental data [23]. Then the low frequency road profile is corrected and obtained by the above steps.Step 7 (signal merging).
After correcting the low frequency and high frequency road profile, the final corrected road profile is obtained by combining the low frequency and high frequency corrected road profile.


## 4. Application

By using the acquisition system shown in Figure1, all road signals had been acquired during the testing vehicle riding through the unstructured proving ground (PG) roads of Beijing vehicle testing ground, which include Ripple Tracks, Belgian Road, Cobblestone Tracks, Washboards, Body Twist Lane, and Potholes Road. The original collected signals mainly include road profiles (with frequency of 1 kHz), vibration acceleration (with frequency of 1 kHz), and gyro attitudes (with frequency of 200 Hz). Then some preprocessing methods including the identification and correction of abnormal errors, the extraction of signal trends, and digital filtering are implemented to the original collected signals [24]. The Belgian Road is a typical unstructured road and man-made test road whose characteristics are determined. When driving on the Belgian Road, the testing vehicle bumps violently, which can cause random vibration of rolling, pitching, and vertical direction. Therefore, the Belgian Road is expressed as an example to verify the validity and accuracy of the error correction algorithm mentioned above in this paper. The average vehicle speed is about 18.5 km/h (5.14 m/s) during the testing. Figure 8 shows the Belgian Road in picture. The average length of the cobbles in the direction of testing vehicle travel is about 150 mm. Figure 9 gives the road profiles corresponding to two wheels measured by laser height sensors. Figure 10 presents the vehicle’s attitudes measured by strapdown gyroscope.Figure 8
The Belgian Road in picture.Figure 9
Measured road profiles of Belgian Road. (a) The left wheel; (b) the right wheel.
(a) (b)Figure 10
Measured vehicle’s attitudes of Belgian Road. (a) The roll angle; (b) the pitch angle; and (c) the yaw angle.
(a) (b) (c)


### 4.1. Frequency Division of Measured Road Profiles

As mentioned above, the vehicle’s attitudes mainly affect the low frequency band of measured road profiles which is about 0.1 Hz~2.0 Hz. Therefore, the road profile is divided into high frequency part (>3 Hz) and low frequency part (0.1 Hz~3 Hz) by frequency division. As shown in Figure11 is the high frequency and low frequency road profile of right wheel.Figure 11
Road profile after frequency division (right wheel). (a) The high frequency part; (b) the low frequency part.
(a) (b)


### 4.2. Acceleration Integration

As shown in Figure12, the integral velocity and displacement signal are obtained by acceleration integration measured by accelerometer fixed on the right bracket (Figure 2). The error of measured road profile caused by vehicle vibration is mainly concentrated in ±0.5 mm (except for the individual), and the impact is about 2%. Due to the relative displacement between the sensor and the road surface measured by laser height sensor, the corrected high frequency road profile can be computed by subtracting integral displacement from the original high frequency road profile. Thus the impact of vehicle vibration to road profile acquisition is removed.Figure 12
Acceleration integration (right wheel). (a) Acceleration; (b) integral velocity; and (c) integral displacement.
(a) (b) (c)


### 4.3. Correlation Analysis

As mentioned previously, the gyro attitudes have great influence on the road profile measuring. However, the impacts of yaw angleγ, pitch angle θ, and roll angle φ on the road profile measuring are different. Generally, the impact size between gyro attitudes and road profile can be analyzed by correlation coefficient ρXY. The correlation coefficient ρXY between signals X and Y is between −1 and 1. When ρXY=0, X and Y are not related. When ρXY=1, X and Y are completely related. When ρXY>0.8, X and Y are highly related. When ρXY<0.3, X and Y are lowly related. When 0.3≤ρXY≤0.8, X and Y are moderately related. The greater the absolute value of ρXY, the higher the correlation between X and Y.To analyze the relation between measured road profile and gyro attitudes, the correlation coefficients between them are computed and shown in Table1. The pitch angle θ and roll angle φ have a high correlation with the measured road profile, which verifies the validity of (8). Besides, the correlation coefficients between gyro attitudes and high frequency road profile are close to zero. This means that they are basically not related. The impact of vehicle’s attitudes on road profile measuring is mainly concentrated in the low frequency band (≤3 Hz), which verifies the feasibility of the frequency division method. Therefore, the impact of vehicle’s attitudes to road profile acquisition can be removed only by correcting the low frequency road profile.Table 1
Correlation coefficients between road profiles and gyro attitudes.
Correlation coefficients Rollφ Pitchθ Yawγ Original signal(f>0.1 Hz) Left road profile −0.4518 0.7421 0.1886 Right road profile 0.5677 0.7943 0.1933 High frequency signal(f>3 Hz) Left road profile 0.0610 0.0037 −0.0114 Right road profile −0.0531 0.0069 0.0184 Low frequency signal(0.1Hz≤f≤3Hz) Left road profile −0.4905 0.7765 0.2169 Right road profile 0.5919 0.8201 0.2181


### 4.4. Error Correction

As shown in Figure2, the laser height sensor and accelerometer are fixed on the bracket in front of the testing vehicle. The distances from the sensors to the vehicle center in each direction are x=4500 mm, y=1300 mm, and z=1050 mm. The curves of low frequency road profile and pitch angle θ are shown in Figure 13. According to the comparison, the low frequency road profile and pitch angle θ have the same change trend, which means high correlation between them.Figure 13
Comparison of low frequency road profile and pitch angle (right wheel). (a) The low frequency road profile; (b) the pitch angle.
(a) (b)Known from Section3 of the paper, the error of vehicle’s attitudes to measured road profile Δz is computed as (8). Then the error correction is completed according to the steps mentioned in Section 3.4. The corrected low frequency road profile is explicitly shown in Figure 14. The large wave of road profile caused by vehicle’s attitudes is well removed. Then the final corrected road profile is obtained by combining low frequency road profile after removing attitudes’ impact and high frequency road profile after removing vibration impact, as shown in Figure 15. The amplitude of road profile decreases from about 50 mm to 20 mm, which is more consistent with the real road features of the Belgian Road in vehicle testing ground.Figure 14
Low frequency road profile after correction (right wheel).Figure 15
Final corrected road profile (right wheel).For comparison, the Root Mean Square (RMS) of the road profiles before and after error correction are calculated and shown in Table2. By the error correction method raised in this paper, the RMS of road profile reduces from 36.1104 mm to 18.2179 mm. Obviously, the validity of the error correction method can be verified easily by comparing Figures 9 and 15.Table 2
RMS comparison of road profile before and after correction.
Road profile RMS (mm) Original Corrected High frequency 9.2798 9.2793 Low frequency 35.3676 15.0620 Final 36.1104 18.2179To further analyze the validity of the error correction method proposed in the paper, the space road spectrum is introduced for comparison. According to standard ISO/DIS 8608 and GB/T 7031-2005, the model and grading method based on the PSD of the road roughness were worked out. The fitting expression of the road PSD using power function can be shown as(12)Gdn=Gdn0nn0-W,where n denotes the space frequency in m-1. n0=0.1m-1 denotes the reference space frequency. Gdn0 denotes the road roughness coefficient, which is the value of PSD at n0 in m3. W denotes the frequency index (the general value is 2).However, the road profile measured in this paper is time domain displacementDτ. The time domain road profile Dτ should transform into space domain displacement DS based on the distance history Sτ, which is obtained by vehicle speed vτ integration measured by GPS module. Then the space domain spectrum Gdn of road profile is calculated through Fast Fourier Transform (FFT) based on DS, as shown in Figure 16.Figure 16
Space PSD of the road profilesGdn.In Figure16, six standard road spectra from Grade A to Grade F according to ISO/DIS 8608 have been plotted as references. The space PSD of corrected and acquisition road profile have also been plotted for comparison. Besides, it is noted that the peak at a space frequency of 6.623 cycles/meter corresponds to the wavelength of about 150 mm which is the average length of the cobbles. It can be concluded that, in the whole interested frequency range, the error correction method raised in the paper shows its advantage by obtaining a more accurate PSD as removing the vehicle vibration and attitudes impacts. The proposed method can adapt various unstructured road profile measuring and correcting and provides accurate road spectra for road simulation test.


## 4.1. Frequency Division of Measured Road Profiles

As mentioned above, the vehicle’s attitudes mainly affect the low frequency band of measured road profiles which is about 0.1 Hz~2.0 Hz. Therefore, the road profile is divided into high frequency part (>3 Hz) and low frequency part (0.1 Hz~3 Hz) by frequency division. As shown in Figure11 is the high frequency and low frequency road profile of right wheel.Figure 11
Road profile after frequency division (right wheel). (a) The high frequency part; (b) the low frequency part.
(a) (b)


## 4.2. Acceleration Integration

As shown in Figure12, the integral velocity and displacement signal are obtained by acceleration integration measured by accelerometer fixed on the right bracket (Figure 2). The error of measured road profile caused by vehicle vibration is mainly concentrated in ±0.5 mm (except for the individual), and the impact is about 2%. Due to the relative displacement between the sensor and the road surface measured by laser height sensor, the corrected high frequency road profile can be computed by subtracting integral displacement from the original high frequency road profile. Thus the impact of vehicle vibration to road profile acquisition is removed.Figure 12
Acceleration integration (right wheel). (a) Acceleration; (b) integral velocity; and (c) integral displacement.
(a) (b) (c)


## 4.3. Correlation Analysis

As mentioned previously, the gyro attitudes have great influence on the road profile measuring. However, the impacts of yaw angleγ, pitch angle θ, and roll angle φ on the road profile measuring are different. Generally, the impact size between gyro attitudes and road profile can be analyzed by correlation coefficient ρXY. The correlation coefficient ρXY between signals X and Y is between −1 and 1. When ρXY=0, X and Y are not related. When ρXY=1, X and Y are completely related. When ρXY>0.8, X and Y are highly related. When ρXY<0.3, X and Y are lowly related. When 0.3≤ρXY≤0.8, X and Y are moderately related. The greater the absolute value of ρXY, the higher the correlation between X and Y.To analyze the relation between measured road profile and gyro attitudes, the correlation coefficients between them are computed and shown in Table1. The pitch angle θ and roll angle φ have a high correlation with the measured road profile, which verifies the validity of (8). Besides, the correlation coefficients between gyro attitudes and high frequency road profile are close to zero. This means that they are basically not related. The impact of vehicle’s attitudes on road profile measuring is mainly concentrated in the low frequency band (≤3 Hz), which verifies the feasibility of the frequency division method. Therefore, the impact of vehicle’s attitudes to road profile acquisition can be removed only by correcting the low frequency road profile.Table 1
Correlation coefficients between road profiles and gyro attitudes.
Correlation coefficients Rollφ Pitchθ Yawγ Original signal(f>0.1 Hz) Left road profile −0.4518 0.7421 0.1886 Right road profile 0.5677 0.7943 0.1933 High frequency signal(f>3 Hz) Left road profile 0.0610 0.0037 −0.0114 Right road profile −0.0531 0.0069 0.0184 Low frequency signal(0.1Hz≤f≤3Hz) Left road profile −0.4905 0.7765 0.2169 Right road profile 0.5919 0.8201 0.2181


## 4.4. Error Correction

As shown in Figure2, the laser height sensor and accelerometer are fixed on the bracket in front of the testing vehicle. The distances from the sensors to the vehicle center in each direction are x=4500 mm, y=1300 mm, and z=1050 mm. The curves of low frequency road profile and pitch angle θ are shown in Figure 13. According to the comparison, the low frequency road profile and pitch angle θ have the same change trend, which means high correlation between them.Figure 13
Comparison of low frequency road profile and pitch angle (right wheel). (a) The low frequency road profile; (b) the pitch angle.
(a) (b)Known from Section3 of the paper, the error of vehicle’s attitudes to measured road profile Δz is computed as (8). Then the error correction is completed according to the steps mentioned in Section 3.4. The corrected low frequency road profile is explicitly shown in Figure 14. The large wave of road profile caused by vehicle’s attitudes is well removed. Then the final corrected road profile is obtained by combining low frequency road profile after removing attitudes’ impact and high frequency road profile after removing vibration impact, as shown in Figure 15. The amplitude of road profile decreases from about 50 mm to 20 mm, which is more consistent with the real road features of the Belgian Road in vehicle testing ground.Figure 14
Low frequency road profile after correction (right wheel).Figure 15
Final corrected road profile (right wheel).For comparison, the Root Mean Square (RMS) of the road profiles before and after error correction are calculated and shown in Table2. By the error correction method raised in this paper, the RMS of road profile reduces from 36.1104 mm to 18.2179 mm. Obviously, the validity of the error correction method can be verified easily by comparing Figures 9 and 15.Table 2
RMS comparison of road profile before and after correction.
Road profile RMS (mm) Original Corrected High frequency 9.2798 9.2793 Low frequency 35.3676 15.0620 Final 36.1104 18.2179To further analyze the validity of the error correction method proposed in the paper, the space road spectrum is introduced for comparison. According to standard ISO/DIS 8608 and GB/T 7031-2005, the model and grading method based on the PSD of the road roughness were worked out. The fitting expression of the road PSD using power function can be shown as(12)Gdn=Gdn0nn0-W,where n denotes the space frequency in m-1. n0=0.1m-1 denotes the reference space frequency. Gdn0 denotes the road roughness coefficient, which is the value of PSD at n0 in m3. W denotes the frequency index (the general value is 2).However, the road profile measured in this paper is time domain displacementDτ. The time domain road profile Dτ should transform into space domain displacement DS based on the distance history Sτ, which is obtained by vehicle speed vτ integration measured by GPS module. Then the space domain spectrum Gdn of road profile is calculated through Fast Fourier Transform (FFT) based on DS, as shown in Figure 16.Figure 16
Space PSD of the road profilesGdn.In Figure16, six standard road spectra from Grade A to Grade F according to ISO/DIS 8608 have been plotted as references. The space PSD of corrected and acquisition road profile have also been plotted for comparison. Besides, it is noted that the peak at a space frequency of 6.623 cycles/meter corresponds to the wavelength of about 150 mm which is the average length of the cobbles. It can be concluded that, in the whole interested frequency range, the error correction method raised in the paper shows its advantage by obtaining a more accurate PSD as removing the vehicle vibration and attitudes impacts. The proposed method can adapt various unstructured road profile measuring and correcting and provides accurate road spectra for road simulation test.


## 5. Conclusions

The acquisition system integrated by laser height sensors, accelerometers, and strapdown gyroscope can be easily mounted and quickly deployed on a testing vehicle to acquire the road profile for road simulation. With the vibration acceleration history and the vehicle’s attitude history, respectively, obtained by the accelerometers and strapdown gyroscope, the measured road profiles can be accurately corrected by the frequency division and sliding block overlap calibration method. The validity of the method has been verified by applying to measure and correct the road profile of the Belgian Road.However, the proposed method is limited by vehicle speed, straight-line driving, long-wave of road, and so forth. Vehicle rapid cornering will affect the accuracy of gyro attitude measurement. The gyro attitudes frequency band and road frequency band of measured road profiles will be difficult to divide due to the improper vehicle speed and long-wave of road. Therefore, the vehicle speed and testing road section should be determined before the testing to improve the applicability of the proposed method.Though the method proposed in this paper is only verified under the Belgian Road situation, the method is applicable for measuring of other kinds of roads after proper amendments, especially for unstructured roads due to their large range vehicle vibration and attitudes change which are easy to be measured by sensors. Moreover, aided with high precision GPS receiver for low frequency road profile measuring (<0.1 Hz), the method can also be applicable to the road profile measuring and Noise Vibration Harshness (NVH) assessment with wider bandwidth and higher accuracy requirement.



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*Source: 5670697-2017-01-24.xml*