CN113353085B - Road surface unevenness identification method based on Kalman filtering theory - Google Patents
Road surface unevenness identification method based on Kalman filtering theory Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
- B60W40/02—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to ambient conditions
- B60W40/06—Road conditions
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
- B60W2050/0001—Details of the control system
- B60W2050/0019—Control system elements or transfer functions
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W2422/00—Indexing codes relating to the special location or mounting of sensors
- B60W2422/70—Indexing codes relating to the special location or mounting of sensors on the wheel or the tire
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W2422/00—Indexing codes relating to the special location or mounting of sensors
- B60W2422/95—Measuring the same parameter at multiple locations of the vehicle
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- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention relates to a road surface unevenness recognition method based on a Kalman filtering theory, belonging to the technical field of vehicle road unevenness recognition in vehicle engineering; firstly, identifying and defining a road contour as a semi-vehicle model inverse problem in a state space, and collecting vertical acceleration signals of a vehicle body, front wheels and rear wheels on a calibration road surface as measurement data of the invention; then inputting the collected data into a well established road surface unevenness recognition algorithm to obtain the dynamic response of the vehicle so as to reversely deduce the road surface unevenness information; the road surface unevenness identification algorithm is established based on a Kalman filtering theory. The invention only needs to collect one kind of measured data such as acceleration signal, the arrangement of the acceleration sensor is simple, the hardware cost is low, and the operability is strong; the method can be used not only to predict the road excitation experienced by a vehicle at an early stage of vehicle design but also to calculate the response of the vehicle to any given vehicle speed.
Description
Technical Field
The invention belongs to the technical field of vehicle road unevenness identification in vehicle engineering, and particularly relates to a road unevenness identification method based on a Kalman filtering theory.
Background
Road surface irregularities are important inputs to vehicle dynamics, especially for some special vehicles, which can lead to fatigue failure of parts or reduced ride comfort. Road surface information is essential for road quality assessment, road irregularity index calculation, vehicle dynamics analysis, suspension design and control system development. However, for technical and economic reasons, these signals cannot be measured in standard vehicles and must therefore be identified by special methods. Identifying the stimulus acting on the system from a given response of the system is a so-called inverse problem, which is usually an ill-posed problem.
In order to facilitate road maintenance and measurements, researchers have developed Longitudinal Profile (LPA) profilers, an instrument used to generate numerical sequences related to the true road profile (Piasco, legay, 1997, 2005). But the application of the contourgraph to a common vehicle is limited due to the high price. (Kim, 2002) studied a contour measurement method based on visual inspection, but this method has limited use in rainy weather. With the development of artificial intelligence methods, some scholars use neural network models to identify road surface unevenness, but the neural network methods require a long calculation time due to the complexity of the models (Mahdi et al, 2010 et al, 2012. (Kim et al, 2002. At the same time, the final reconstruction result depends to a large extent on the quality of the model.
It is a typical inverse problem to reverse the road excitation experienced by a vehicle based on the dynamic response of the vehicle structure traveling on the ground, and reference may be made to related methods in this field. In recent years, methods combining determinism and randomness have been developed. These methods treat noise as a random process and assume that noise is present not only on the measured values but also on the state variables. Steven Gillijns and Bart De Moor (2007a, 2007b) developed a recursive filter that identified the input and state of the system from the system output. E.lourens (2012) developed an enhanced kalman filter for structural dynamics force identification, where unknown forces are contained in a state vector and identified with the state. In order to obtain a cost-effective, easy-to-implement method, the proposed input force recognition method is based on acceleration measurements. However, since the method based on acceleration measurement is inherently unstable, f.naets et al (2015) proposes virtual measurement of position in order to stabilize the result. Furthermore, since it is a formula built on one spatial state, it can easily incorporate information from different sensors on the vehicle.
The kalman filtering theory was proposed in early 1961, and a state prediction close to the actual state was obtained by filtering a random signal in the time domain using a recursive algorithm. Briefly, kalman filtering is a recursive linear least square error estimate that acts as an optimal linear filter and is therefore applied to identify the excitation acting on the system.
Disclosure of Invention
The technical problem to be solved is as follows:
in order to avoid the defects of the prior art, the invention provides a road surface unevenness recognition method based on a Kalman filtering theory, firstly, a road profile is recognized and defined as a semi-vehicle model inverse problem in a state space, and vertical acceleration signals of a vehicle body, a front wheel and a rear wheel are collected on a calibrated road surface to be used as measurement data of the invention; then inputting the collected data into a well established road surface unevenness recognition algorithm to obtain the dynamic response of the vehicle so as to reversely deduce the road surface unevenness information; the road surface unevenness identification algorithm is established based on a Kalman filtering theory.
The technical scheme of the invention is as follows: a road surface unevenness identification method based on a Kalman filtering theory is characterized by comprising the following specific steps:
the method comprises the following steps: acquiring actual data to be identified, wherein the actual data to be identified is obtained by acquiring vertical acceleration of a vehicle body, a front wheel and a rear wheel on a calibrated road surface;
step two: inputting the data collected in the step one into a well established road surface unevenness recognition algorithm to obtain road surface unevenness information;
the road surface unevenness recognition algorithm is established based on a Kalman filtering theory, and specifically comprises the following steps:
a) Establishing a semi-vehicle two-dimensional model considering a vehicle and an object to be carried, wherein the motion equation of the semi-vehicle model excited by a road surface is expressed as follows:
wherein M, C and K respectively represent a mass, damping and rigidity matrix of the structure;
and Y represents acceleration, velocity and displacement of the structure, respectively; s p Is a load distribution matrix corresponding to F (t), which represents an external force vector;
b) Selecting displacement and speed as state quantities on a calibrated road surface, selecting an acceleration sensor as an observed quantity, introducing a state vector X (t) and a measurement response vector Z (t) into a motion equation of a semi-vehicle model, and then respectively deducing a state equation and an observation equation of the system as follows:
X k+1 ＝A c X k +B c F k +w k (11)
Z k ＝GX k +JF k +v k (12)
wherein, w k And v k Respectively representing the uncertainty and measurement noise of the system;
X k ＝X(kDt),F k ＝F(kDt),Z k ＝Z(kDt),k＝1,...,N),A c ＝exp(AΔt),B c ＝[A c -I]A - 1 b; state variable set to
The response vector is Z = [ y ] 1 ,y 2 ,y 3 ,y 4 ,θ] T (ii) a The output impact matrix and the direct transmission matrix are defined as: g = [ S ] d -S a M -1 K S v -S a M -1 C],J＝[S a M -1 S p ]；
c) Introducing augmented state vectors according to the state equation and observation equation obtained in step b)
The obtained augmented state equation and observation equation are respectively:
wherein the content of the first and second substances,
G a ＝[G J]，
d) Applying a recursive prediction scheme to an augmented observation equation based on a Kalman filtering theory, updating and estimating by observation variables through time updating and measurement updating, and calculating measurement estimators, namely the vertical acceleration responses of a vehicle body, front wheels and rear wheels under a given state vector according to vehicle parameter conditions;
and (3) time updating process:
wherein prior estimates of the state vector and the error covariance are represented separately,
and (3) state updating process:
the error covariance matrix of the estimated values and the true values is updated as follows:
P k|k ＝P k|k-1 -L k G a P k|k-1 (19)
wherein, the kalman gain formula is:
the dynamic response of the vehicle obtained through the process is used for reversely deducing the road surface excitation u 1 (t) and u 2 (t) identifying the road surface irregularity information u 1 (t) and u 2 (t) respectively representing road surface excitations to the front and rear wheels; assuming that the front and rear wheels of the vehicle are identicalThe strips travelling in a straight line, whereby the road surface excitation u 1 (t) and u 2 (t) same, different excitation times, and therefore, u 1 (t) and u 2 The relationship in the time domain between (t) is expressed as:
the further technical scheme of the invention is as follows: in the first step, the data to be identified is acquired by mounting acceleration sensors at the bottom of the vehicle body, the centers of the front wheels and the rear wheels in advance, and acquiring vertical acceleration signals of the wheels during the driving process of the vehicle on a calibrated road surface.
The further technical scheme of the invention is as follows: in the second step, the establishment of the two-dimensional model of the semi-vehicle is as follows:
firstly, setting the transportation equipment to be placed on a middle line of longitudinal symmetry with the vehicle, and neglecting the vehicle rolling vibration;
then, simplifying the model into a two-dimensional plane model;
there are 6 degrees of freedom in the model, representing the motion of the suspension, body and equipment in the x and y directions, respectively; establishing a coordinate system on a moving vehicle, wherein the rigidity kt of a tire is involved, the rigidity of the tire is related to the road surface displacement u (t), and meanwhile, the damping of the tire is assumed to be ignored; parameters on each shaft of two suspension systems of an actual vehicle are combined, so that the following differential equation of motion with six degrees of freedom is obtained:
the formulas (1) to (6) are six-degree-of-freedom nonlinear coupling dynamic differential equation systems; in equation (1), θ 2 (t) and
solving after neglecting; when studying the vibration of vehicles and equipment, the solution and calculation with equations (2) - (5) are considered; wherein L is 1 Distance of the center of gravity of the vehicle to the rear wheels, L 2 Distance from the center of gravity of the vehicle to the front wheel, e vehicle mass eccentricity, m 1 Is the weight of the vehicle equipment, m 2 Is the vehicle body weight, m 3 ,m 4 Is the vehicle tire weight, I is the vehicle moment of inertia, k 1 ,k 2 As the transverse rigidity of the vehicle, k 3 As vertical stiffness of the vehicle, k 4 For vehicle suspension stiffness, k 5 For vehicle tire stiffness, c 1 ,c 2 For lateral damping of the vehicle, c 3 For vertical damping of the vehicle, c 4 Damping the vehicle suspension;
equations (1) - (6) are written in matrix form as equation (7), where:
u 1 (t) and u 2 (t) represents road surface excitations to the front and rear wheels, respectively, assuming that the front and rear wheels of the vehicle are travelling on the same straight line, the road surface excitation u is therefore 1 (t) and u 2 (t) are the same, but the timing of the activation is different. Therefore, u 1 (t) and u 2 The relationship in the time domain between (t) can be represented by:
advantageous effects
The invention has the beneficial effects that: the invention provides a road surface unevenness recognition method based on a Kalman filtering theory, 1) only one kind of measurement data such as an acceleration signal needs to be acquired, an acceleration sensor is simple to arrange, the hardware cost is low, and the operability is strong; 2) The Kalman filtering theory is utilized to carry out filtering processing on the acceleration signal in a time domain by adopting a recursion algorithm, a formula in a space state is established, information from different sensors can be easily brought into a vehicle, so that state prediction close to an actual state is obtained, the real-time computation amount is small, and the road surface unevenness recognition rate is improved; 3) The excitation acting on the system is simulated randomly through white noise filtering to reflect the actual road condition of the vehicle, and the problem solving capability of the vehicle under a random framework is highlighted. Meanwhile, the identification accuracy in actual use is improved by integrating the measured data and the simulation result for comparison; 4) The method can be used not only to predict the road excitation experienced by a vehicle at an early stage of vehicle design but also to calculate the response of the vehicle to any given vehicle speed.
Drawings
FIG. 1 is a diagram of a model of vehicle dynamics in accordance with an embodiment of the present invention;
FIG. 2 is a power spectrum of an E-grade road surface according to an embodiment of the present invention;
FIG. 3 is a graph of the dynamic response of a vehicle at 10m/s according to an example of the present invention;
FIG. 4 is a comparison of an identified road surface and a real road surface of an example of the present invention;
Detailed Description
The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
1.1. Collecting vertical acceleration of a vehicle body, a front wheel and a rear wheel on a calibrated road surface;
specifically, firstly, in order to measure the road surface unevenness, some actual data to be identified need to be acquired, acceleration sensors are mounted at the bottom of a vehicle body, the centers of a front wheel and a rear wheel in advance, and wheel vertical acceleration signals are acquired in the driving process of a vehicle.
1.2. And step two, inputting the collected data into a well established road surface unevenness recognition algorithm to obtain the road surface unevenness information. The road surface unevenness identification algorithm is established based on a Kalman filtering theory;
specifically, the road unevenness recognition algorithm is established by the following steps:
a) Establishing a semi-vehicle two-dimensional model considering a vehicle and an object to be carried, writing a motion differential equation considering the motion of a suspension, a vehicle body and equipment in the x and y directions, and converting the motion differential equation into a matrix form to obtain a motion equation of the semi-vehicle model;
when a certain device is transported, the vehicle is placed on a middle line of longitudinal symmetry with the vehicle, and the model can be simplified into a two-dimensional plane model because the vehicle has small rolling vibration in general.
There are 6 degrees of freedom in the model, representing the motion of the suspension, body and equipment in the x and y directions, respectively. A coordinate system is established on a moving vehicle, wherein the stiffness kt of the tire is involved, which is related to the road surface displacement u (t), while the damping of the tire is assumed to be negligible. There are typically two suspension systems in a real vehicle, but for ease of calculation we combine the parameters on each axle. Thereby obtaining the following differential equation of motion with six degrees of freedom:
the formulas (1) to (6) are six-degree-of-freedom nonlinear coupling dynamic differential equation systems. In the first equation, there is a nonlinear coupling term θ with respect to the vehicle pitch motion θ 2 (t) and
because the length of the vehicle body is about 10 meters, the pitching motion of the vehicle body in the actual driving test is far less than the vertical vibration of the vehicle body, and therefore theta is measured 2 (t) and
are omitted. Since the first equation is not coupled to the following five equations, the first equation can be solved separately. In studying the vibration of vehicles and equipment, the following five equations may be considered for solution and calculation. The parametric and physical meanings of the vehicle and equipment models are shown in table 1:
TABLE 1 model parameters
The equation of motion of the semi-vehicle model excited by the road surface can be expressed by the following formula:
where M, C and K represent the mass, damping and stiffness matrices of the structure, respectively.
And Y represents acceleration, velocity and displacement of the structure, respectively. S p Is a load distribution matrix corresponding to F (t), which represents an external force vector.
The above equations (1) to (6) can be written in the form of a matrix as in equation (7), where:
u 1 (t) and u 2 (t) represents road surface excitations to the front and rear wheels, respectively, and the road surface excitation u is therefore assumed to be the same for the front and rear wheels of the vehicle, which are travelling on the same straight line 1 (t) and u 2 (t) are the same, but the timing of the activation is different. Therefore, u 1 (t) and u 2 The relationship in the time domain between (t) can be represented by:
u 1 (t)＝u 2 (t-Δt),
b) Selecting displacement and speed as state quantities on a calibrated road surface, selecting an acceleration sensor as an observed quantity, introducing a state vector X (t) and a measurement response vector Z (t) into a motion equation of a semi-vehicle model, and then respectively deducing a state equation and an observation equation of the system;
by introducing state vectors
Formula (7) may be expressed in the form of formula (8):
wherein A and B are each:
considering the measured response vector Z (t), the linear combination of displacement, velocity, acceleration vectors is expressed as follows:
wherein S a ,S v And S d Respectively selection matrices for acceleration, velocity and displacement. Equation (8) can be expressed as:
Z(t)＝GX(t)+JF(t) (10)
wherein the output impact matrix and the direct transmission matrix are defined as:
G＝[S d -S a M -1 K S v -S a M -1 C],J＝[S a M -1 S p ]
the state equation and the observation equation of the system can be deduced to be respectively:
X k+1 ＝A c X k +B c F k +w k (11)
Z k ＝GX k +JF k +v k (12)
wherein w k And v k Representing the uncertainty of the system and the measurement noise, respectively.
X k ＝X(kDt),F k ＝F(kDt),Z k ＝Z(kDt),k＝1,...,N),A c ＝exp(AΔt),B c ＝[A c -I]A - 1 B, setting the state variable to be in the invention
The response vector is Z = [ y ] 1 ,y 2 ,y 3 ,y 4 ,θ] T 。
c) Introducing an augmented state vector based on the state equation and observation equation obtained in b)
Obtaining an augmented state equation and an observation equation;
F k+1 can be regarded as F k Adding a disturbance eta k ,
F k+1 ＝F k +η k (13)
By introducing an augmented state vector X a
The state equation and the observation equation which can be obtained by the augmentation are respectively:
wherein
G a ＝[G J],
d) Applying a recursive prediction scheme to an augmented observation equation based on a Kalman filtering theory, updating and estimating by observation variables through time updating (prediction) and measurement updating (correction), and calculating measurement estimators, namely the vertical acceleration responses of the vehicle body, the front wheels and the rear wheels under a given state vector according to parameter conditions given in table 1;
the variation of the known acceleration in the sampling period can be simulated by white Gaussian noise w with the mean value of zero and the variance of
Noise matrix
And
the general Kalman filter can be defined as a recursive linear state estimator, which is optimal in the meaning of minimum variance, and the minimum mean square error of the recursive linear state estimator is solved for the measured value and the predicted value at each moment by utilizing a recursive mode, so that more accurate optimal estimation is obtained. In this case, a recursive prediction scheme may be applied to Z k . Assume initial value
There, the calculation is performed by:
time update (prediction) procedure:
wherein prior estimates of the state vector and the error covariance are represented separately,
state update (correction) process:
the kalman gain formula is:
the Kalman gain is the proportion of the predicted minimum mean square error of the k time state in the medium error of the k time by using the k-1 time prediction, and the probability that the true value is close to the predicted value is higher when the proportion is higher.
From an observed variable Z k And updating estimation to obtain a posterior estimator of the state vector at the time k, wherein the posterior estimator is the latest state estimator, is the measurement estimator obtained by the invention, and is also the prior state estimator predicted next time. The state update formula is as follows:
the error covariance matrix of the estimated values and the true values is updated as follows:
P k|k ＝P k|k-1 -L k G a P k|k-1 (19)
the dynamic response of the vehicle obtained through the process can reversely deduce road surface excitation u 1 (t) and u 2 (t) identifying road surface irregularity information therefrom;
example (b):
referring to fig. 1, in this example, the vehicle is placed on the center line of longitudinal symmetry with the vehicle, and since the vehicle rolling vibration is generally small, the model can be simplified to a two-dimensional planar model as shown in fig. 1. There are 6 degrees of freedom in the model, representing suspension, body and equipment motion respectively. A coordinate system is established on a moving vehicle, wherein the stiffness kt of the tire is involved, which is related to the road surface displacement u (t), while the damping of the tire is assumed to be negligible.
The following is a specific embodiment using the proposed method, in which the data used is generated by simulation. Considering that the road surface evenness is a stable and Gaussian random process, the method has zero mean value and a random process of traversal, and the random input can reflect the actual road condition of the vehicle. Therefore, with white noise filtering to generate a large number of different road roughness signals, referring to ISO8608, the power spectral density of the road roughness can be fit as:
wherein n represents the spatial frequency, represents the number of cycles of the contained wave per meter, and has a unit of m -1 .n 0 ＝0.1m -1 Representing the spatial reference frequency. G q (n 0 ) The power spectral density is referred to as the power spectral density of the road flatness at the spatial frequency, which is related to the road surface level and is also called the road flatness coefficient. W =2 is the frequency index, i.e. the frequency of the diagonal line in log-log coordinates, which determines the frequency structure of the coarseness power spectral density. Considering that road roughness is a limited bandwidth noise, the time domain road roughness with the required road power spectral density can then be modeled by first order filtering with a specific white noise:
wherein n is 1 ＝0.01m -1 Denotes the lowest cut-off frequency, [ omega ] (t) denotes zero-mean white noise, u r (t) represents vertical excitation, v represents the form speed of the vehicle(v =10 m/s). The power spectrum of the class E road surface is shown in FIG. 2.
Under the Matlab environment, the method provided by the invention is applied to a road unevenness signal set generated by white noise filtering to respectively calculate the vertical acceleration response of a vehicle body, front wheels and rear wheels under the vehicle speed. The simulated sampling frequency was 200Hz and the vehicle dynamic response is shown in figure 3.
An important feature of the proposed method is how to determine the parameters, including the covariance and initial values. In the embodiment of the invention, the diagonal element of Q is set to [1e-4 1e-4 1e-2 1e-2 1e-4 1e-8 1e-8 1e-7 1e-7 1e-8]And the diagonal line element of R is set to [1e-4 1e-4 1e-2 1e-2 1e-4].P 0|-1 Is set to 5e-5. The method is characterized in that acceleration sensors are arranged at the bottom of a vehicle body, the centers of front wheels and rear wheels, vertical acceleration signals of the wheels are collected in the driving process of the vehicle, and then the algorithm is applied to measured data to obtain the dynamic response of the vehicle so as to identify the road surface unevenness information. The road profile in the above simulation case is compared, as shown in fig. 4. The figure shows that the road contour identification is relatively accurate, and the effectiveness of the method is proved.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.
Claims (2)
1. A road surface unevenness identification method based on a Kalman filtering theory is characterized by comprising the following specific steps:
the method comprises the following steps: acquiring actual data to be identified, wherein the actual data to be identified is obtained by acquiring the vertical acceleration of a vehicle body, a front wheel and a rear wheel on a calibrated road surface;
step two: inputting the data collected in the first step into a built road surface unevenness recognition algorithm to obtain road surface unevenness information;
the road surface unevenness recognition algorithm is established based on a Kalman filtering theory, and specifically comprises the following steps:
a) Establishing a semi-vehicle two-dimensional model considering a vehicle and an object to be carried, wherein the motion equation of the semi-vehicle model excited by a road surface is expressed as follows:
wherein M, C and K respectively represent a mass, damping and rigidity matrix of the structure;
and Y represents acceleration, velocity and displacement of the structure, respectively; s p Is a load distribution matrix corresponding to F (t), which represents an external force vector;
b) Selecting displacement and speed on a calibrated road surface as state quantities, selecting an acceleration sensor as observed quantities, introducing a state vector X (t) and a measurement response vector Z (t) into a motion equation of a semi-vehicle model, and respectively deducing a state equation and an observation equation of the system to be respectively:
X k+1 ＝A c X k +B c F k +w k (11)
Z k ＝GX k +JF k +v k (12)
wherein, w k And v k Respectively representing the uncertainty and the measurement noise of the system; x k ＝X(kDt),F k ＝F(kDt),Z k ＝Z(kDt),k＝1,...,N),A c ＝exp(AΔt),B c ＝[A c -I]A -1 B; state variable set to
The response vector is Z = [ y ] 1 ,y 2 ,y 3 ,y 4 ,θ] T (ii) a The output impact matrix and the direct transmission matrix are defined as: g = [ S ] d -S a M -1 K S v -S a M -1 C],J＝[S a M -1 S p ](ii) a t represents the time of day and t represents the time of day,
respectively representing a state transition matrix and a control matrix, S a ，S v And S d Selection matrices for acceleration, velocity and displacement, respectively;
c) Introducing augmented state vectors according to the state equation and observation equation obtained in step b)
The obtained augmented state equation and observation equation are respectively:
wherein the content of the first and second substances,
G a ＝[G J],
η k representing a disturbance;
d) Applying a recursive prediction scheme to an augmented observation equation based on a Kalman filtering theory, updating and estimating by observation variables through time updating and measurement updating, and calculating measurement estimators, namely the vertical acceleration responses of a vehicle body, front wheels and rear wheels under a given state vector according to vehicle parameter conditions;
and (3) time updating process:
wherein the content of the first and second substances,
and P k|k Respectively representing a priori estimates of the state vector and the error covariance,
and (3) state updating process:
the error covariance matrix of the estimated values and the true values is updated as follows:
P k|k ＝P k|k-1 -L k G a P k|k-1 (19)
wherein, the Kalman gain formula is:
r represents a matrix of observed noise;
the dynamic response of the vehicle obtained through the process is used for reversely deducing the road surface excitation u 1 (t) and u 2 (t) identifying the road surface irregularity information u 1 (t) and u 2 (t) respectively representing road surface excitations to the front and rear wheels; assuming that the front and rear wheels of the vehicle travel on the same straight line, the road excitation u is therefore 1 (t) and u 2 (t) same, different excitation times, and therefore, u 1 (t) and u 2 The relationship in the time domain between (t) is expressed as:
u 1 (t)＝u 2 (t-Δt),
in the second step, the establishment of the two-dimensional model of the semi-vehicle is as follows:
firstly, setting the transportation equipment to be placed on a middle line of longitudinal symmetry with the vehicle, and neglecting the vehicle rolling vibration;
then, simplifying the model into a two-dimensional plane model;
there are 6 degrees of freedom in the model, representing the motion of the suspension, body and equipment in the x and y directions, respectively; establishing a coordinate system on a moving vehicle, wherein the rigidity kt of a tire is involved, the rigidity of the tire is related to the road surface displacement u (t), and meanwhile, the damping of the tire is assumed to be ignored; parameters on each shaft of two suspension systems of an actual vehicle are combined, so that the following differential equation of motion with six degrees of freedom is obtained:
the formulas (1) to (6) are six-degree-of-freedom nonlinear coupling dynamic differential equation systems; in equation (1), θ 2 (t) and
solving after neglecting; when studying the vibration of vehicles and equipment, the solution and calculation with equations (2) - (5) are considered; wherein L is 1 Is a vehicleDistance of vehicle center of gravity to rear wheel, L 2 Distance from the center of gravity of the vehicle to the front wheel, e vehicle mass eccentricity, m 1 Is the weight of the vehicle equipment, m 2 Is the vehicle body weight, m 3 ,m 4 Is the vehicle tire weight, I is the vehicle moment of inertia, k 1 ,k 2 As the transverse rigidity of the vehicle, k 3 As vertical stiffness of the vehicle, k 4 For vehicle suspension stiffness, k 5 For vehicle tire stiffness, c 1 ,c 2 For lateral damping of the vehicle, c 3 For vertical damping of the vehicle, c 4 Damping the vehicle suspension;
equations (1) - (6) are written in matrix form as equation (7), where:
2. the Kalman filtering theory-based road surface irregularity identification method according to claim 1, characterized in that: in the first step, the data to be identified is acquired by mounting acceleration sensors at the bottom of the vehicle body, the centers of the front wheels and the rear wheels in advance, and acquiring vertical acceleration signals of the wheels during the driving process of the vehicle on a calibrated road surface.
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