CN110184885B - Method for testing pavement evenness based on smart phone - Google Patents

Method for testing pavement evenness based on smart phone Download PDF

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CN110184885B
CN110184885B CN201910369899.7A CN201910369899A CN110184885B CN 110184885 B CN110184885 B CN 110184885B CN 201910369899 A CN201910369899 A CN 201910369899A CN 110184885 B CN110184885 B CN 110184885B
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张鹏
张丽丽
邬冰
徐斌
吕培芹
陈莎莎
黄建平
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Nanjing Jiaoke Shuzhi Technology Development Co.,Ltd.
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Abstract

The invention belongs to the technical field of road maintenance detection, and particularly relates to a method for testing road flatness based on a smart phone. The built-in equipment of the smart phone comprises a triaxial acceleration sensor, a gyroscope, a magnetic inductor, an azimuth sensor, GPS sensing equipment and data acquisition equipment, and the specific method comprises the following steps: acquiring acceleration data; step (2) acceleration data calibration; step (3) smooth denoising of acceleration data; step (4) a space-time coordinate conversion algorithm; step (5), establishing a BP neural network calculation model; the BP neural network model adopts a three-layer neural network, sample data input vectors are acceleration and vehicle speed, and output vectors are international flatness index IRI. The method utilizes a BP neural network method to establish regression prediction models of acceleration values and IRI under different detection speeds, and optimizes the models according to different application conditions. The model has high prediction precision and good stability, and can accurately reflect the relation between the acceleration value and the IRI.

Description

Method for testing pavement evenness based on smart phone
Technical Field
The invention belongs to the technical field of road maintenance detection, and particularly relates to a method for testing road flatness based on a smart phone.
Background
With the increase of road operation time, the service performance of the asphalt pavement is increasingly reduced, so that the running speed, the running safety and the running comfort of a vehicle are seriously influenced. In order to ensure the driving performance of the road surface, a road manager needs to timely and accurately grasp the road condition.
At present, conventional road detection is mainly carried out by methods such as a 3m straight ruler, a vehicle-mounted bump accumulation instrument, a continuous flatness meter vehicle-mounted bump accumulation instrument, a laser section instrument, a multifunctional road detection vehicle and the like, and a method combining daily inspection and periodic detection is mostly adopted, so that the accuracy, the cost, the timeliness and the like of a test result cannot be considered at all.
Vehicle occupants are the first time acquirers of road condition information and are the most important recipients of road conditions. Thus, a large number of vehicle occupants can serve as an important "tool" for obtaining large data on road conditions.
At present, the smart phone is gradually becoming a necessary product widely used by drivers. The smart phone not only has a simple communication function, but also is an intelligent terminal with strong external sensing capability and mathematical calculation capability. The smart phone is generally provided with a three-axis acceleration sensor, a gyroscope and a gravity sensor, and the three-axis acceleration sensor, the gyroscope and the gravity sensor can effectively feed back the motion state of the vehicle in the running process. The mobile phone is characterized by portability, so that the coordination consistency of the mobile phone and the motion state of the vehicle is determined, and a precondition is provided for recording the motion state of the vehicle.
In the prior art, there are also methods for acquiring data by using a mobile terminal such as a mobile phone to obtain flatness, for example, patent documents CN2014103798494, CN2015107475275 and CN2016111735138, but some of the above patents require the use of other auxiliary devices, and the data acquisition and processing means are complex, and the accuracy of the obtained effect is not high.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for testing the road flatness based on a smart phone, establishing a relation model of an acceleration signal and the road flatness based on a BP neural network method, and overcoming the problems of complicated process and low testing precision in the prior art.
The technical solution for realizing the purpose of the invention is as follows:
a method for testing pavement evenness based on a smart phone comprises the following specific steps that the built-in equipment of the smart phone comprises a three-axis acceleration sensor, a gyroscope, a magnetic inductor, an azimuth sensor, GPS sensing equipment and data acquisition equipment:
step (1) acceleration data acquisition: recording acceleration data of vehicle motion behaviors by using data acquisition equipment, wherein the acceleration data are digital discrete sampling signals, and the numerical values are divided into X, Y, Z three axes;
step (2) acceleration data calibration: calculating a rotation matrix R by utilizing the three-axis acceleration data and the magnetic induction data, and converting the three-axis acceleration data into a world coordinate system from a standard coordinate system of the smart phone by the rotation matrix R;
step (3) smooth denoising of acceleration data;
step (4), a space-time coordinate conversion algorithm: converting the displacement amount from a spatial domain to a time domain;
step (5), establishing a BP neural network calculation model; the BP neural network model adopts a three-layer neural network, the dimension of the number of nodes of an input layer is determined to be 2, the dimension of the number of nodes of an output layer is determined to be 1, sample data input vectors are acceleration and vehicle speed, and output vectors are international flatness index IRI.
Further, the standard coordinate system of the intelligent mobile phone in the step (2) is as follows: the Y axis is tangent to the ground of the current position of the smart phone and points to the north; the Z-axis direction points to the sky and is vertical to the ground; the X-axis is perpendicular to the Y-Z plane and points in the east-ward direction.
Further, the calibration formula in the step (2) is
ggv(x′，y′，z′)＝ggv(x，y，z)R
Wherein g isdv(x, y, z) is the smartphone three-axis acceleration, g, collected at a timegv(x ', y ', z ') is the three-axis acceleration converted to the world coordinate system by the rotation matrix R, which is the rotation matrix.
Further, the rotation matrix of X, Y, Z in three directions is Rot (θ)x)、Rot(θy)、Rot(θz) The angle of rotation of the smartphone about the X axis is called the pitch angle, and is denoted as θy(ii) a The angle of rotation about the Y axis is called the roll angle and is denoted as θz(ii) a The angle of rotation about the Z axis is called the azimuth angle, and is denoted as θxBy rotating the matrix Rot (θ)y) Calibrating the positive Y-axis direction to the north orientation of the geomagnetic field, where Rot (theta)x)、Rot(θy)、Rot(θz) As shown in formulas (1), (2) and (3),
Figure BDA0002049555880000021
Figure BDA0002049555880000022
Figure BDA0002049555880000031
further, the directions of the X axis and the Y axis in the world coordinate system do not represent the lateral acceleration and the longitudinal acceleration of the vehicle, and the vehicle needs to rotate around the Z axis to the initial azimuth again, and the rotation matrix R should satisfy:
R＝Rinitial value×Rot(θz)-1 (4)
If the angle of the Z-axis rotation satisfies equation (3), Rot (θ)z)-1Is shown as
Figure BDA0002049555880000032
And satisfy
Rot(θz)Rot(θz)-1＝1 (6)。
Further, in the step (3), a moving average filtering method is adopted to perform smooth filtering processing on the data, and the moving average filtering method is realized by a recursive algorithm.
Further, the moving average filtering method specifically includes:
for a given time response sequence:
x(0)＝[x(0)(1)，x(0)(2)，，… x(0)(n)] (8)
wherein n is the number of data;
performing a moving average process, and processing the endpoint data according to the following formula:
Figure BDA0002049555880000033
the intermediate point data is processed by the following formula:
Figure BDA0002049555880000034
furthermore, during the actual movement of the vehicle A, the vehicle runs on the ground at a speed v, the ground is taken as a reference object, the displacement of the vehicle is accumulated according to the formula (12),
Figure BDA0002049555880000041
in the formula: pxIs a discretized displacement sequence; w is the vehicle length.
Further, the vehicle a runs on an infinitely long train B running at a constant speed V,
if the vehicle A and the train use B as a motion reference coordinate system, the displacement x of the A relative to the B is considered, and the time T of the vehicle edge of the vehicle A and the train B reaching the same point of the earth coordinate system is calculatediAnd T0The calculation method is as follows:
the A and B movement methods are the same, then Ti<T0Therefore, it is
Figure BDA0002049555880000042
Therefore, it is
Figure BDA0002049555880000043
The displacement of a relative to B during this time period is:
Figure BDA0002049555880000044
if the moving methods of the vehicle A and the train B are opposite, Ti>T0Therefore, it is
Figure BDA0002049555880000045
Therefore, it is
Figure BDA0002049555880000046
The displacement of a relative to B during this time period is:
Figure BDA0002049555880000047
further, the specific algorithm of the BP neural network calculation model is as follows:
the input of the model input node is xjThe output of the model is then represented as:
Figure BDA0002049555880000048
in the formula: omegaijIs the connection weight; thetaiIs the node threshold.
The output of the BP neural network model output node is as follows:
Figure BDA0002049555880000051
in the formula: t isijIs the connection weight; thetalIs a threshold value for the node(s),
if the expected output of the output node is tlThen all sample errors are:
Figure BDA0002049555880000052
epsilon is the allowable error of the data,
one of the sample errors is:
Figure BDA0002049555880000053
in the formula: p is the number of samples; n is the number of output nodes, K is the number of sample data
The error formula is expressed by:
δl＝(tl-Ol)·Ol·(1-Ol) (23)
δlis the partial derivative of the error function to each neuron in the output layer,
the weight correction formula is as follows:
Tli(k+1)＝Tli(k)+ηδlyi (24)
in the formula: k is the iteration number, eta is the learning rate between (0,1),
the threshold correction formula is as follows:
θl(k+1)＝θl(k)+η'δ'l (25)
the hidden node error formula is as follows:
Figure BDA0002049555880000054
δl'is the partial derivative of the error function to each neuron in the middle hidden layer of the network,
the weight correction formula is as follows:
ωij(k+1)＝ωij(k)+η'δ'ixj (27)
the threshold correction formula is as follows:
θi(k+1)＝θi(k)+η'δ'i (28)
selecting an acceleration value as an independent variable, taking IRI as a dependent variable, and carrying out normalization processing on the IRI and the dependent variable by using the following formula:
X＝(λmax-λmin)×(x-xmin)/(xmax-xmin)+λmin (29)
in the formula: x is original data; x is normalized data; lambda [ alpha ]maxAnd λminA mapped range parameter.
Compared with the prior art, the invention has the following remarkable advantages:
(1) through the deep development of the Android operating system and the sensors, the acquisition of acceleration signals by the Android system acceleration sensor is realized.
(2) Through extraction and removal of noise data and smoothing processing of the detection data by using a moving average algorithm, singularity of abnormal points is removed and weakened, a mathematical relation between the abnormal points and other detection data is established, and inconsistency of the detection data is solved.
(3) And (3) establishing a regression prediction model of the acceleration value and the IRI under different detection speeds by using a BP neural network method, and optimizing the model according to different application conditions. The model has high prediction precision and good stability, and can accurately reflect the relation between the acceleration value and the IRI.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a schematic view of an acceleration test angle of the present application.
FIG. 2 is a graph showing acceleration signal fluctuations when the vehicle is stationary.
FIG. 3 is a diagram showing the fluctuation of an acceleration signal when a vehicle is stationary after being subjected to a moving average filtering process.
FIG. 4 displacement measurement of a stationary moving object.
FIG. 5 is a diagram of a neural network model architecture of the present application.
FIG. 6 shows the mean square error of the prediction model of the present application.
FIG. 7 illustrates a BP neural network model prediction error distribution of the present application.
Detailed Description
The application relates to a method for testing pavement evenness based on a smart phone, wherein built-in equipment of the smart phone comprises a triaxial acceleration sensor, a gyroscope, a magnetic inductor, an azimuth sensor and GPS sensing equipment, and data acquisition equipment is manufactured in a fitting mode and used for acquiring triaxial acceleration values generated in the driving process of a vehicle and uploading the triaxial acceleration values.
The vehicle motion belongs to irregular motion, so the vehicle motion behavior is researched by using a pattern analysis method.
Pattern analysis method: when the object moves irregularly, the acceleration of the object is the motion acceleration of the object besides the gravity acceleration, the spatial orientation of the object cannot be obtained by calculating the distribution of values on three axes, but the sensor data can be subjected to pattern analysis, and the motion behavior of the object can be classified and recognized.
The method comprises the following specific steps:
(1) acceleration data acquisition
And a data reading program is programmed into the mobile phone, the acceleration data of the vehicle motion behavior is recorded, and then the acceleration data is sent to a background for analysis. The acceleration sensor data provided by the mobile phone is a digital discrete sampling signal, and the numerical value is divided into X, Y, Z three axes.
(2) Acceleration data calibration
The rotation matrix R can be calculated by utilizing the three-axis acceleration data and the magnetic induction data, and can convert the standard coordinate system of the smart phone into a World Coordinate System (WCS). WCS is an orthonormal basis whose coordinates are described as: the Y axis is tangent to the ground at the current position of the equipment and points to the positive north direction; the Z-axis direction points to the sky and is vertical to the ground; the X-axis is perpendicular to the Y-Z plane and points in the east-ward direction.
And calibrating the acceleration data through the acceleration sensor and the magnetic inductor. As shown in fig. 1, the angle of rotation of the Android smartphone around the X axis is called a pitch angle, and is denoted as θ y; the angle of rotation around the Y axis is called the roll angle and is marked as theta z; the angle of rotation about the Z axis is called the azimuth angle, and is denoted as θ x. In the world coordinate system, rotation matrices formed around the X-axis, the Y-axis, and the Z-axis are expressed as expression (1), expression (2), and expression (3), respectively, where θ represents the magnitude of the angle of rotation around the three axes.
Figure BDA0002049555880000071
Figure BDA0002049555880000072
Figure BDA0002049555880000073
The positive direction of the Y axis can be calibrated to the true north direction of the geomagnetic field through the rotation matrix R, but the directions of the X axis and the Y axis in the WCS system do not represent the transverse acceleration and the longitudinal acceleration of the automobile, the automobile needs to rotate around the Z axis again to reach the initial azimuth angle, and the rotation matrix R should meet the following requirements:
R＝Rinitial value×Rot(θz)-1 (4)
If the angle theta of the Z-axis rotation satisfies equation (3), Rot (theta)z)-1Is shown as
Figure BDA0002049555880000081
And satisfy
Rot(θz)Rot(θz)-1＝1 (6)
Suppose that the three-axis acceleration of the smart phone collected at a certain moment is recorded as gdv(x, y, z) three-axis acceleration converted to WCS by rotating matrix R is recorded as ggv(x ', y ', z '), then the calibration formula is:
ggv(x′，y′，z′)＝ggv(x，y，z)R (7)
(3) acceleration data smoothing denoising
Random noise is generated during the actual driving process of the vehicle, but the noise intensity is difficult to determine, and the noise intensity varies according to the road condition and the driving speed. The low-frequency noise generated by the vibration inside the vehicle body can generate noise interference on the acceleration data collected by the smart phone. The fluctuation phenomenon of the acquired acceleration signal occurs even when the vehicle is stationary, as shown in fig. 2.
The data is smoothed by adopting a moving average filtering technology.
The moving average filtering method can be implemented by a recursive algorithm, for a given time response sequence:
x(0)＝[x(0)(1),x(0)(2),,… x(0)(n)] (8)
and n is the number of data.
The moving average processing is carried out on the data, and the endpoint data is processed by the following formula:
Figure BDA0002049555880000082
the intermediate point data is processed by the following formula:
Figure BDA0002049555880000083
the acceleration data after the moving average filtering process is shown in fig. 3.
(4) Space-time coordinate conversion algorithm
The space is measured in time, and for a stationary moving object, the displacement can be measured either in a spatial or temporal graduation, as shown in fig. 4
As can be seen from fig. 5, the object displacement is:
Figure BDA0002049555880000091
in the formula: x is the object displacement; v is the speed of the object movement; ptIs a discretized time series.
During the actual movement of the vehicle, the vehicle a travels on the ground at a speed v, and the displacement of the vehicle a is accumulated as in equation (12) with the ground as a reference.
Figure BDA0002049555880000092
In the formula: pxIs a discretized displacement sequence; w is the vehicle length.
Another complication is that the vehicle a runs on an infinitely long train B running at a constant speed V,
if the vehicle A and the train are in a motion reference coordinate system with B, the displacement x of A relative to B is considered. In this case, the time Ti and T0 for the vehicle edge of the vehicle a and the train B to reach the same point in the geodetic coordinate system are calculated in sequence as follows: the motion method of B is the same, Ti is less than T0, so
Figure BDA0002049555880000093
Therefore, it is
Figure BDA0002049555880000094
The displacement of a relative to B during this time period is:
Figure BDA0002049555880000095
if the moving methods of the vehicle A and the train B are opposite, Ti>T0Therefore, it is
Figure BDA0002049555880000096
Therefore, it is
Figure BDA0002049555880000097
The displacement of a relative to B during this time period is:
Figure BDA0002049555880000098
thus, a translation of the displacement from the spatial domain to the temporal domain is achieved.
(5) BP neural network calculation model establishing process
A BP neural network method is utilized to establish a relation model of acceleration and flatness. The BP neural network is a multi-layer feed-forward algorithm with one-way propagation, and the internal relation between input data and output data is established through a transfer function, so that the arbitrary nonlinear mapping from data input to data output is realized.
The BP neural network algorithm is as follows:
the input of the model input node is xjThe output of the model is then represented as:
Figure BDA0002049555880000101
in the formula: omegaijIs the connection weight; thetaiIs the node threshold.
The output of the BP neural network model output node is as follows:
Figure BDA0002049555880000102
in the formula: t isijIs the connection weight; thetalIs the node threshold.
If the expected output of the output node is tlThen all sample errors are:
Figure BDA0002049555880000103
ε is the allowable error.
One of the sample errors is:
Figure BDA0002049555880000104
in the formula: p is the number of samples; n is the number of output nodes, K is the number of sample data
The error formula is expressed by:
δl＝(tl-Ol)·Ol·(1-Ol) (23)
δ1is the partial derivative of the error function to each neuron in the output layer.
The weight correction formula is as follows:
Tli(k+1)＝Tli(k)+ηδlyi (24)
in the formula: k is the iteration number, and eta is the value of the learning rate between (0, 1).
The threshold correction formula is as follows:
θl(k+1)＝θl(k)+η'δ'l (25)
the hidden node error formula is as follows:
Figure BDA0002049555880000111
δ1'is the partial derivative of the error function to each neuron in the middle hidden layer of the network.
The weight correction formula is as follows:
ωij(k+1)＝ωij(k)+η'δ'ixj (27)
the threshold correction formula is as follows:
θi(k+1)＝θi(k)+η'δ'i (28)
selecting an acceleration value as an independent variable, taking IRI as a dependent variable, and carrying out normalization processing on the IRI and the dependent variable by using the following formula:
X＝(λmax-λmin)×(x-xmin)/(xmax-xmin)+λmin (29)
in the formula: x is original data; x is normalized data; lambda [ alpha ]maxAnd λminThe range parameter of the mapping, set herein as λmax＝1，λmin＝-1。
The BP neural network model adopts a three-layer neural network, sample data input vectors are acceleration data and test vehicle speed, and output vectors are international flatness index IRI, so that the dimension of the number of nodes of an input layer is determined to be 2, and the dimension of the number of nodes of an output layer is determined to be 1. And selecting the number of the hidden layer nodes through trial algorithm, and finally selecting the number of the hidden layer nodes as 5 through multiple trial comparison. And training acceleration sample data by adopting a momentum BP algorithm, and stopping the algorithm when the learning error is less than 0.001 or the training times reach 10000. The model structure of the BP neural network is shown in FIG. 5.
The BP neural network model is used for calculating and predicting the international flatness index IRI, and the mean square error of the model is calculated, and the calculation result is shown in fig. 6.
As can be seen from the mean square error of model fitting in FIG. 6, the maximum value of the mean square error of the BP neural network model is 0.60, the minimum value is only 0.01, and the average value is 0.32. Therefore, the BP neural network method can give consideration to all data, has higher fitting precision, avoids the phenomena of over-fitting and under-fitting, and can better reflect the relation between acceleration and IRI.
The model prediction error is analyzed for the accuracy of the model calculation. And comparing the IRI measured data with the IRI prediction result of the model. The error analysis result of the BP neural network model is shown in FIG. 7.
Compared with the measured data, the maximum error value of the BP neural network method is 28.98%, the minimum error value is 0.18%, the average error value is 9.75%, and the prediction data has certain fluctuation. In the calculation process, the BP neural network method has smaller prediction errors at a plurality of points and relatively better stability because the number of hidden layer nodes is continuously adjusted. The BP neural network model can effectively solve the problems of large samples and nonlinearity in the text and has strong popularization capability.

Claims (8)

1. A method for testing pavement evenness based on a smart phone is characterized in that built-in equipment of the smart phone comprises a three-axis acceleration sensor, a gyroscope, a magnetic inductor, an orientation sensor, GPS sensing equipment and data acquisition equipment, and the specific method comprises the following steps:
step (1) acceleration data acquisition: recording acceleration data of vehicle motion behaviors by using data acquisition equipment, wherein the acceleration data are digital discrete sampling signals, and the numerical values are divided into X, Y, Z three axes;
step (2) acceleration data calibration: calculating a rotation matrix R by utilizing the three-axis acceleration data and the magnetic induction data, and converting the three-axis acceleration data into a world coordinate system from a standard coordinate system of the smart phone by the rotation matrix R;
step (3) smooth denoising of acceleration data; carrying out smooth filtering processing on the data by adopting a moving average filtering method, wherein the moving average filtering method is realized by a recursive algorithm; the moving average filtering method specifically comprises the following steps:
for a given time response sequence:
x(0)＝[x(0)(1),x(0)(2),,…x(0)(n)] (8)
wherein n is the number of data;
performing a moving average process, and processing the endpoint data according to the following formula:
Figure FDA0002975673660000011
the intermediate point data is processed by the following formula:
Figure FDA0002975673660000012
step (4), a space-time coordinate conversion algorithm: converting the displacement amount from a spatial domain to a time domain;
step (5), establishing a BP neural network calculation model; the BP neural network model adopts a three-layer neural network, the dimension of the number of nodes of an input layer is determined to be 2, the dimension of the number of nodes of an output layer is determined to be 1, sample data input vectors are acceleration and vehicle speed, and output vectors are international flatness index IRI.
2. The method according to claim 1, wherein the smart phone standard coordinate system in step (2) is: the Y axis is tangent to the ground of the current position of the smart phone and points to the north; the Z-axis direction points to the sky and is vertical to the ground; the X-axis is perpendicular to the Y-Z plane and points in the east-ward direction.
3. The method of claim 2, wherein the calibration formula in step (2) is
ggv(x′，y′，z′)＝ggv(x，y，z)R
Wherein g isdv(x, y, z) is the smartphone three-axis acceleration, g, collected at a timegv(x ', y ', z ') is the three-axis acceleration converted to the world coordinate system by the rotation matrix R, which is the rotation matrix.
4. The method of claim 3, wherein the X, Y, Z rotation matrices for three directions are Rot (θ)x)、Rot(θy)、Rot(θz) The angle of rotation of the smartphone about the X axis is called the pitch angle, and is denoted as θy(ii) a The angle of rotation about the Y axis is called the roll angle and is denoted as θz(ii) a The angle of rotation about the Z axis is called the azimuth angle, and is denoted as θxBy rotating the matrix Rot (θ)y) Calibrating the positive Y-axis direction to the north orientation of the geomagnetic field, where Rot (theta)x)、Rot(θy)、Rot(θz) As shown in formulas (1), (2) and (3),
Figure FDA0002975673660000021
Figure FDA0002975673660000022
Figure FDA0002975673660000023
5. the method of claim 4, wherein the directions of the X-axis and the Y-axis in the world coordinate system do not represent the lateral and longitudinal acceleration of the vehicle, and the rotation matrix R should satisfy the following requirement:
R＝Rinitial value×Rot(θz)-1 (4)
If the angle of the Z-axis rotation satisfies equation (3), Rot (θ)z)-1Is shown as
Figure FDA0002975673660000024
And satisfy
Rot(θz)Rot(θz)-1＝1 (6)。
6. Method according to claim 1, characterized in that during the actual movement of the vehicle A, the vehicle is travelling on the ground at a speed v, the displacement of the vehicle is accumulated according to equation (12) with reference to the ground,
Figure FDA0002975673660000025
in the formula: pxIs a discretized displacement sequence; w is the vehicle length.
7. Method according to claim 1, characterized in that the vehicle A is travelling on an infinitely long train B travelling at a constant velocity V,
if the vehicle A uses the train B as a motion reference coordinate system, the displacement x of the vehicle A relative to the vehicle B is considered, and the time T of the vehicle edge of the vehicle A and the vehicle edge of the train B reaching the same point of the earth coordinate system is calculatediAnd T0The calculation method is as follows:
the A and B movement methods are the same, then Ti<T0Therefore, it is
Figure FDA0002975673660000031
Therefore, it is
Figure FDA0002975673660000032
The displacement of a relative to B during this time period is:
Figure FDA0002975673660000033
if the moving methods of the vehicle A and the train B are opposite, Ti>T0Therefore, it is
Figure FDA0002975673660000034
Therefore, it is
Figure FDA0002975673660000035
The displacement of a relative to B during this time period is:
Figure FDA0002975673660000036
8. the method of claim 1, wherein the BP neural network computational model specific algorithm is as follows:
the input of the model input node is xjThe output of the model is then represented as:
Figure FDA0002975673660000037
in the formula: omegaijIs the connection weight; thetaiIs a node threshold;
the output of the BP neural network model output node is as follows:
Figure FDA0002975673660000038
in the formula: t isijIs the connection weight; thetalIs a threshold value for the node(s),
if the expected output of the output node is tlThen all sample errors are:
Figure FDA0002975673660000041
epsilon is the allowable error of the data,
one of the sample errors is:
Figure FDA0002975673660000042
in the formula: p is the number of samples; n is the number of output nodes, K is the number of sample data
The error formula is expressed by:
δl＝(tl-Ol)·Ol·(1-Ol) (23)
δ1is the partial derivative of the error function to each neuron in the output layer,
the weight correction formula is as follows:
Tli(k+1)＝Tli(k)+ηδlyi (24)
in the formula: k is the iteration number, eta is the learning rate between (0,1),
the threshold correction formula is as follows:
θl(k+1)＝θl(k)+η'δ'l (25)
the hidden node error formula is as follows:
Figure FDA0002975673660000043
δl' is the partial derivative of the error function to each neuron in the middle hidden layer of the network,
the weight correction formula is as follows:
ωij(k+1)＝ωij(k)+η'δ'ixj (27)
the threshold correction formula is as follows:
θi(k+1)＝θi(k)+η'δ'i (28)
selecting an acceleration value as an independent variable, taking IRI as a dependent variable, and carrying out normalization processing on the IRI and the dependent variable by using the following formula:
X＝(λmax-λmin)×(x-xmin)/(xmax-xmin)+λmin (29)
in the formula: x is original data; x is normalized data; lambda [ alpha ]maxAnd λminA mapped range parameter.
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