CN113326975B - Ultrahigh prediction method for track irregularity based on random oscillation sequence gray model - Google Patents

Ultrahigh prediction method for track irregularity based on random oscillation sequence gray model Download PDF

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CN113326975B
CN113326975B CN202110493436.9A CN202110493436A CN113326975B CN 113326975 B CN113326975 B CN 113326975B CN 202110493436 A CN202110493436 A CN 202110493436A CN 113326975 B CN113326975 B CN 113326975B
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谢勇君
黄佳滨
贺志超
黎晨
凡鸿儒
殷怡
严冬松
武建华
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Abstract

The invention discloses a random oscillation sequence gray model-based track irregularity ultrahigh prediction method, which comprises the following steps: a data preprocessing step: carrying out mean value processing on the detected height deviations of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence; a preliminary prediction step: carrying out random oscillation sequence gray prediction based on a gray model to obtain a preliminary prediction height deviation; and a prediction correction step: correcting the preliminary predicted height residual error based on the height residual error average value to obtain a corrected height residual error, and performing normalization processing; and (3) optimizing an Elman neural network: optimizing the initial weight and the threshold of the Elman neural network through the ant lion algorithm to further obtain an optimized Elman neural network; ultra-high prediction step: and obtaining an orbit prediction correction height residual error based on the optimized Elman neural network. The method overcomes the defect of non-ideal prediction results of the random oscillation sequence by combining the random oscillation sequence gray model and the Elman neural network, so that the ultrahigh prediction results are more accurate.

Description

Ultrahigh prediction method for track irregularity based on random oscillation sequence gray model
Technical Field
The invention relates to the field of track detection, in particular to a random oscillation sequence gray model-based track irregularity ultrahigh prediction method.
Background
The detection of the running safety condition of the urban rail transit is an important part for guaranteeing the running of the rail, the existing method can carry out dynamic accurate detection on the parameters of the rail, but how to analyze and predict the quality of the rail from the data detected on the rail is very important for the research on the rail detection.
Most of the current researches are used for predicting the comprehensive quality TQI of the track, and from the experimental result, the prediction of the comprehensive quality TQI is more accurate by a combination method of gray prediction and a neural network;
the super-high value is different from TQI which is a random oscillation sequence, but the traditional grey prediction is only suitable for data types with exponential growth, the prediction effect on the random oscillation sequence is poor, and the variation trend of the sequence cannot be fitted, so that the error of the prediction result on the random oscillation sequence is larger.
Disclosure of Invention
In order to overcome the defects and shortcomings of the prior art, the invention provides a random oscillation sequence gray model-based track irregularity ultrahigh prediction method, which realizes the initial prediction of an ultrahigh sequence and can accurately predict the variation trend of the ultrahigh sequence and the attached ultrahigh sequence.
The invention also provides a system for predicting the track irregularity based on the random oscillation sequence gray model.
In order to achieve the first object, the invention adopts the following technical scheme:
a random oscillation sequence gray model-based track irregularity ultrahigh prediction method comprises the following steps:
a data preprocessing step: carrying out mean value processing on the detected height deviation of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
a preliminary prediction step: performing random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain a preliminary prediction height deviation;
and a prediction correction step: obtaining a preliminary predicted height residual error based on the preliminary predicted height deviation and the original data, calculating a height residual error average value, correcting the preliminary predicted height residual error based on the height residual error average value to obtain a corrected height residual error, and performing normalization processing on the preliminary predicted height residual error and the corrected height residual error;
and (3) optimizing an Elman neural network: dividing a training set and a test set based on the preliminary prediction height residual error and the correction height residual error, building an Elman neural network, training based on the preliminary prediction height residual error and the correction height residual error of the training set, and optimizing an initial weight and a threshold of the Elman neural network through an ant lion algorithm to obtain an optimized Elman neural network;
ultra-high prediction step: and inputting the preliminary prediction height residual error based on the optimized Elman neural network to obtain the orbit prediction correction height residual error.
As a preferred technical solution, the data preprocessing step specifically includes: and acquiring the height deviation of the preset interval at equal detection time intervals, and carrying out average value processing on the height deviation to obtain the average height deviation representing the interval.
As a preferred technical solution, the preliminary prediction step specifically includes the following steps:
transformation of random oscillation sequence:
detecting and detecting the detection sections at the same time to obtain an equidistant average height deviation sequence, wherein the equidistant average height deviation sequence is set as follows: x(0)＝{X(0)(1),X(0)(2)，…，X(0)(n)}；
Translating the equidistant average height deviation sequence to a full value, and setting the following parameters:
Max＝max{x(0)(k)|k,k∈{1,2,…,n}}；
Min＝min{x(0)(k)|k,k∈{1,2,…,n}}；
Figure GDA0003649373790000021
max represents the maximum value in the original equidistant average height deviation sequence, Min represents the minimum value in the original equidistant average height deviation sequence, T represents the maximum oscillation ratio of the original equidistant average height deviation sequence, and n is the maximum value of the sequence;
the sequence obtained by performing accelerated exponential transformation on the equidistant average height deviation sequence is a monotonically increasing height deviation sequence, namely:
XD1＝{x(1)d1,x(2)d1,…,x(n)d1}；
wherein x (k) d1K is 1,2,3 … n, which is the k-th monotonically increasing height deviation value after the acceleration exponential transformation;
to XD1And performing geometric mean generation transformation on the sequence to obtain a geometric mean processing height deviation sequence which keeps monotonous increase but the increase amplitude is reduced, namely an ideal height deviation sequence, namely:
XD2＝{x(1)d2,x(2)d2,…,x(n)d2}；
x(k)d2the k-th geometric mean processing height deviation value is defined as k, wherein k is 1, …, n is a positive integer;
judging the grade ratio:
Figure GDA0003649373790000031
if the stage ratio k (i) is in the interval
Figure GDA0003649373790000032
If so, the ideal height deviation sequence is directly used for a prediction model;
if the step ratio k (i) is not satisfied
Figure GDA0003649373790000033
Selecting a proper translation coefficient z to carry out integral translation on the sequence so as to meet the level ratio k (i) in the interval
Figure GDA0003649373790000034
The method comprises the following steps:
Figure GDA0003649373790000035
wherein
Figure GDA0003649373790000036
Indicating the ideal height deviation after the ith translation,
Figure GDA0003649373790000037
representing the ideal height deviation before the ith translation;
and establishing a gray model to solve the predicted height deviation.
As a preferred technical scheme, the establishing of the gray model for solving the predicted height deviation specifically comprises the following steps:
to sequence XD2Performing primary accumulation to obtain:
X(1)＝{x(1)(1),x(1)(2),…,x(1)(n)}；
establishing a GM (1,1) model, wherein a whitening formal differential equation is as follows:
Figure GDA0003649373790000041
the discretized difference equation is:
x(k)d2+az(1)(k)＝u；
wherein a is a development coefficient, and u is a gray acting amount;
let z(1)(k) Represents the average of the kth value and the previous value in the ideal altitude deviation sequence:
Figure GDA0003649373790000042
and (3) solving a development coefficient a and a gray action amount u by using a least square method:
(a,u)T＝(BTB)-1BTY.
wherein B represents an ideal height deviation average matrix, and Y represents an ideal height deviation original data matrix;
substituting the development coefficient a and the gray action quantity u into a differential equation to solve to obtain an unreduced first prediction height deviation:
Figure GDA0003649373790000043
when i < n, the differential processing sequence is processed
Figure GDA0003649373790000044
Subtracting the sequences to obtain an ideal altitude deviation accumulation sequence, and sequentially performing decrement, geometric mean transformation and accelerated exponential transformation to restore to a second predicted altitude deviation:
Figure GDA0003649373790000045
the first reduction, the second reduction and the third reduction are respectively reduced by decrement, geometric mean transformation and accelerated exponential transformation;
the first reduction is specifically as follows:
Figure GDA0003649373790000051
the second reduction is specifically as follows:
Figure GDA0003649373790000052
the third reduction is specifically:
Figure GDA0003649373790000053
when i is larger than n, the first reduction and the second reduction are performed in sequence, if X is larger than n(0)(n+1)＜X(0)(n), then performing a fourth reduction:
Figure GDA0003649373790000054
if X is(0)(n+1)＞X(0)(n), then a fifth reduction is performed:
Figure GDA0003649373790000055
reducing to a third predicted altitude deviation, wherein the preliminary predicted altitude deviation comprises the first predicted altitude deviation, the second predicted altitude deviation and the third predicted altitude deviation, and the first predicted altitude deviation, the second predicted altitude deviation and the third predicted altitude deviation are obtained
Figure GDA0003649373790000056
Indicating the ith value in the sequence of differential processing.
As a preferred technical scheme, the construction of the Elman neural network specifically comprises the following steps:
establishing a first layer as an input layer, inputting the preprocessed data into a network, and determining an input numerical value and an input node number, wherein the input numerical value is a preliminary prediction height residual error;
establishing a second layer as a hidden layer, determining the number of nodes according to an empirical formula, and selecting a nonlinear function as a first activation function according to the range of input numerical values;
establishing a third layer as a receiving layer, receiving a feedback signal from the hidden layer, wherein each hidden layer node is connected with a corresponding node, and the hidden layer state at the previous moment and the network input at the current moment are taken as the input of the hidden layer through connection memory;
establishing a fourth layer as an output layer, selecting a linear transfer function as a second activation function, and outputting a neural network calculation result;
and learning the neural network by using a reverse error propagation algorithm, and continuously updating the weight value by using a gradient descent method.
As a preferred technical solution, the empirical formula specifically includes:
Figure GDA0003649373790000061
wherein n isiTo input the number of nodes, noM is any integer value between 1 and 10 for the number of output nodes.
As a preferred technical solution, the first activation function selects a hyperbolic tangent sigmoid function, where the hyperbolic tangent sigmoid function is expressed as:
Figure GDA0003649373790000062
wherein x1E represents a natural constant, which is an input variable of the hidden layer;
the second activation function is:
f(x2)＝x2；
wherein x is2Representing the input variables of the output layer.
As a preferred technical scheme, the optimization of the initial weight and the threshold of the Elman neural network by the ant lion algorithm specifically comprises the following steps:
a condition initialization step:
the initial weight and the threshold value of the neural network are coded by adopting a real number coding mode, and the coding formula is as follows:
S＝R×S1+S1×S1+S1×S2+S1+S2，
wherein R is the number of input nodes, S1 is the number of hidden layer nodes, and S2 is the number of output nodes;
taking the weight and threshold coding number of the Elman neural network as a population, initially setting ant lion and ant as the same population and the same population size, setting the number of each individual in the population as a random number in a preset individual number interval, and setting the weight and threshold of the neural network corresponding to each individual in the population;
a first neural network training step:
training parameter initialization: taking the preliminary predicted height residual as training input, taking the corresponding corrected height residual as a training result, and evaluating the ant position based on the network training error;
screening the elite lion: according to the updating of ant positions, giving and evaluating values, and selecting the ant lion with the highest evaluating value as the elite ant lion;
judging the training degree: inputting a test height residual error, outputting to obtain a first test predicted height residual error, and adjusting training according to whether the first test predicted height residual error reaches a first preset residual error accuracy value or not;
when the first test predicted height residual does not reach a first preset residual precision value, ant lion optimization is carried out, and the first neural network training step is repeated;
when the first test prediction height residual reaches a first preset residual precision value, executing a parameter updating step;
updating parameters: reassigning the training parameters: assigning the optimal weight and the optimal threshold value after the ant lion algorithm is optimized to the weight parameter and the threshold value parameter corresponding to the neural network, namely replacing the initial weight and the threshold value;
ant lion optimization: after the elite ant lion captures the ants, the ant lion position is updated to be the ant position, the ant position updating is influenced by the elite ant lion, and finally the optimal weight and the threshold are found;
a second neural network training step:
carrying out Elman neural network training, and updating the weight parameter and the threshold parameter based on the network training error;
and judging a training ending condition, adjusting training according to whether the second test predicted height residual reaches a second preset residual precision value, ending the second neural network training step when the second test predicted height residual reaches the second preset residual precision value, and otherwise, repeating the second neural network training step.
In order to achieve the second object, the invention adopts the following technical scheme:
a random-oscillatory-sequence-grey-model-based ultra-high prediction system of rail irregularity, comprising: the system comprises a data preprocessing module, a preliminary prediction module, a prediction correction module, a neural network module and an ultrahigh prediction module;
the data preprocessing module is used for carrying out mean value processing on the detected height deviation of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
the preliminary prediction module is used for carrying out random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain preliminary prediction height deviation;
the prediction correction module is used for obtaining a preliminary prediction height residual error based on the preliminary prediction height deviation and original data, calculating a height residual error average value, correcting the preliminary prediction height residual error based on the height residual error average value to obtain a corrected height residual error, and normalizing the preliminary prediction height residual error and the corrected height residual error;
the neural network module is used for dividing a training set and a test set based on the preliminary prediction height residual error and the correction height residual error, building an Elman neural network, training based on the preliminary prediction height residual error and the correction height residual error of the training set, and optimizing an initial weight and a threshold of the Elman neural network through an ant lion algorithm so as to obtain an optimized Elman neural network;
and the ultrahigh prediction module is used for inputting a preliminary prediction height residual error based on the optimized Elman neural network to obtain a track prediction correction height residual error.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the method overcomes the defect that the prediction result of the traditional grey model on the random oscillation sequence is not ideal by combining the random oscillation sequence grey model and the Elman neural network, enriches the single index prediction method on the rail irregularity, solves the error problem of the prediction result of the random oscillation sequence grey model by adopting the Elman neural network optimized by the ant lion algorithm, enables the ultrahigh prediction result to be more accurate, predicts the real ultrahigh historical detection data on the method, and shows that the method has better prediction capability and higher prediction precision by the prediction result.
(2) According to the Elman neural network optimization method, the initial weight and the threshold of the Elman neural network are optimized through the ant lion algorithm, the problem that the Elman neural network is easy to fall into a local optimal solution is solved, and the optimized Elman neural network achieves the global optimal correction effect.
Drawings
FIG. 1 is a flowchart illustrating the steps of a random oscillation gray model-based superelevation prediction method in example 1 of the present invention;
fig. 2 is a diagram of a training procedure for optimizing an Elman neural network in the ultrahigh prediction method based on the random oscillation gray model in embodiment 1 of the present invention;
fig. 3 is a schematic structural diagram of an optimized Elman neural network in embodiment 1 of the present invention.
Detailed Description
In the description of the present disclosure, it should be noted that the terms "first", "second", and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Also, the use of the terms "a," "an," or "the" and similar referents do not denote a limitation of quantity, but rather denote the presence of at least one. The word "comprising" or "comprises", and the like, means that the element or item appearing before the word, includes the element or item listed after the word and its equivalent, but does not exclude other elements or items.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
Examples
Example 1
As shown in fig. 1, the present embodiment provides a method for predicting superelevation of track irregularity based on a random oscillation sequence gray model, which includes the following steps:
a data preprocessing step: carrying out mean value processing on the detected height deviation of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
a preliminary prediction step: performing random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain a preliminary prediction height deviation;
and a prediction correction step: obtaining a preliminary prediction height residual error based on the preliminary prediction height deviation and original data, calculating a height residual error average value, correcting the preliminary prediction height residual error based on the height residual error average value to obtain a corrected height residual error, and normalizing the preliminary prediction height residual error and the corrected height residual error;
and (3) optimizing an Elman neural network: dividing a training set and a test set based on the preliminary prediction height residual error and the correction height residual error, building an Elman neural network, training based on the preliminary prediction height residual error and the correction height residual error of the training set, and optimizing an initial weight and a threshold of the Elman neural network through an ant lion algorithm to further obtain an optimized Elman neural network;
ultra-high prediction step: and inputting the preliminary prediction height residual error based on the optimized Elman neural network to obtain a track prediction correction height residual error, wherein the height deviation conforming to the natural change trend of track abrasion is obtained by adding the preliminary prediction height to the track prediction correction height residual error.
In this embodiment, the data preprocessing step specifically includes: and acquiring the height deviation of the preset interval at equal detection time intervals, carrying out average value processing on the height deviation to obtain the average height deviation representing the interval, wherein the preset interval is 200m, and in addition, the preset interval can be adjusted according to the actual condition.
In this embodiment, the preliminary prediction step specifically includes the following steps:
transformation of random oscillation sequence:
detecting and detecting the detection sections at the same time to obtain an equidistant average height deviation sequence, wherein the equidistant average height deviation sequence is as follows: x(0)＝{X(0)(1),X(0)(2)，…，X(0)(n) }; the equidistant average height deviation sequence belongs to a super high sequence value, and because the super high sequence value is different in positive and negative, the original super high average value sequence is translated to a full value, and the following parameters are set:
Max＝max{x(0)(k)|k,k∈{1,2,…,n}}；
Min＝min{x(0)(k)|k,k∈{1,2,…,n}}；
Figure GDA0003649373790000111
wherein Max represents the maximum value in the original equidistant average height deviation sequence, Min represents the minimum value in the original equidistant average height deviation sequence, T represents the maximum oscillation ratio of the original equidistant average height deviation sequence, and n is the maximum value of the sequence;
the sequence obtained by performing accelerated exponential transformation on the equidistant average height deviation sequence is a monotonically increasing height deviation sequence, namely:
XD1＝{x(1)d1,x(2)d1,…,x(n)d1}；
wherein x (k) d1Where k is 1,2,3 … n, which is the k-th monotonically increasing height deviation value after being subjected to the acceleration exponential transformation, in this embodiment, the acceleration exponential transformation specifically is:
x(k)d1＝x(0)(k)Tk-1，k＝1,2,3…n；
to XD1And performing geometric mean generation transformation on the sequence to obtain a geometric mean processing height deviation sequence which keeps monotonous increase but the increase amplitude is reduced, namely an ideal height deviation sequence, namely:
XD2＝{x(1)d2,x(2)d2,…,x(n)d2}；
x(k)d2and k is the k-th geometric mean processing height deviation value, k is 1 and …, and n is a positive integer. In this embodiment, the geometric mean transformation specifically includes:
Figure GDA0003649373790000112
judging the grade ratio:
Figure GDA0003649373790000113
if the stage ratio k (i) is in the interval
Figure GDA0003649373790000114
Then the ideal height deviation sequence can be directly used for a prediction model;
if not, a proper translation coefficient z needs to be selected to perform integral translation on the sequence, and further the level ratio k (i) is satisfied in the interval
Figure GDA0003649373790000115
The method comprises the following steps:
Figure GDA0003649373790000121
wherein
Figure GDA0003649373790000122
Indicating the ideal height deviation after the ith translation,
Figure GDA0003649373790000123
representing the ideal height deviation before the ith translation;
establishing a gray model:
for sequence XD2Performing primary accumulation to obtain:
X(1)＝{x(1)(1),x(1)(2),…,x(1)(n)}；
establishing a GM (1,1) model, wherein a whitening formal differential equation is as follows:
Figure GDA0003649373790000124
the discretized difference equation is:
x(k)d2+az(1)(k)＝u；
wherein a is a development coefficient, and u is a gray acting amount;
let z(1)(k) Represents the average of the kth value and the previous value in the ideal altitude deviation sequence:
Figure GDA0003649373790000125
and (3) solving a development coefficient a and a gray action amount u by using a least square method:
(a,u)T＝(BTB)-1BTY.
wherein B represents an ideal height deviation average matrix, and Y represents an ideal height deviation original data matrix:
Figure GDA0003649373790000126
Figure GDA0003649373790000127
substituting the parameters a and u into a differential equation to solve to obtain an unreduced first prediction height deviation:
Figure GDA0003649373790000131
when i < n, the sequence of differential processing is applied
Figure GDA0003649373790000132
Subtracting the sequences to obtain an ideal altitude deviation accumulation sequence, and sequentially performing decrement, geometric mean transformation and accelerated exponential transformation to restore to a second predicted altitude deviation:
Figure GDA0003649373790000133
during actual application, sequentially executing first reduction, second reduction and third reduction, wherein the first reduction, the second reduction and the third reduction respectively correspond to decrement, geometric mean transformation and accelerated exponential transformation reduction;
the first reduction is specifically:
Figure GDA0003649373790000134
the second reduction is specifically:
Figure GDA0003649373790000135
the third reduction is specifically:
Figure GDA0003649373790000136
when i > n, performing the first reduction and the second reduction in sequence, if X(0)(n+1)＜X(0)(n), then performing a fourth reduction:
Figure GDA0003649373790000137
if X(0)(n+1)＞X(0)(n), then a fifth reduction is performed:
Figure GDA0003649373790000138
reducing the height deviation to a third predicted height deviation, wherein the preliminary predicted height deviation comprises a first predicted height deviation, a second predicted height deviation and a third predicted height deviation;
wherein
Figure GDA0003649373790000139
Represents the ith value in the differential processing sequence;
as shown in fig. 2 and 3, the Elman neural network is built, and the method specifically comprises the following steps:
establishing a first layer as an input layer, inputting the preprocessed data into a network, and determining an input numerical value and an input node number, wherein the input numerical value is a preliminary prediction height residual error;
establishing a second layer as a hidden layer, determining the number of nodes according to an empirical formula, and selecting a nonlinear function as a first activation function according to the range of input numerical values;
establishing a third layer as a receiving layer, receiving a feedback signal from the hidden layer, wherein each hidden layer node is connected with a corresponding node, and the hidden layer state at the previous moment and the network input at the current moment are used as the input of the hidden layer through connection memory;
establishing a fourth layer as an output layer, selecting a linear transfer function as a second activation function, and outputting a neural network calculation result;
and learning the neural network by using a reverse error propagation algorithm, and continuously updating the weight value by a gradient descent method.
In this embodiment, the empirical formula is specifically:
Figure GDA0003649373790000141
wherein n isiFor the number of input nodes, noM is any integer value between 1 and 10 for the number of output nodes.
In this embodiment, the first activation function is selected from a hyperbolic tangent sigmoid function, where the hyperbolic tangent sigmoid function is expressed as:
Figure GDA0003649373790000142
wherein x1E represents a natural constant, which is an input variable of the hidden layer;
in this embodiment, the second activation function is the following function:
f(x2)＝x2；
wherein x2Representing the input variables of the output layer.
In addition, the first activation function and the second activation function may adopt other activation functions, and are not limited herein.
With reference to fig. 2 and 3, the optimization of the initial weight and the threshold of the Elman neural network by the ant lion algorithm specifically includes the following steps:
a condition initialization step:
the initial weight and the threshold value of the neural network are coded by adopting a real number coding mode, and the coding formula is as follows:
S＝R×S1+S1×S1+S1×S2+S1+S2，
wherein R is the number of input nodes, S1 is the number of hidden layer nodes, and S2 is the number of output nodes;
taking the weight and threshold coding number of the Elman neural network as a population, initially setting ant lion and ant as the same population and the same population size, setting the number of each individual of the population as a random number in a preset individual number interval, and setting the weight and threshold of the neural network corresponding to each individual in the population, wherein the preset individual number interval in the embodiment adopts [ -3,3 ];
a first neural network training step:
initializing training parameters: taking the preliminary prediction height residual error as training input, taking the corresponding correction height residual error as a training result, and evaluating the ant position based on the network training error;
screening the elite lion: according to the updating of ant positions, giving and evaluating values, and selecting the ant lion with the highest evaluating value as the elite ant lion;
judging the training degree: inputting a test height residual error, outputting to obtain a first test prediction height residual error, and adjusting training according to whether the first test prediction height residual error reaches a first preset residual error precision value, wherein the test height residual error is obtained by a test set;
when the first test predicted height residual does not reach a first preset residual precision value, ant lion optimization is carried out, and the first neural network training step is repeated;
when the first test prediction height residual reaches a first preset residual precision value, executing a parameter updating step;
updating parameters: reassigning the training parameters: assigning the optimal weight and the optimal threshold value after the ant lion algorithm is optimized to the weight parameter and the threshold value parameter corresponding to the neural network, namely replacing the initial weight and the threshold value;
ant lion optimization: after the elite ant lion captures the ants, the ant lion position is updated to be the ant position, the ant position updating is influenced by the elite ant lion, and finally the optimal weight and the threshold are found;
a second neural network training step:
carrying out Elman neural network training, and updating the weight parameter and the threshold parameter based on the network training error;
and judging a training ending condition, adjusting training according to whether the second test predicted height residual reaches a second preset residual precision value, ending the second neural network training step when the second test predicted height residual reaches the second preset residual precision value, and otherwise, repeating the second neural network training step.
Example 2
The embodiment provides a system for predicting the superelevation of the rail irregularity based on a random oscillation sequence gray model, which comprises: the system comprises a data preprocessing module, a preliminary prediction module, a prediction correction module, a neural network module and an ultrahigh prediction module;
the data preprocessing module is used for carrying out mean processing on the detected height deviation of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
the preliminary prediction module is used for carrying out random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain preliminary prediction height deviation;
the prediction correction module is used for obtaining a preliminary prediction height residual error based on the preliminary prediction height deviation and original data, calculating a height residual error average value, correcting the preliminary prediction height residual error based on the height residual error average value to obtain a corrected height residual error, and normalizing the preliminary prediction height residual error and the corrected height residual error;
the neural network module is used for dividing a training set and a test set based on the preliminary prediction height residual error and the correction height residual error, building an Elman neural network, training the preliminary prediction height residual error and the correction height residual error based on the training set, and optimizing an initial weight and a threshold of the Elman neural network through an ant lion algorithm to further obtain an optimized Elman neural network;
and the ultrahigh prediction module is used for inputting the preliminary prediction height residual error based on the optimized Elman neural network to obtain the track prediction correction height residual error.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (9)

1. A track irregularity ultrahigh prediction method based on a random oscillation sequence gray model is characterized by comprising the following steps:
a data preprocessing step: carrying out mean value processing on the detected height deviations of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
a preliminary prediction step: performing random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain a preliminary prediction height deviation;
the preliminary prediction step specifically comprises the following steps:
transformation of random oscillation sequence:
detecting and detecting the detection sections at the same time to obtain an equidistant average height deviation sequence, wherein the equidistant average height deviation sequence is set as follows: x(0)＝{X(0)(1)，X(0)(2)，…，X(0)(n)}；
Translating the equidistant average height deviation sequence to a full value, and setting the following parameters:
Max＝max{x(0)(k)|k，k∈{1，2，…，n}}；
Min＝min{x(0)(k)|k，k∈{1，2，…，n}}；
Figure FDA0003649373780000011
max represents the maximum value in the original equidistant average height deviation sequence, Min represents the minimum value in the original equidistant average height deviation sequence, T represents the maximum oscillation ratio of the original equidistant average height deviation sequence, and n is the maximum value of the sequence;
the sequence obtained by performing accelerated exponential transformation on the equidistant average height deviation sequence is a monotonically increasing height deviation sequence, namely:
XD1＝{x(1)d1，x(2)d1，…，x(n)d1}；
wherein x (k) d1K is 1,2,3 … n, which is the k-th monotonically increasing height deviation value after the acceleration exponential transformation;
for XD1And performing geometric mean generation transformation on the sequence to obtain a geometric mean processing height deviation sequence which keeps monotonous increase but the increase amplitude is reduced, namely an ideal height deviation sequence, namely:
XD2＝{x(1)d2，x(2)d2，…，x(n)d2}；
x(k)d2the k-th geometric mean processing height deviation value is defined as k, wherein k is 1, …, n is a positive integer;
and a prediction correction step: obtaining a preliminary prediction height residual error based on the preliminary prediction height deviation and original data, calculating a height residual error average value, correcting the preliminary prediction height residual error based on the height residual error average value to obtain a corrected height residual error, and normalizing the preliminary prediction height residual error and the corrected height residual error;
and (3) optimizing an Elman neural network: performing normalization processing based on the preliminary prediction height residual error and the correction height residual error, dividing a training set and a test set, building an Elman neural network, performing training based on the preliminary prediction height residual error and the correction height residual error of the training set, and optimizing an initial weight and a threshold of the Elman neural network through an ant lion algorithm to obtain an optimized Elman neural network;
ultra-high prediction step: and inputting the preliminary prediction height residual error based on the optimized Elman neural network to obtain the orbit prediction correction height residual error.
2. The method for ultrahigh prediction of rail irregularity based on random oscillation sequence gray model according to claim 1, wherein the data preprocessing step is specifically: and acquiring the height deviation of the preset interval at equal detection time intervals, and carrying out average value processing on the height deviation to obtain the average height deviation representing the interval.
3. The method for ultrahigh prediction of orbit irregularity based on stochastic oscillatory sequence gray model of claim 1, wherein the preliminary prediction step comprises the following steps:
judging the grade ratio:
Figure FDA0003649373780000021
if the step ratio k (i) is in the interval
Figure FDA0003649373780000022
If so, the ideal height deviation sequence is directly used for a prediction model;
if the step ratio k (i) is not satisfied
Figure FDA0003649373780000023
Selecting a proper translation coefficient z to carry out integral translation on the sequence so as to meet the level ratio k (i) in the interval
Figure FDA0003649373780000031
The method comprises the following steps:
Figure FDA0003649373780000032
wherein
Figure FDA0003649373780000033
Indicating the ideal height deviation after the ith translation,
Figure FDA0003649373780000034
representing the ideal height deviation before the ith translation;
and establishing a gray model to solve the predicted height deviation.
4. The ultrahigh prediction method of track irregularity based on the random oscillation sequence gray model as claimed in claim 3, wherein the establishing of the gray model to solve the predicted height deviation specifically comprises the following steps:
to sequence XD2Performing primary accumulation to obtain:
X(1)＝{x(1)(1)，x(1)(2)，…，x(1)(n)}；
establishing a GM (1,1) model, wherein a whitening form differential equation is as follows:
Figure FDA0003649373780000035
the discretized difference equation is:
x(k)d2+az(1)(k)＝u；
wherein a is a development coefficient, and u is a gray acting amount;
let z(1)(k) Represents the average of the kth value and the previous value in the ideal altitude deviation sequence:
Figure FDA0003649373780000036
and (3) solving a development coefficient a and a gray action amount u by using a least square method:
(a，u)T＝(BTB)-1BTY.
wherein B represents an ideal height deviation average matrix, and Y represents an ideal height deviation original data matrix;
substituting the development coefficient a and the gray action quantity u into a differential equation to solve to obtain an unreduced first prediction height deviation:
Figure FDA0003649373780000041
when i < n, differentiateProcessing sequence
Figure FDA0003649373780000042
Subtracting the sequences to obtain an ideal altitude deviation accumulation sequence, and sequentially performing decrement, geometric mean transformation and accelerated exponential transformation to restore to a second predicted altitude deviation:
Figure FDA0003649373780000043
the first reduction, the second reduction and the third reduction are respectively corresponding to decrement, geometric mean transformation and accelerated exponential transformation reduction;
the first reduction is specifically:
Figure FDA0003649373780000044
the second reduction is specifically as follows:
Figure FDA0003649373780000045
the third reduction is specifically as follows:
Figure FDA0003649373780000046
when i is larger than n, the first reduction and the second reduction are performed in sequence, if X is larger than n(0)(n+1)＜X(0)(n), then a fourth reduction is performed:
Figure FDA0003649373780000047
if X(0)(n+1)＞X(0)(n), then a fifth reduction is performed:
Figure FDA0003649373780000048
reducing the height deviation to a third predicted height deviation, wherein the preliminary predicted height deviation comprises the first predicted height deviation, the second predicted height deviation and the third predicted height deviation, and the third predicted height deviation
Figure FDA0003649373780000049
Indicating the ith value in the sequence of differential processing.
5. The method for predicting the track irregularity in the ultrahigh environment based on the random oscillation sequence gray model according to claim 1, wherein the construction of the Elman neural network specifically comprises the following steps:
establishing a first layer as an input layer, inputting the preprocessed data into a network, and determining an input numerical value and an input node number, wherein the input numerical value is a preliminary prediction height residual error;
establishing a second layer as a hidden layer, determining the number of nodes according to an empirical formula, and selecting a nonlinear function as a first activation function according to the range of input numerical values;
establishing a third layer as a receiving layer, receiving a feedback signal from the hidden layer, wherein each hidden layer node is connected with a corresponding node, and the hidden layer state at the previous moment and the network input at the current moment are taken as the input of the hidden layer through connection memory;
establishing a fourth layer as an output layer, selecting a linear transfer function as a second activation function, and outputting a neural network calculation result;
and learning the neural network by using a reverse error propagation algorithm, and continuously updating the weight value by a gradient descent method.
6. The method for ultrahigh prediction of orbit irregularity based on stochastic oscillation sequence gray model of claim 5, wherein the empirical formula is specifically:
Figure FDA0003649373780000051
wherein n isiFor the number of input nodes, noM is any integer value between 1 and 10 for the number of output nodes.
7. The stochastic oscillation sequence gray model-based ultrahigh prediction method of orbital irregularity according to claim 5, wherein the first activation function is selected from a hyperbolic tangent sigmoid function, wherein the hyperbolic tangent sigmoid function is represented as:
Figure FDA0003649373780000052
wherein x is1E represents a natural constant, which is an input variable of the hidden layer;
the second activation function is:
f(x2)＝x2；
wherein x2Representing the input variables of the output layer.
8. The ultrahigh prediction method of orbit irregularity based on the random oscillation sequence gray model as claimed in claim 1, wherein the optimization of the initial weight and threshold of the Elman neural network by the ant lion algorithm specifically comprises the following steps:
a condition initialization step:
the initial weight and the threshold value of the neural network are coded by adopting a real number coding mode, and the coding formula is as follows:
S＝R×S1+S1×S1+S1×S2+S1+S2，
wherein R is the number of input nodes, S1 is the number of hidden layer nodes, and S2 is the number of output nodes;
taking the weight and threshold coding number of the Elman neural network as a population, initially setting ant lion and ant as the same population and the same population size, setting the number of each individual in the population as a random number in a preset individual number interval, and setting the weight and threshold of the neural network corresponding to each individual in the population;
a first neural network training step:
training parameter initialization: taking the preliminary prediction height residual error as training input, taking the corresponding correction height residual error as a training result, and evaluating the ant position based on the network training error;
screening elite ant lions: according to the updating of ant positions, giving and evaluating values, and selecting the ant lion with the highest evaluating value as the elite ant lion;
judging the training degree: inputting a test height residual error, outputting to obtain a first test prediction height residual error, and adjusting training according to whether the first test prediction height residual error reaches a first preset residual error precision value;
when the first test predicted height residual does not reach a first preset residual precision value, ant lion optimization is carried out, and the first neural network training step is repeated;
when the first test prediction height residual reaches a first preset residual precision value, executing a parameter updating step;
and updating parameters: reassigning the training parameters: assigning the optimal weight and the optimal threshold value after the ant lion algorithm optimization to the weight parameter and the threshold value parameter corresponding to the neural network, namely replacing the initial weight and the threshold value;
ant lion optimization: after the elite ant lion captures the ants, the ant lion position is updated to be the ant position, the ant position updating is influenced by the elite ant lion, and finally the optimal weight and the threshold are found;
a second neural network training step:
carrying out Elman neural network training, and updating weight parameters and threshold parameters based on network training errors;
and judging a training ending condition, adjusting training according to whether the second test predicted height residual reaches a second preset residual precision value, ending the second neural network training step when the second test predicted height residual reaches the second preset residual precision value, and otherwise, repeating the second neural network training step.
9. An ultrahigh prediction system of rail irregularity based on a random oscillation sequence gray model, comprising: the device comprises a data preprocessing module, a preliminary prediction module, a prediction correction module, a neural network module and an ultrahigh prediction module;
the data preprocessing module is used for carrying out mean value processing on the detected height deviation of the left rail surface and the right rail surface to obtain an equidistant average height deviation sequence;
the preliminary prediction module is used for carrying out random oscillation sequence gray prediction on the equidistant average height deviation sequence based on a gray model to obtain preliminary prediction height deviation;
the grey prediction of the random oscillation sequence is carried out on the equidistant average height deviation sequence based on a grey model, and the method specifically comprises the following steps:
transformation of random oscillation sequence:
detecting and detecting the detection sections at the same time to obtain an equidistant average height deviation sequence, wherein the equidistant average height deviation sequence is as follows: x(0)＝{X(0)(1)，X(0)(2)，…，X(0)(n)}；
Translating the equidistant average height deviation sequence to a full value, and setting the following parameters:
Max＝max{x(0)(k)|k，k∈{1，2，…，n}}；
Min＝min{x(0)(k)|k，k∈{1，2，…，n}}；
Figure FDA0003649373780000071
max represents the maximum value in the original equidistant average height deviation sequence, Min represents the minimum value in the original equidistant average height deviation sequence, T represents the maximum oscillation ratio of the original equidistant average height deviation sequence, and n is the maximum value of the sequence;
the sequence obtained by performing accelerated exponential transformation on the equidistant average height deviation sequence is a monotonically increasing height deviation sequence, namely:
XD1＝{x(1)d1，x(2)d1，…，x(n)d1}；
wherein x (k) d1Where k is 1,2,3 … n, which is the kth accelerated exponential transformThe later monotonically increasing height deviation value;
for XD1And performing geometric mean generation transformation on the sequence to obtain a geometric mean processing height deviation sequence which keeps monotonous increase but the increase amplitude is reduced, namely an ideal height deviation sequence, namely:
XD2＝{x(1)d2，x(2)d2，…，x(n)d2}；
x(k)d2the k is the k-th geometric mean processing height deviation value, k is 1, …, n is a positive integer;
the prediction correction module is used for obtaining a preliminary prediction height residual error based on the preliminary prediction height deviation and original data, calculating a height residual error average value, correcting the preliminary prediction height residual error based on the height residual error average value to obtain a corrected height residual error, and normalizing the preliminary prediction height residual error and the corrected height residual error;
the neural network module is used for dividing a training set and a testing set after normalization processing based on the preliminary prediction height residual error and the correction height residual error, building an Elman neural network, training based on the preliminary prediction height residual error and the correction height residual error of the training set, and optimizing an initial weight and a threshold of the Elman neural network through a ant lion algorithm so as to obtain an optimized Elman neural network;
and the ultrahigh prediction module is used for inputting the preliminary prediction height residual error based on the optimized Elman neural network to obtain an orbit prediction correction height residual error.
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