CN102567576B - Method for predicting rate of wheel load reduction - Google Patents

Abstract

The invention discloses a method for predicting rate of wheel load reduction in the technical field of railroad safety. The method comprises the following steps: first, collecting left track longitudinal irregularity, left track direction irregularity, right track longitudinal irregularity and right track direction irregularity data by adopting a track inspection car; then, simulating the data by using professional software ADAMS (automatic dynamic analysis of mechanical systems)/RAIL to obtain rail-wheel load data, namely vertical rail-wheel load and horizontal rail-wheel load, thereby obtaining and normalizing the rate of wheel load reduction; selecting a training sample to train a NARX (nonlinear auto-regression with exogenous input) neural network model; testing the trained NARX neural network prediction model and outputting the rate of wheel load reduction data after the test; and analyzing the rate of wheel load reduction data in the training sample and the rate of wheel load reduction data obtained from the neural network after the test and valuing performance of the NARX neural network prediction model. By using the method, derailment coefficient is precisely predicted and accuracy of railway operation safety evaluation is improved. Therefore, the method has important realistic meanings to railway traffic safety control.

Description

A kind of Forecasting Methodology of rate of wheel load reduction

Technical field

The invention belongs to the railway security technical field, relate in particular to a kind of Forecasting Methodology of rate of wheel load reduction.

Background technology

Towards high speed, heavy duty, large conveying quantity and highdensity future development, guarantee that the safety and steady operation of train becomes a current vital task along with transportation by railroad.Rate of wheel load reduction is one of dynamics of vehicle leading indicator, for the safe coefficient of the suspension derailment of examining wheel to cause due to wheel unloading.Therefore, the prediction of off-load rate has great importance for the traffic safety of railway.

The off-load amount of rate of wheel load reduction limiting wheel for China standard GB/T 5599-85 regulation, rate of wheel load reduction is defined as the wheel unloading amount and the ratio of taking turns right average quiet wheel load of off-load sidecar wheel, is denoted as

its safety standard is:

At present, various countries generally adopt the physics force-measuring wheel to detecting track/Vehicular system running status.The physics force-measuring wheel is to utilizing the elastic body of wheel as transmitting element, when the used time of doing that is subject to wheel rail force, wheel produces distortion, by detecting and resolve the corresponding relation between this distortion and wheel rail force, can determine the value of wheel track Interaction Force, and then calculate the off-load rate.But the physics force-measuring wheel is to there being the defects such as cost is excessive, failure rate is high, thereby limited right the promoting the use of of physics force-measuring wheel.

Utilizing dynamics simulation software to build the wheel rail dynamics coupling model is a kind of effective ways that obtain the off-load rate.By the Dynamic Modeling to related systems such as rail truck, track, Wheel Rail Contacts, carry out the simulation calculation of kinetic parameter in simulation software, thereby obtain the parameters such as off-load rate.

Part Study scholar proposes to utilize the method for modelling by mechanism to obtain the off-load rate, Eric has built the vertical dynamics system model of wheel-rail interaction, comprise the auto model of wheel to, car body and suspension, the linear model of model trajectory and Wheel Rail Contact, then calculate the vertical wheel rail force produced by the vertical irregularity of track, and then calculate the off-load rate; Fujie has proposed the vehicle inversion model based on modelling by mechanism, according to values of lateral, vertical acceleration with sidewinder acceleration etc. and calculate wheel rail force, off-load rate etc.Therefore owing in the modelling by mechanism process, Complex Nonlinear System having been carried out to more simplification and approximate processing, there are the problems such as the low and wheel rail force estimated performance of modeling accuracy is poor.

Summary of the invention

For mentioning the deficiencies such as the cost that has the existence of rate of wheel load reduction Forecasting Methodology now is high, precision of prediction is low in the above-mentioned background technology, the present invention proposes a kind of Forecasting Methodology of rate of wheel load reduction.

Technical scheme of the present invention is that a kind of Forecasting Methodology of rate of wheel load reduction is characterized in that the method comprises the following steps:

Step 1: utilize track detection vehicle to detect the irregularity data of track;

Step 2: the irregularity data that gather by step 1, utilize ADAMS/RAIL software to set up vertical wheel rail force and horizontal wheel rail force that model emulation is tried to achieve track, and then try to achieve rate of wheel load reduction, and to the rate of wheel load reduction normalized;

Step 3: utilize the derailment coefficients after normalization to be trained improved NARX neural network prediction model, and determine the weights of NARX neural network prediction model and the effect of optimization of threshold value by the specified network validity function;

Step 4: the improved NARX neural network prediction model after the data input training that step 1 is gathered obtains rate of wheel load reduction, uses the root-mean-square error method to this model evaluation.

Described track irregularity data comprise that left rail is uneven and are uneven along data and right rail rail to the irregularity data to irregularity data, right rail along data, left rail rail.

Described normalization formula is:

${x_i}^{\mathrm{scal}}=\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$

Wherein:

for the data after normalization;

X _ifor the data before normalization;

X _maxand x _minbe respectively maximal value and the minimum value of variable x.

The structure of described NARX neural network prediction model comprises between ，Liang Ge middle layer, 2 middle layers without contact.

The described method that the improved NARX neural network prediction model of algorithm is trained is improved regularization algorithm.

The network performance evaluation function of described improved regularization algorithm:

F(w)＝(1-γ)E _D+γE _w

In formula:

F (w) is the network performance evaluation functional value;

W is weights;

γ is modifying factor, 0≤γ≤1, value 0.3;

E _wquadratic sum for all weights of network or threshold value;

E _dquadratic sum for network error.

Described E _wand E _dcomputing formula be respectively:

${E_D}^{\left(p\right)}=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\frac{{({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})}^2}{2}$

${E_w}^{\left(p\right)}=\frac{1}{N_w}[\underset{j=1}{\overset{h}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left({w_{\mathrm{ij}}}^{\left(p\right)}\right)}^2+\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{h}{\mathrm{\Σ}}}{\left({w_{\mathrm{jk}}}^{\left(p\right)}\right)}^2]$

In formula:

E _d ^(p)be the network error quadratic sum of p to the input and output sample data;

D _kbe the target output of k output layer node;

Y _kbe the network output of k output layer node;

E _w ^(p)be the network weight quadratic sum of p to the input and output sample data;

N _wadjustable weights number for network;

W _ijbe that i time delay node layer is to weights between j middle layer node;

W _jkbe the weights of j middle layer node to k output layer node;

N time delay node layer;

H middle layer node;

M output number.

The activation function in described middle layer is the linear process function of output layer is f ₀(x)=x, and output layer and middle layer weights correction are respectively:

$\mathrm{\Δ}{w_{\mathrm{jk}}}^{\left(p\right)}=(1-\mathrm{\γ})\·({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})\·{{\mathrm{hx}}_j}^{\left(p\right)}+\mathrm{\γ}\·\frac{2}{N_w}\·{w_{\mathrm{jk}}}^{(p-1)}$

$\mathrm{\Δ}{w_{\mathrm{ij}}}^{\left(p\right)}=(1-\mathrm{\γ})\·\underset{l=1}{\overset{m}{\mathrm{\Σ}}}({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})\·{w_{\mathrm{jk}}}^{\left(p\right)}\·\frac{\mathrm{\λ}}{2}(1-{\left({{\mathrm{ox}}_j}^{\left(p\right)}\right)}^2)\·{{\mathrm{ox}}_i}^{\left(p\right)}+\mathrm{\γ}\·\frac{2}{N_w}\·{w_{\mathrm{ij}}}^{(p-1)}$

In formula:

Δ w _jk ^(p)be the output layer weights correction of p to the input and output sample data;

be the middle layer weights correction of p to the input and output sample data;

The parameter that λ is the middle layer activation function, value is 1;

D _k ^(p)be the target output of p to k output layer node of input and output sample data;

Y _k ^(p)be the network output of p to k output layer node of input and output sample data;

W _jk ^(p-1)the weights to k output layer node that are p-1 to j middle layer node of input and output sample data;

be j the middle layer node input of p to the input and output sample data;

be the input of p to i output layer node of input and output sample data.The adjustment of described output layer and middle layer weights is respectively:

w _jk ^(p)＝w _jk ^(p-1)-ηΔw _jk ^(p)

w _ij ^(p)＝w _ij ^(p-1)-ηΔw _ij ^(p)

In formula:

η is learning rate, and value is 0.006.

The formula of described root-mean-square error method is:

$\mathrm{RMSE}(y,y_m)=\sqrt{\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{(y\left(i\right)-y_m\left(i\right))}^2}$

Wherein:

RMSE (y, y _m) be the value of root-mean-square error;

Y is desired value in test sample book;

Y _mpredicted value for the model after renormalization;

N is the data sample number.

The present invention is to provide a kind of neural net method of predicting rate of wheel load reduction, utilize actual measurement track irregularity data and rate of wheel load reduction emulated data, the NARX neural network model of employing based on algorithm improvement and architecture advances, the accurately predicting rate of wheel load reduction, thereby improved the accuracy that railway operation safety is estimated, the track traffic safety is controlled and had important practical significance.

The accompanying drawing explanation

Fig. 1 is improved NARX neural network structure figure;

Fig. 2 is the process flow diagram of improved NARX neural network prediction rate of wheel load reduction;

Fig. 3 is the output of rate of wheel load reduction test data and improved NARX neural network output comparison diagram;

Fig. 4 is the correlation analysis of the output of rate of wheel load reduction test data and the output of improved NARX neural network.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that, following explanation is only exemplary, rather than in order to limit the scope of the invention and to apply.

The objective of the invention is, in order to realize the Accurate Model to rate of wheel load reduction by track irregularity, to utilize track irregularity to predict rate of wheel load reduction, to improve the precision of prediction of rate of wheel load reduction.Employing improves based on algorithm and the NARX neural network of architecture advances can realize the accurately predicting to rate of wheel load reduction.

The present invention to the Forecasting Methodology of rate of wheel load reduction is:

(1) Gather and input data

By the track irregularity data of actual measurement, comprise that left rail is uneven to be uneven along data and right rail rail to the irregularity data to irregularity data, right rail along data, left rail rail, after being arranged as the input data of neural network model.

(2) emulation obtains the rate of wheel load reduction data

Utilize dynamics simulation software ADAMS/RAIL, the track irregularity data after input arranges, carry out emulation, obtains the rate of wheel load reduction data, is kept in text, as the target output data of neural network model.

(3) data pre-service

Because the inputoutput data size is uneven, larger order of magnitude difference is even arranged, there is convergence preferably in order to make neural network, before the input network training, data normalization can be processed.

(4) set up the NARX neural network prediction model

Bayesian regularization (BR) algorithm is using the weighting of network weight quadratic sum and error sum of squares as validity function, adopt Lay Weinberg-Ma quart (LM) algorithm to carry out weights (and threshold value) adjustment, can under the prerequisite that guarantees the network fitting precision, dwindle network size, thereby reduce network complexity to obtain good Generalization Capability.But this algorithmic procedure complexity, definite method that undetermined parameter is more and shortage is ripe, by Bayesian formula correction probability density function the time, calculated amount is large, therefore this paper improves traditional Bayesian regularization algorithm, abandoned the process of utilizing Bayesian formula correction weights probability density, adopt the regularization algorithm to carry out the weights correction, and be simply referred to as improved Bayesian regularization (Improved bayesian Regularization, IR) algorithm.Utilize the IR algorithm can make to train the network weight of gained less, the network response is smooth-out, reduces the possibility of over-fitting.

The research discovery, longer input and output delayed data sequence can be learnt the dynamics of real system preferably.But, in the dynamic system of wheel-rail interaction, some peak value in wheel rail dynamics response, generally exceed the average amplitude of system dynamics, these peak values are difficult to carry out modeling by conventional neural network.This research discovery, these peak values can adopt shorter input and output delayed data sequence to be similar to.Therefore this research is on the improved basis of its algorithm, its network structure is further improved, obtain the neural network that comprises 2 centres, longer input and output delayed data sequence is responsible for receiving in one of them middle layer, another middle layer is responsible for receiving shorter input and output delayed data sequence, nothing contact between two middle layers.

Network performance evaluation function shown in employing formula (1) in the IR method

F(w)＝(1-γ)E _D+γE _w (1)

In formula:

γ is modifying factor, 0≤γ≤1, value 0.3;

E _wquadratic sum for all weights of network (and threshold value);

E _dquadratic sum for network error.

Be provided with n time delay node layer, h middle layer node, the NARX neural network of m output has the input and output sample data its p:

${E_D}^{\left(p\right)}=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\frac{{({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})}^2}{2}---\left(2\right)$

${E_w}^{\left(p\right)}=\frac{1}{N_w}[\underset{j=1}{\overset{h}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left({w_{\mathrm{ij}}}^{\left(p\right)}\right)}^2+\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{h}{\mathrm{\Σ}}}{\left({w_{\mathrm{jk}}}^{\left(p\right)}\right)}^2]---\left(3\right)$

In formula:

E _d ^(p)being the network error quadratic sum of p to the input and output sample data, is (p) numbering;

D _kbe the target output of k output layer node;

Y _kbe the network output of k output layer node;

E _w ^(p)be the network weight quadratic sum of p to the input and output sample data;

N _wadjustable weights number for network;

W _ijbe that i time delay node layer is to weights between j middle layer node;

W _jkbe the weights of j middle layer node to k output layer node;

N time delay node layer;

H middle layer node;

M output number.

Weights optimization adopts gradient descent method, establishes the middle layer activation function and is

output layer linear process function is f ₀(x)=x, output layer and middle layer weights correction are respectively:

$\mathrm{\Δ}{w_{\mathrm{jk}}}^{\left(p\right)}=(1-\mathrm{\γ})\·({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})\·{{\mathrm{hx}}_j}^{\left(p\right)}+\mathrm{\γ}\·\frac{2}{N_w}\·{w_{\mathrm{jk}}}^{(p-1)}---\left(4\right)$

$\mathrm{\Δ}{w_{\mathrm{ij}}}^{\left(p\right)}=(1-\mathrm{\γ})\·\underset{l=1}{\overset{m}{\mathrm{\Σ}}}({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})\·{w_{\mathrm{jk}}}^{\left(p\right)}\·\frac{\mathrm{\λ}}{2}(1-{\left({{\mathrm{ox}}_j}^{\left(p\right)}\right)}^2)\·{{\mathrm{ox}}_i}^{\left(p\right)}+\mathrm{\γ}\·\frac{2}{N_w}\·{w_{\mathrm{ij}}}^{(p-1)}---\left(5\right)$

Output layer and middle layer weights are adjusted by formula (6) and formula (7) respectively:

w _jk ^(p)＝w _jk ^(p-1)-ηΔw _jk ^(p) (6)

w _ij ^(p)＝w _ij ^(p-1)-ηΔw _ij ^(p) (7)

In formula (4)～formula (7):

Δ w _jk ^(p)be the output layer weights correction of p to the input and output sample data;

be the middle layer weights correction of p to the input and output sample data;

The parameter that λ is the middle layer activation function, value is 1;

D _k ^(p)be the target output of p to k output layer node of input and output sample data;

Y _k ^(p)be the network output of p to k output layer node of input and output sample data;

W _jk ^(p-1)the weights to k output layer node that are p-1 to j middle layer node of input and output sample data;

be j the middle layer node input of p to the input and output sample data;

be the input of p to i output layer node of input and output sample data;

η is learning rate, value 0.006.

The present invention adopts the NARX neural network based on algorithm improvement and architecture advances to predict rate of wheel load reduction, and training adopts the regularization algorithm that improves and simplify, and neural network structure is parallel two middle layers neural networks, and its structure as shown in Figure 1.

(5) training NARX neural network prediction model

Extract 2500 groups of input and output in data after normalization as training sample, the parameter that needs training to optimize in training process is weights and threshold value, error function is larger on the impact of network performance, when the structure of network fixedly the time, the problem of the network promotion aspect produced due to the size of how much of training is mainly network over-fitting problem.For overcoming the over-fitting problem, this neural metwork training adopts improved regularization algorithm.

(6) test NARX neural network prediction model

Extract in addition 500 groups of input and output as test sample book in normalized data.Utilize and to have trained complete NARX neural network prediction model, the left rail in the input test sample suitable, the left rail rail that is uneven to be uneven suitable, right rail rail to irregularity to irregularity, right rail, the output rate of wheel load reduction.

(7) performance evaluation of NARX neural network prediction model

In order to estimate the performance of NARX neural network prediction model, the present invention is respectively to the accuracy of model, and curve situation and the correlativity of model output and target output are analyzed.

Specifically be implemented as follows:

(1) prepare the input data

Certain rail track is carried out to the track detection, extract the data of 3000 groups of track irregularities, comprise that left rail suitable, the left rail rail that is uneven is uneven suitable, right rail rail to irregularity to irregularity, right rail.

(2) prepare target output data

By dynamics simulation software ADAMS/RAIL, set up vehicle/dynamics of orbits model, input 3000 groups of track irregularity data, carry out emulation, obtain corresponding rate of wheel load reduction data, as the target output data of neural network model.

(3) data pre-service

Because the inputoutput data size is uneven, larger order of magnitude difference is even arranged.And, in the employing neural network is carried out the process of system modelling, the random initial weight arranged of network, in same level, if data differences is very large, by the imbalance caused on neural network learning, affects the convergence of network.Therefore, in modeling process, in order to make it, there is convergence preferably, before the input network training, data normalization can be processed.This paper has carried out following linear normalization processing to the inputoutput data of system:

${x_i}^{\mathrm{scal}}=\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$

Wherein:

for the data after normalization;

X _ifor the data before normalization;

X _maxand x _minbe respectively maximal value and the minimum value of variable x.

(4) set up the NARX neural network prediction model

The NARX neural network of architecture advances comprises two parallel middle layers, longer input and output delayed data sequence is responsible for receiving in one of them middle layer, shorter input and output delayed data sequence is responsible for receiving in another middle layer, the hidden interstitial content in two middle layers is 20, input and output delayed data sequence total length is 45, wherein the long sequence of input and output delayed data is [30 45], and the short sequence of input and output delayed data is [15].

(5) the NARX neural network is trained

Extract front 2500 groups of data in track irregularity after normalization and rate of wheel load reduction data as training sample.This neural metwork training adopts improved regularization algorithm, according to repetition test, determines that the training iterations is 1000.

(6) NARX neural network prediction model training completed is tested

After extracting in track irregularity after normalization and rate of wheel load reduction data, 500 groups of data, as test sample book, are tested the NARX neural network prediction model after training.

(7) performance of NARX neural network prediction model is estimated

Target rate of wheel load reduction in model output rate of wheel load reduction and test sample book is once analyzed, estimated the performance of NARX neural network prediction model.

The present invention adopts root-mean-square error (Root Mean Square Error, RMSE) to estimate the performance of neural network:

$\mathrm{RMSE}(y,y_m)=\sqrt{\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{(y\left(i\right)-y_m\left(i\right))}^2}$

Wherein:

RMSE (y, y _m) be the value of root-mean-square error;

Y is desired value in test sample book;

Y _mpredicted value for the model after renormalization;

N is the data sample number.

The RMSE value is less, means that the precision of prediction of model is higher, and predicted value more approaches desired value.

Secondly, model output and target output are carried out curve fitting, can reflect more intuitively the degree of approximation between target output value and model output valve.

Finally, model output and target output are carried out to linear regression analysis, can accurately calculate the related coefficient between target output value and model output valve.

The above; be only the present invention's embodiment preferably, but protection scope of the present invention is not limited to this, anyly is familiar with in technical scope that those skilled in the art disclose in the present invention; the variation that can expect easily or replacement, within all should being encompassed in protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (3)

1. the Forecasting Methodology of a rate of wheel load reduction is characterized in that the method comprises the following steps:

Step 1: utilize track detection vehicle to detect the irregularity data of track;

Step 2: the irregularity data that gather by step 1, utilize ADAMS/RAIL software to set up vertical wheel rail force and horizontal wheel rail force that model emulation is tried to achieve track, and then try to achieve rate of wheel load reduction, and to the rate of wheel load reduction normalized;

Step 3: utilize the rate of wheel load reduction after normalization to be trained improved NARX neural network prediction model, and determine the weights of NARX neural network prediction model and the effect of optimization of threshold value by the specified network validity function;

Described normalization formula is:

${x_i}^{\mathrm{scal}}\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$

Wherein:

X _i ^scalfor the data after normalization;

X _ifor the data before normalization;

X _maxand x _minbe respectively maximal value and the minimum value of variable x;

The structure of described NARX neural network prediction model comprises 2 middle layers, longer input and output delayed data sequence is responsible for receiving in one of them middle layer, another middle layer is responsible for receiving shorter input and output delayed data sequence, nothing contact between two middle layers;

The described method that improved NARX neural network prediction model is trained is improved regularization algorithm; The network performance evaluation function of described improved regularization algorithm:

F(w)=(1-γ)E _D+γE _w

In formula:

F (w) is the network performance evaluation functional value;

W is weights;

γ is modifying factor, 0≤γ≤1, value 0.3;

E _wquadratic sum for all weights of network or threshold value;

E _dquadratic sum for network error;

Described E _wand E _dcomputing formula be respectively:

${E_D}^{\left(p\right)}=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\frac{{({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})}^2}{2}$

${E_w}^{\left(p\right)}=\frac{1}{N_w}[\underset{j=1}{\overset{h}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left({w_{\mathrm{ij}}}^{\left(p\right)}\right)}^2+\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{h}{\mathrm{\Σ}}}{\left({W_{\mathrm{jk}}}^{\left(p\right)}\right)}^2]$

In formula:

E _d ^(p)be the network error quadratic sum of p to the input and output sample data;

D _kbe the target output of k output layer node;

Y _kbe the network output of k output layer node;

E _w ^(p)be the network weight quadratic sum of p to the input and output sample data;

N _wadjustable weights number for network;

W _ijbe that i time delay node layer is to weights between j middle layer node;

W _jkbe the weights of j middle layer node to k output layer node;

W _ij ^(p)be p to i time delay node layer of input and output sample data to weights between j middle layer node;

W _jk ^(p)the weights to k output layer node that are p to j middle layer node of input and output sample data;

N time delay node layer;

H middle layer node;

M output number;

The activation function in described middle layer is

the linear process function of output layer is f ₀(x)=x, and output layer and middle layer weights correction are respectively:

$\mathrm{\Δ}{w_{\mathrm{jk}}}^{\left(p\right)}=(1-\mathrm{\γ})\·({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)})\·{{\mathrm{hx}}_j}^{\left(p\right)}+\mathrm{\γ}\·\frac{2}{N_w}\·{w_{\mathrm{jk}}}^{(p-1)}$

$\mathrm{\Δ}{w_{\mathrm{ij}}}^{\left(p\right)}=(1-\mathrm{\γ}).\underset{l=1}{\overset{m}{\mathrm{\Σ}}}({d_k}^{\left(p\right)}-{y_k}^{\left(p\right)}).{w_{\mathrm{jk}}}^{\left(p\right)}.\frac{\mathrm{\λ}}{2}(1-{\left({{\mathrm{ox}}_j}^{\left(p\right)}\right)}^2).{{\mathrm{ox}}_i}^{\left(p\right)}+\mathrm{\γ}.\frac{2}{N_w}.{w_{\mathrm{ij}}}^{(p-1)}$

In formula:

Δ w _jk ^(p)be the output layer weights correction of p to the input and output sample data;

Δ w _ij ^(p)be the middle layer weights correction of p to the input and output sample data;

The parameter that λ is the middle layer activation function, value is 1;

D _k ^(p)be the target output of p to k output layer node of input and output sample data;

Y _k ^(p)be the network output of p to k output layer node of input and output sample data;

W _jk ^(p-1)the weights to k output layer node that are p-1 to j middle layer node of input and output sample data;

Hx _i ^(p)be j the middle layer node input of p to the input and output sample data;

Ox _i ^(p)be the input of p to i output layer node of input and output sample data;

The adjustment of described output layer and middle layer weights is respectively:

${w_{\mathrm{jk}}}^{\left(p\right)}={w_{\mathrm{jk}}}^{(p-1)}-{{\mathrm{\η\Δw}}_{\mathrm{jk}}}^{\left(p\right)}$

${w_{\mathrm{ij}}}^{\left(p\right)}={w_{\mathrm{ij}}}^{(p-1)}-{{\mathrm{\η\Δw}}_{\mathrm{ij}}}^{\left(p\right)}$

In formula:

η is learning rate, and value is 0.006;

Step 4: the improved NARX neural network prediction model after the data input training that step 1 is gathered obtains rate of wheel load reduction, uses the root-mean-square error method to this model evaluation.

2. the Forecasting Methodology of a kind of rate of wheel load reduction according to claim 1, is characterized in that described track irregularity data comprise that left rail is uneven and are uneven along data and right rail rail to the irregularity data to irregularity data, right rail along data, left rail rail.

3. the Forecasting Methodology of a kind of rate of wheel load reduction according to claim 1 is characterized in that the formula of described root-mean-square error method is:

$\mathrm{RMSE}(y,y_m)=\sqrt{\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{(y\left(i\right)-y_m\left(i\right))}^2}$

Wherein:

RMSE (y, y _m) be the value of root-mean-square error;

Y is desired value in test sample book;

Y _mpredicted value for the model after renormalization;

N is the data sample number.

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