Track irregularity prediction method based on data generation and LS-SVR under Bayesian framework

Abstract

The invention discloses a track irregularity prediction method based on data generation and LS-SVR under a Bayesian framework, and the method specifically comprises the following steps: 1, fixing a time interval, and collecting the geometric deformation data of a track section; step 2, calculating a track quality state based on the data collected in the step 1, obtaining a comprehensive irregularity state of the track, and recording a maintenance operation time point; 3, converting the track irregularity state data into three-dimensional data through sliding window shift sampling, and inputting the generated three-dimensional data into a data generation model to output generated data; step 4, constructing an LS-SVR track irregularity prediction model under a Bayesian framework by using the data obtained in the step 2 and the step 3; and step 5, obtaining the future irregularity state and probability distribution of the orbit by using LS-SVR. The track irregularity prediction method solves the problems that an existing track irregularity prediction method is not high in precision and poor in reliability, and uncertainty and prediction errors are difficult to measure.

Description

Technical Field

[0001] The present invention belongs to the technical field of information prediction methods, and in particular relates to a track irregularity prediction method based on LS-SVR under a Bayesian framework and data generation. Background Art

[0002] According to the global railway transport development forecast for 2023-2030, the demand for railway passenger and freight transport is expected to continue to grow in the next few years. The track is a key and basic part of the transportation system, but due to the influence of traffic loads and geological factors, the railway track will undergo geometric deformation. This geometric deformation causes the train to interact with the track, resulting in cumulative plastic strain, that is, track unevenness, which leads to increased dynamics at the wheel-rail interface. When the uneven state of the track exceeds the threshold, the interaction process between the train and the track will cause noise and vibration pollution to the surrounding area, and even cause the train to derail, resulting in huge loss of life and property.

[0003] Currently, the infrastructure management departments (Instruction Managers, IMs) restore the track unevenness to normal through track maintenance operations. The quality of maintenance operations depends on the time point of maintenance operations. Too frequent maintenance operations will not only bring high maintenance costs and affect the normal operation of railway transportation; however, untimely maintenance operations will cause the track unevenness to exceed the threshold, affecting the quality of railway transportation services, causing noise and vibration pollution, and even safety accidents. In 2018 alone, the EU spent more than 20.6 billion euros on railway maintenance, accounting for more than 50% of the total annual railway facility maintenance costs. Therefore, the ideal track maintenance operation plan is to ensure that the track unevenness is carried out before the threshold is approached and the track is restored to its uneven state.

[0004] Accurately predicting the track irregularity is the key for IMs to develop reliable and cost-effective track maintenance plans for railway transportation systems. Existing track irregularity prediction methods can be roughly divided into: physical model-based prediction methods and data-driven prediction methods. Physical model-based methods rely on modeling track irregularity, but the formation and development of track irregularity is very complex, and it is generally difficult to establish an accurate physical model, which results in existing prediction methods being limited to irregularity prediction under specific conditions, such as track irregularity prediction under foundation settlement. Data-driven track irregularity prediction methods rely on track irregularity data and usually use statistical methods for prediction. However, the scarcity of track irregularity data has resulted in most data-driven prediction methods being limited to linear regression methods with low prediction accuracy. In addition, researchers rarely incorporate uncertainty into prediction methods, resulting in unreliable prediction results. Summary of the invention

[0005] The purpose of the present invention is to provide a track irregularity prediction method based on data generation and LS-SVR under a Bayesian framework, which solves the problems of low accuracy, poor reliability and difficulty in quantification of existing track irregularity prediction methods.

[0006] The technical solution adopted by the present invention is a track irregularity prediction method based on LS-SVR under data generation and Bayesian framework, which is specifically implemented in the following steps:

[0007] Step 1, collecting geometric deformation data of the track section at fixed time intervals;

[0008] Step 2: Based on the data collected in step 1, calculate the track quality status, obtain the comprehensive unevenness status of the track, and record the maintenance operation time point;

[0009] Step 3, converting the track irregularity state data into three-dimensional data by sliding window shift sampling, and inputting the generated three-dimensional data into a data generation model to output generated data;

[0010] Step 4, using the data obtained in Steps 2 and 3, construct a LS-SVR track irregularity prediction model under a Bayesian framework;

[0011] Step 5: Use LS-SVR to obtain the future irregularity of the track.

[0012] The present invention is also characterized in that:

[0013] Step 2 is implemented as follows:

[0014] Step 2.1, calculate the mean of the track deformation data and standard deviation Get track status indicators

[0015] Step 2.2, calculate the minimum TQI of all time points min and maximum TQI max ;

[0016] Step 2.3, map the data obtained in step 2.2 to the real number interval [0,1] through the minimum and maximum normalization method.

[0017] Step 3 is implemented as follows:

[0018] Step 3.1: Based on the data obtained in step 2 and the recorded maintenance time points, the track irregularity status data is divided into Where T is the time point of data collection, and M is the number of maintenance operations;

[0019] Step 3.2, sample the data obtained in step 3.1 along the time axis with a sliding window of length l, and the sliding window moves at an interval of h to obtain T-1 two-dimensional matrices with a time axis length of l;

[0020] Step 3.3, concatenate the two-dimensional matrix obtained in step 3.2 into a three-dimensional matrix along the sliding window moving sequence, with a shape of [T-1, l, M];

[0021] Step 3.4, input the data obtained in step 3.3 into the TimeGAN network to output generated data.

[0022] Step 4 is implemented according to the following steps:

[0023] Step 4.1: construct the training set through sliding window, that is, through [x i-1 ,x i-2 ,…x i-k ]Predict x i ;

[0024] Step 4.2, construct the objective function of LS-SVR;

[0025] Step 4.3, maximize the likelihood function P(D|σ) through linear search σ to obtain the optimal kernel function σ MP ;

[0026] Step 4.4, based on σ MP pass Infer the optimal hyperparameter μ MP and The prediction model H is LS-SVR, μ and is the variable hyperparameter of the LS-SVR objective function, and D is the concatenation result of the data obtained in step 3 and step 4;

[0027] Step 4.5, based on the real data and generated data obtained in steps 2 and 3, maximize the posterior probability Get the optimal parameter ω of the prediction model H MP and b MP .

[0028] Step 5 is implemented according to the following steps:

[0029] Step 5.1: Marginalize the model parameters ω and b to obtain the marginal distributions of ω and b

[0030] Step 5.2, the expectation of the prediction result can be expressed as The prediction variance can be expressed as in

[0031] Step 5.3, based on the expected y and variance σ 2The upper and lower bounds of the 95% confidence interval [y-(1.96×σ),y+(1.96×σ)] can be obtained.

[0032] The beneficial effects of the present invention are:

[0033] The track irregularity prediction method of LS-SVR based on data generation and Bayesian framework is considered, the uncertainty of the track smoothness state itself and the uncertainty of the prediction model error are taken into account, and a more accurate and reliable track irregularity prediction is achieved by replacing the predicted value with the expectation and expressing the uncertainty with the variance, thus overcoming the problem of poor accuracy of the data-driven method under small sample conditions. The hyperparameters of LS-SVR are determined by Bayesian framework, and the uncertainty of the track irregularity state is taken into account, so that LS-SVR outputs the probability distribution of the prediction results instead of a single prediction value, and finally a reliable track irregularity state prediction result is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is an overall flow chart of the track irregularity prediction method based on data generation and LS-SVR under the Bayesian framework of the present invention;

[0035] Figure 2 It is a track irregularity state diagram in the track irregularity prediction method based on LS-SVR under the Bayesian framework of the present invention;

[0036] Figure 3 It is the real data and generated number of track irregularity in the track irregularity prediction method based on data generation and LS-SVR under the Bayesian framework of the present invention;

[0037] Figure 4 It is a track irregularity state prediction result diagram in the track irregularity prediction method of LS-SVR based on data generation and Bayesian framework in the present invention. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] The present invention provides a track irregularity prediction method based on data generation and LS-SVR under a Bayesian framework, as shown in the following embodiments:

[0040] Example 1

[0041] like Figure 1As shown, the present invention is based on the track irregularity prediction method of LS-SVR under the data generation and Bayesian framework, collects track deformation data, calculates the track quality status, obtains the comprehensive irregularity state of the track, converts the track irregularity state data into three-dimensional data, and then inputs it into the data generation model, and then constructs the LS-SVR track irregularity prediction model under the Bayesian framework, and uses LS-SVR to obtain the future irregularity state of the track.

[0042] Example 2

[0043] The track irregularity prediction method based on data generation and LS-SVR under the Bayesian framework is implemented in the following steps:

[0044] Step 1: At fixed time intervals, the track inspection vehicle collects geometric deformation data of a 200m long track section in units of 0.25m;

[0045] The geometric deformation data in step 1 specifically include left track height deformation, right track height deviation, left track deviation, right track deviation, track gauge deviation, horizontal deviation and triangular pit deviation;

[0046] Step 2: Based on the data collected in step 1, calculate the track quality status, obtain the comprehensive unevenness status of the track, and record the maintenance operation time point;

[0047] Step 2 is implemented as follows:

[0048] Step 2.1, calculate the mean of the seven deformation data of the track and standard deviation Get track status indicators

[0049] Step 2.2, calculate the minimum TQI of all time points min and maximum TQI max ;

[0050] Step 2.3, map the data obtained in step 2.2 to the real number interval [0,1] by the minimum and maximum normalization method;

[0051] Step 3, converting the track irregularity state data into three-dimensional data by sliding window shift sampling, and inputting the generated three-dimensional data into a data generation model to output generated data;

[0052] Step 3 is implemented as follows:

[0053] Step 3.1: Based on the data obtained in step 2 and the recorded maintenance time points, the track irregularity status data is divided into Where T is the time point of data collection, and M is the number of maintenance operations;

[0054] Step 3.2, sample the data obtained in step 3.1 along the time axis with a sliding window of length l, and the sliding window moves at an interval of h to obtain T-1 two-dimensional matrices with a time axis length of l;

[0055] Step 3.3, concatenate the two-dimensional matrix obtained in step 3.2 into a three-dimensional matrix along the sliding window moving sequence, with a shape of [T-1, l, M];

[0056] Step 3.4, input the data obtained in step 3.3 into the TimeGAN network to output generated data;

[0057] Step 4, using the data obtained in Steps 2 and 3, construct a LS-SVR track irregularity prediction model under a Bayesian framework;

[0058] Step 4 is implemented according to the following steps:

[0059] Step 4.1: construct the training set through sliding window, that is, through [x i-1 ,x i-2 ,…x i-k ]Predict x i ;

[0060] Step 4.2, construct the objective function of LS-SVR;

[0061] Step 4.3, maximize the likelihood function P(D|σ) through linear search σ to obtain the optimal kernel function σ MP ;

[0062] Step 4.4, based on σ MP The optimal hyperparameter μ is inferred by formula 1 MP and The prediction model H is LS-SVR, μ and is the variable hyperparameter of the LS-SVR objective function, and D is the concatenation result of the data obtained in step 3 and step 4;

[0063]

[0064] Step 4.5, based on the real data and generated data obtained in steps 2 and 3, maximize the posterior probability Get the optimal parameter ω of the prediction model H MP and b MP , as shown in formula 2;

[0065]

[0066] Step 5, use LS-SVR to obtain the future track irregularity;

[0067] Step 5.1, marginalize the model parameters ω and b by formula 3 to obtain the marginal distribution of ω and b;

[0068]

[0069] Step 5.2, the expectation of the prediction result can be expressed as The prediction variance can be expressed as in

[0070] Step 5.3, based on the expected y and variance σ 2 The upper and lower bounds of the 95% confidence interval [y-(1.96×σ),y+(1.96×σ)] can be obtained.

[0071] Example 3

[0072] The track irregularity prediction method based on data generation and LS-SVR under the Bayesian framework is implemented in the following steps:

[0073] Step 1: At fixed time intervals, the track inspection vehicle collects geometric deformation data of a 200m long track section in units of 0.25m. The geometric deformation data includes: left height deformation, right height deviation, left track deviation, right track deviation, track gauge deviation, horizontal deviation and triangular pit deviation, recorded as The acquisition time point i = {1, 2, ..., n}, and the 7 track deformation indicators i = {1, 2, ..., 7};

[0074] Step 2: Based on the data collected in step 1, calculate the track quality index (TQI), obtain the comprehensive unevenness of the track, and record the maintenance operation time. The results are as follows: Figure 2 As shown;

[0075] Step 2 is implemented as follows:

[0076] Step 2.1, calculate the mean of the seven track deformation data with 800 data as units and standard deviation Get track status indicators

[0077] Step 2.2, calculate the minimum TQI of all time points min and maximum TQI max ;

[0078] Step 2.3: Based on the data obtained in step 2.2, obtain normalized TQI data using formula (4).

[0079]

[0080] Step 3: divide the data obtained in step 2 based on the maintenance operation time point, and transform the track irregularity data into three-dimensional data through sliding window shift sampling. The generated three-dimensional data is input into the TimeGAN network to output the generated data. The result is as follows: Figure 3 As shown;

[0081] Step 3 is implemented as follows:

[0082] Step 3.1: Based on the data obtained in step 2 and the recorded maintenance time points, the track irregularity status data is divided into Where T is the time point of data collection, and M is the number of maintenance operations.

[0083] Step 3.2, sample the data obtained in step 3.1 along the time axis with a sliding window of length l, and the sliding window moves at an interval of h (h is usually 1), and obtain nl two-dimensional matrices with a time axis length of l;

[0084] Step 3.3, concatenate the two-dimensional matrix obtained in step 3.2 into a three-dimensional matrix along the sliding window moving sequence, with a shape of [T-1, l, M];

[0085] Step 3.4, input the data obtained in step 3.3 into the TimeGAN network to output generated data;

[0086] Step 4, using the data obtained in Steps 2 and 3, construct a LS-SVR track irregularity prediction model under a Bayesian framework;

[0087] Step 4 is implemented according to the following steps:

[0088] Step 4.1: Based on the data obtained in Steps 2 and 3, construct a training set through a sliding window, that is, through [x i-1 ,x i-2 ,…x i-k ]Predict x i The TQI value of k in this example is usually 5 or 6;

[0089] Step 4.2, construct the objective function of LS-SVR as shown in formula (5), where is a nonlinear mapping function, b is a bias term, and ω is a weight vector;

[0090]

[0091]

[0092] Step 4.3, according to formula 7, the optimal kernel function σ is obtained by linear search σ to maximize the likelihood function P(D|σ) MP ;

[0093] P(σ|D)∝P(D|σ)P(σ) (7)

[0094] Step 4.4, based on σ MP And formula (8) to infer the optimal hyperparameter μ MP and The prediction model H is LS-SVR, μ and is the variable hyperparameter of the LS-SVR objective function, and D is the concatenation result of the data obtained in step 2 and step 4;

[0095]

[0096] Step 4.5, based on the real data and generated data obtained in steps 2 and 3, maximize the posterior probability The optimal parameter ω of the prediction model H MP and b MP , as shown in formula (9);

[0097]

[0098] Step 5 is implemented according to the following steps:

[0099] Step 5.1: marginalize the model parameters ω and b using formula (10) to obtain the marginal distribution of ω and b

[0100]

[0101] Step 5.2, the expectation of the prediction result can be expressed as The prediction variance can be expressed as in

[0102] Step 5.3, based on the expected y and variance σ 2 The upper and lower bounds of the 95% confidence interval of the prediction result are obtained by formula (11).

[0103] CI=y±(1.96×σ) (11)

[0104] Step 5.4, use LS-SVR to obtain the future track irregularity. The result is as follows: Figure 4 As shown, Figure 4 a is the first stage track irregularity state prediction result diagram, Figure 4 b is the track irregularity prediction result diagram of the second stage. Figure 4 c is the second-stage track irregularity prediction result diagram. The error comparison of different prediction models is shown in Table 1. We use RMSE as the metric to measure the prediction error and reliability, as shown in formula (12). tand are the actual value and predicted value at time t respectively.

[0105]

[0106] Table 1 Comparison results of RMSE of prediction models

[0107]

[0108]

[0109] The track irregularity prediction method of LS-SVR based on data generation and Bayesian framework in this invention takes into account the uncertainty of the track smoothness state itself and the uncertainty of the prediction model error, and realizes a more accurate and reliable track irregularity prediction that replaces the prediction value with the expectation and describes the uncertainty with the variance, thus overcoming the limitation of the poor accuracy of the data-driven method under the condition of small samples. The hyperparameters of LS-SVR are determined by Bayesian framework, so that LS-SVR outputs the probability distribution of the prediction results instead of a single prediction value, filling the gap that the prediction model does not consider the uncertainty of the track irregularity state, and finally obtains a reliable track irregularity state prediction result.

Claims

1. A track irregularity prediction method based on LS-SVR in a Bayesian framework based on data generation is characterized by: Please follow the steps below to implement: Step 1, collecting geometric deformation data of the track section at fixed time intervals; Step 2: Based on the data collected in step 1, calculate the track quality status, obtain the comprehensive unevenness status of the track, and record the maintenance operation time point; Step 3, converting the track irregularity state data into three-dimensional data by sliding window shift sampling, and inputting the generated three-dimensional data into a data generation model to output generated data; Step 4, using the data obtained in Steps 2 and 3, construct a LS-SVR track irregularity prediction model under a Bayesian framework; Step 5: Use LS-SVR to obtain the future irregularity of the track.

2. The track irregularity prediction method based on data generation and LS-SVR under Bayesian framework according to claim 1 is characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1, calculate the mean of the seven track deformation data and standard deviation Get track status indicators Step 2.2, calculate the minimum TQI of all time points min and maximum TQI max ; Step 2.3, map the data obtained in step 2.2 to the real number interval [0,1] through the minimum and maximum normalization method.

3. The track irregularity prediction method based on data generation and LS-SVR under Bayesian framework according to claim 1 is characterized in that: The step 3 is specifically implemented according to the following steps: Step 3.1: Based on the data obtained in step 2 and the recorded maintenance time points, the track irregularity status data is divided into Where T is the time point of data collection, and M is the number of maintenance operations; Step 3.2, sample the data obtained in step 3.1 along the time axis with a sliding window of length l, and the sliding window moves at an interval of h to obtain T-1 two-dimensional matrices with a time axis length of l; Step 3.3, concatenate the two-dimensional matrix obtained in step 3.2 into a three-dimensional matrix along the sliding window moving sequence, with a shape of [T-1, l, M]; Step 3.4, input the data obtained in step 3.3 into the TimeGAN network to output generated data.

4. The track irregularity prediction method based on data generation and LS-SVR under Bayesian framework according to claim 1 is characterized in that: The step 4 is specifically implemented according to the following steps: Step 4.1: construct the training set through sliding window, that is, through [x i-1 ,x i-2 ,…x i-k ]Predict x i ; Step 4.2, construct the objective function of LS-SVR; Step 4.3, maximize the likelihood function P(D|σ) through linear search σ to obtain the optimal kernel function σ MP ; Step 4.4, based on σ MP pass Infer the optimal hyperparameter μ MP and The prediction model H is LS-SVR, μ and is the variable hyperparameter of the LS-SVR objective function, and D is the concatenation result of the data obtained in step 3 and step 4; Step 4.5, based on the real data and generated data obtained in steps 2 and 3, maximize the posterior probability Get the optimal parameter ω of the prediction model H MP and b MP .

5. The track irregularity prediction method based on data generation and LS-SVR under Bayesian framework according to claim 1 is characterized in that: Described step 5 is specifically implemented according to the following steps: Step 5.1, marginalize the model parameters ω and b to obtain the marginal distributions of ω and b; Step 5.2, the expectation of the prediction result can be expressed as The prediction variance can be expressed as in Step 5.3, based on the expected y and variance σ 2 Calculate the upper and lower bounds of the 95% confidence interval [y-(1.96×σ),y+(1.96×σ)].

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