Track irregularity chord extension inversion method driven by embedded physical neural network

Abstract

The invention discloses a track irregularity chord extension inversion method driven by an embedded physical neural network, and the method comprises the steps: optimizing chord measurement chord extension process matrix expression: condensing a matrix expression form from a track irregularity sequence to a reference chord sequence, and deducing a matrix expression form of an extension chord sequence from the reference chord sequence; establishing a forward extension calculation layer based on multi-channel convolution, and obtaining a reference chord and a plurality of extension chord values at the same time through one-time forward calculation; establishing a deep Bayesian feature extraction layer, wherein the deep Bayesian feature extraction layer is used for learning a complex structure and advanced abstraction in the input data; establishing an embedded multi-chordal measurement equation set to invert a loss function: taking the chordal measurement and extension sequences obtained in the second step as target values, realizing inversion by minimizing the difference between the target values and model estimation values, and establishing the loss function; self-adaptive early stop iteration is used for ensuring rapid and accurate convergence stop of the model; the large-scale data processing requirement in the practical application process is met.

Description

Technical Field

[0001] The invention relates to the technical field of railway track smoothness detection, in particular to a track unevenness chord expansion inversion method embedded with a physical neural network drive. Background Art

[0002] Track irregularity is the main cause of high-speed train vibration instability and track structure performance degradation. The chord measurement method is the most common basic principle in the process of track static detection, and it is also the most intuitive method to express track irregularity. In fact, with the deepening of research, scholars have found that the track irregularity obtained by the chord measurement method is not the original track irregularity waveform, and its measurement wavelength will have different degrees of magnification effect with different chord lengths, also known as "transfer function". If the original waveform cannot be effectively restored, the chord measurement results can only be used to analyze the relative size of track irregularity, and cannot accurately guide maintenance and adjustment work. Therefore, scholars have carried out a series of restoration algorithm research. Japanese scholar Yosh imura first proposed in 1995 to design the measurement process as a finite impulse response (FIR) filter, and construct an inverse filter with the opposite frequency response to achieve restoration; Munoz developed a lateral irregularity detection method based on Kalman filtering. Another idea was proposed by Chinese scholar Wang Yuan in 2019, using the inverse structure of the detection system to construct an inverse system to directly solve this problem. Cong Jianli added a regularization term coefficient on this basis to improve stability. In addition, some partial point and multi-point restoration methods have been derived. However, the existing methods all have a common problem, which is that they cannot consider multiple detection system processes simultaneously in one inversion process. Most of them are combinations of multiple single system results, and they do not use the powerful solving ability of neural networks to solve large-scale data analysis problems. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a track irregularity chord expansion inversion method embedded in a physical neural network drive. The present invention realizes the inversion of wide-band information of track irregularity by fusing multiple processes to meet the large-scale data processing requirements in practical applications.

[0004] To achieve the above object, the technical solution adopted by the present invention is: a track unevenness chord extension inversion method embedded in a physical neural network drive, comprising the following steps:

[0005] Step 1: Optimize the matrix expression of the chord measurement and chord expansion process: condense the matrix expression from the track unevenness sequence to the reference chord sequence, and derive the matrix expression of the extended chord sequence from the reference chord sequence;

[0006] Step 2: Establish a forward extension calculation layer based on multi-channel convolution, and obtain the reference chord and multiple extended chord values ​​at the same time through one forward calculation;

[0007] Step 3: Establish a deep Bayesian feature extraction layer: Through multiple layers of nonlinear transformations and Monte Carlo random dropout neurons, the deep Bayesian feature extraction layer is used to learn complex structures and high-level abstractions in the input data;

[0008] Step 4: Establish the inversion loss function of the embedded multi-string measurement equation group: take the string measurement and expansion sequence obtained in the second step as the target value, realize the inversion by minimizing the difference between the target value and the model estimation value, and establish the loss function;

[0009] Step 5: Adaptive early stopping iteration is used to ensure that the model converges quickly and accurately.

[0010] As a further improvement of the present invention, the step 1 is specifically as follows:

[0011] First, we condense the sequence from the orbital unevenness sequence d to the reference chord sequence V B The matrix expression of is as follows:

[0012]

[0013] Where L is the chord length, s is the sampling step, γ and They represent the chord length division ratios on the left and right sides of the division point, a and b represent the lengths of the left and right sides after division, M and m represent the track irregularity and the length of the reference chord sequence, respectively. (1) In the formula, the chord length division ratio coefficient matrix can be condensed into a fixed parameter measurement matrix H;

[0014] Secondly, condense the reference string sequence V B Derivation of the extended chord sequence V E The matrix expression of is as follows (2):

[0015]

[0016] Among them, V B and V E Represent the reference chord and the extended chord sequence respectively, m and N represent the length of the reference chord and the extended chord sequence respectively, and n represents the number of steps the reference chord moves in the extended chord.

[0017] As a further improvement of the present invention, the step 2 is specifically as follows:

[0018] Based on the one-dimensional effective convolutional network layer, the equivalent calculation layer of equation (1) and equation (2) is established. The convolution calculation equation is as follows:

[0019]

[0020] in, Represents the feature map corresponding to the convolution kernel at position u in layer l; Represents the feature map corresponding to the convolution kernel at position i+u in layer l-1; δ i represents the i-th convolution operation; c l represents the bias of the lth layer; represents the i-th convolution kernel in layer l; z represents the maximum number of convolution kernels.

[0021] As a further improvement of the present invention, in step 3, the deep Bayesian feature extraction layer extracts each input z p×u implement:

[0022] Z p×o =z p×u ·w u×o +c (4)

[0023] Among them, Z represents the extracted features of the output, p and o are the input and output feature lengths respectively; u represents the potential feature dimension; w represents the parameters to be learned by the model; c represents the bias of the o-dimensional vector; considering that the distribution characteristics of track irregularities conform to the characteristics close to the normal distribution, the hyperbolic tangent Tanh function is used for nonlinear activation in the low-dimensional space.

[0024] As a further improvement of the present invention, the step 4 is specifically as follows:

[0025] After multiple sets of chord length data targets are expanded, corresponding sets of chord measurement equations are established as the basis for loss function design:

[0026]

[0027] Where H represents the measurement matrix; d represents the uneven sequence column; V x 、V y Represent the chord measurement sequence for converting chord length to x meters and y meters respectively;

[0028] The string measurement and expansion sequence obtained in the second step are used as the target value, and the inversion is achieved by minimizing the difference between the target value and the model estimation value. The loss function is established as follows:

[0029]

[0030] Among them, Loss CI represents the loss of string inversion process; v j and Represent different extended chord sequences V E The j-th extended chord prediction value and target value in ; N represents the length of the extended chord sequence.

[0031] The beneficial effects of the present invention are:

[0032] The present invention solves the problems existing in existing track irregularity expansion and inversion methods in terms of large-scale data processing, wide-band information compensation, multi-process fusion inversion, etc. By embedding the classical string expansion theory and inversion principle in the neural network, a new track irregularity string expansion and inversion method based on embedded physical neural network is established, which realizes the inversion of wide-band information of track irregularity by fusion of multiple processes, and meets the large-scale data processing requirements in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flow chart of an embodiment of the present invention;

[0034] Figure 2 Schematic diagram of the structure of a forward expansion calculation layer based on multi-channel convolution in an embodiment of the present invention;

[0035] Figure 3 A schematic diagram of the network structure of a deep Bayesian feature extraction layer in an embodiment of the present invention;

[0036] Figure 4 Schematic diagram of the convergence of the loss function in an embodiment of the present invention;

[0037] Figure 5 This is a schematic diagram of the expansion results and error comparison obtained by the method of this embodiment;

[0038] Figure 6 This is a schematic diagram comparing the inversion results of the traditional method with the true value;

[0039] Figure 7 Schematic diagram of the comparison between the inversion result of the method in this embodiment and the true value. DETAILED DESCRIPTION

[0040] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0041] Example 1

[0042] like Figure 1 As shown, a track irregularity chord extension inversion method embedded in a physical neural network drive includes the following steps:

[0043] 1) Optimize the matrix expression of string measurement and string expansion process:

[0044] Based on the existing research results, we first condense the sequence from the orbital unevenness sequence d to the reference chord sequence V B The matrix expression of is as follows:

[0045]

[0046] Where L is the chord length, s is the sampling step, γ and They represent the chord length division ratios on the left and right sides of the division point, a and b represent the lengths of the left and right sides after division, M and m represent the track irregularity and the length of the reference chord sequence, respectively. In the above formula, the chord length division ratio coefficient matrix can be condensed into a fixed parameter measurement matrix H.

[0047] Secondly, condense the reference string sequence V B Derivation of the extended chord sequence V E The matrix expression of is as follows (2):

[0048]

[0049] Among them, V B and V E Represent the reference chord and the extended chord sequence respectively, m and N represent the length of the reference chord and the extended chord sequence respectively, and n represents the number of steps the reference chord moves in the extended chord.

[0050] 2) Establish a forward expansion calculation layer based on multi-channel convolution:

[0051] The process of string measurement and expansion is similar to one-dimensional convolution in neural networks, including full convolution, similar convolution and effective convolution. Comparing the calculation process of full convolution and effective convolution, if the convolution kernel is close to the sequence, part of the sequence will be extended outside the convolution kernel, while effective convolution only considers the movement of the convolution kernel within the sequence. Therefore, based on the one-dimensional effective convolution network layer, an equivalent calculation layer of formulas (1) and (2) is established, with the structure as follows: Figure 2 shown.

[0052] The convolution calculation equation is as follows:

[0053]

[0054] in, Represents the feature map corresponding to the convolution kernel at position u in layer l; Represents the feature map corresponding to the convolution kernel at position i+u in layer l-1; δ i represents the i-th convolution operation; c l represents the bias of the lth layer; represents the i-th convolution kernel in layer l; z represents the maximum number of convolution kernels.

[0055] The convolution kernel of the neural network is fixed, and the convolution result under the same motion step size is essentially equivalent to the inspection and expansion process. Through one forward calculation, the reference chord and multiple extended chord values ​​are obtained at the same time.

[0056] 3) Establish a deep Bayesian feature extraction layer:

[0057] Mining the underlying structure and data features is the basis for achieving accurate inversion iteration. Different network layers are connected by neurons, which can theoretically approximate any continuous function, which means they have great flexibility and the ability to express complex patterns. Through multiple layers of nonlinear transformations and Monte Carlo random dropout neurons, the deep Bayesian feature extraction layer is able to learn complex structures and high-level abstractions in the input data, such as Figure 3 shown.

[0058] For each input z p×u implement:

[0059] Z p×o =Z p×u ·w u×o +c (4)

[0060] Among them, Z represents the extracted features of the output, p and o are the input and output feature lengths respectively; u represents the potential feature dimension; w represents the parameters to be learned by the model; c represents the bias of the o-dimensional vector; considering that the distribution characteristics of track irregularity conform to the characteristics close to the normal distribution, the Tanh (hyperbolic tangent) function is used in the low-dimensional space for nonlinear activation. The specific network layer parameter settings are shown in Table 1.

[0061] Table 1 Deep Bayesian feature extraction layer structure

[0062]

[0063] Where m represents the length of the input signal, and k represents the number of estimated track irregularity types.

[0064] 4) Embed the inversion loss function of the multi-chord measurement equation group:

[0065] Referring to formula (1), after expanding multiple groups of chord length data targets, corresponding multiple groups of chord measurement equations can be established respectively. Taking 10m, 30m and 60m lengths as examples, the following three equations can be established as the basis for loss function design:

[0066]

[0067] Where H represents the measurement matrix; d represents the uneven sequence column; V 10 、V 30 and V 60 Represent 10m, 30m and 60m chord measurement sequences respectively.

[0068] The inversion process is essentially to solve d when H and V are known. Therefore, we take the string measurement and expansion sequence obtained in the second step as the target value, and achieve inversion by minimizing the difference between the target value and the model estimate. The loss function is established as follows:

[0069]

[0070] Among them, Loss CI represents the loss of string inversion process; v j and Represent different extended chord sequences V E The j-th extended chord prediction value and target value in ; N represents the length of the extended chord sequence.

[0071] 5) Adaptive early stopping iteration:

[0072] The implementation of the model also requires an appropriate early stopping (ES) mechanism to ensure that the model converges quickly and accurately. The design of the ES mechanism mainly considers three indicators:

[0073] Max_epoch: maximum number of model runs;

[0074] Patience: The number of runs allowed before the model cannot be improved;

[0075] Delta: The minimum change in a monitored quantity to qualify as an improvement.

[0076] Example 2

[0077] This embodiment uses a data segment with a length of 1.6 kilometers and a sampling frequency of 1 meter as an example to apply the method. The specific implementation method is as follows:

[0078] (1) Optimize the matrix expression of string measurement and string expansion process:

[0079] Taking the 10m chord and 60m chord as examples, the measurement and expansion coefficient matrices H1, H2 and H3 under the midpoint chord measurement system are established respectively.

[0080]

[0081] (2) Establish a forward expansion calculation layer based on multi-channel convolution:

[0082] The first row parameters in the measurement and expansion coefficient matrix are set as the detection kernel and expansion kernel parameters, two detection kernels and one expansion kernel are established respectively, and a forward calculation is performed.

[0083] (3) Establish a deep Bayesian feature extraction layer:

[0084] The feature extraction network parameters are set according to the length of the input track unevenness sequence, and the four parameters of left height, right height, left track direction, and right track direction are estimated, as shown in Table 2.

[0085] Table 2 Parameters of deep Bayesian feature extraction layer

[0086]

[0087]

[0088] (4) Embed the inversion loss function of the multi-chord measurement equation group:

[0089] Considering the measurement process logic of 10m and 60m, the loss function is set as follows:

[0090]

[0091] Among them, N1 and N2 represent the length of the chord sequence of 10m and 60m respectively. and v s They represent the estimated and target values ​​of the sth 10m chord respectively; and w k They represent the estimated and target values ​​of the kth 60m chord, respectively.

[0092] (5) Adaptive early stopping iteration:

[0093] Max_epoch: The maximum number of model runs is set to 1000;

[0094] Patience: The number of runs allowed before the model can’t be improved is 10;

[0095] Delta: The minimum change in a monitored quantity is 0.02.

[0096] (6) Convergence effect and inversion results:

[0097] After completing the parameter setting, this embodiment can quickly reach the convergence state and meet the accuracy requirements by running only 350 times. Figure 4 shown.

[0098] In order to compare the effects of the traditional method and the method of this embodiment in the expansion process, the same data is sampled for expansion calculation. The 10m chord data is used as the basic data before expansion, and then it is expanded to the 60m chord data. The expansion results and errors obtained by this method are shown in Figure 5 The results show that the two methods are consistent under the same conditions and the extended results can be used for subsequent calculations.

[0099] The traditional method performs an approximate estimation of "one chord to one chord" based on equation (2), while the method of this embodiment can break away from this constraint and perform estimation in the form of "multiple chords to one chord". Therefore, the different frequency band information estimated by the method of this embodiment is closer to the actual result. Under the guidance of the calculation logic of equation (5), the method of this embodiment is not affected by the regularization coefficient parameter. During the inversion process, multiple chord measurement processes are simultaneously carried out, and the inversion capability of each chord is fully utilized to achieve stable estimation with minimal interference, such as Figure 6 and Figure 7shown.

[0100] The method of this embodiment does not require the regularization parameter optimization process, and the estimation result can be obtained in one step. Considering multiple string inspection processes at the same time, the inversion results are linked to multiple string measurement matrices, which is more in line with the real detection logic. Compared with the inversion results of the traditional method, the average error of the result is 0.503mm, which meets the requirements of inversion accuracy.

[0101] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A track irregularity chord extension inversion method embedded in a physical neural network driver, characterized in that: The following steps are involved: Step 1: Optimize the matrix expression of the chord measurement and chord expansion process: condense the matrix expression from the track unevenness sequence to the reference chord sequence, and derive the matrix expression of the extended chord sequence from the reference chord sequence; Step 2: Establish a forward extension calculation layer based on multi-channel convolution, and obtain the reference chord and multiple extended chord values ​​at the same time through one forward calculation; Step 3: Establish a deep Bayesian feature extraction layer: Through multiple layers of nonlinear transformations and Monte Carlo random dropout neurons, the deep Bayesian feature extraction layer is used to learn complex structures and high-level abstractions in the input data; Step 4: Establish the inversion loss function of the embedded multi-string measurement equation group: take the string measurement and expansion sequence obtained in the second step as the target value, realize the inversion by minimizing the difference between the target value and the model estimation value, and establish the loss function; Step 5: Adaptive early stopping iteration is used to ensure that the model converges quickly and accurately.

2. The track irregularity chord extension inversion method embedded in physical neural network drive according to claim 1 is characterized in that: The step 1 is specifically as follows: First, we condense the sequence from the orbital unevenness sequence d to the reference chord sequence V B The matrix expression of is as follows (1): Where L is the chord length, s is the sampling step, γ and They represent the chord length division ratios on the left and right sides of the division point, a and b represent the lengths of the left and right sides after division, M and m represent the track irregularity and the length of the reference chord sequence, respectively. (1) In the formula, the chord length division ratio coefficient matrix can be condensed into a fixed parameter measurement matrix H; Secondly, condense the reference string sequence V B Derivation of the extended chord sequence V E The matrix expression of is as follows (2): Among them, V B and V E Represent the reference chord and the extended chord sequence respectively, m and N represent the length of the reference chord and the extended chord sequence respectively, and n represents the number of steps the reference chord moves in the extended chord.

3. The track irregularity chord extension inversion method embedded in physical neural network drive according to claim 2 is characterized in that: The step 2 is specifically as follows: Based on the one-dimensional effective convolutional network layer, the equivalent calculation layer of equation (1) and equation (2) is established. The convolution calculation equation is as follows: in, Represents the feature map corresponding to the convolution kernel at position u in layer l; Represents the feature map corresponding to the convolution kernel at position i+u in layer l-1; δ i represents the i-th convolution operation; c l represents the bias of the lth layer; represents the i-th convolution kernel in layer l; z represents the maximum number of convolution kernels.

4. The track irregularity chord extension inversion method embedded in physical neural network drive according to claim 3 is characterized in that: In step 3, the deep Bayesian feature extraction layer performs a p×u implement: WITH p×o =from p×u ·In u×o +c (4) Among them, Z represents the extracted features of the output, p and o are the input and output feature lengths respectively; u is the potential feature dimension; w represents the parameters to be learned by the model; c represents the bias of the o-dimensional vector; considering that the distribution characteristics of track irregularities conform to the characteristics close to the normal distribution, the hyperbolic tangent Tanh function is used for nonlinear activation in the low-dimensional space.

5. The track irregularity chord extension inversion method embedded in physical neural network drive according to claim 4 is characterized in that: The step 4 is specifically as follows: After multiple sets of chord length data targets are expanded, corresponding sets of chord measurement equations are established as the basis for loss function design: Where H represents the measurement matrix; d represents the uneven sequence column; V x 、V y Represent the chord measurement sequence for converting chord length to x meters and y meters respectively; The string measurement and expansion sequence obtained in the second step are used as the target value, and the inversion is achieved by minimizing the difference between the target value and the model estimation value. The loss function is established as follows: Among them, Loss CI represents the loss of string inversion process; v j and Represent different extended chord sequences V E The j-th extended chord prediction value and target value in ; N represents the length of the extended chord sequence.

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