Rail corrugation detection method based on anomaly detection and dynamic adaptation

Abstract

This invention relates to the field of rail transit technology and discloses a rail corrugation detection method based on anomaly detection and dynamic adaptation. The method includes: acquiring the axle box acceleration vibration signal of the rail; performing state prediction using a Kalman filter model to obtain a priori state estimate and calculating the measurement residual; dynamically adjusting the process noise covariance matrix of the Kalman filter model based on the measurement residual; determining a dynamic threshold based on the measurement residual; comparing the measurement residual with the dynamic threshold to determine whether the measurement residual is an outlier; if so, robustly correcting the priori state estimate to obtain a posterior state estimate. This invention effectively solves the problem that traditional fixed-parameter models cannot accommodate different track conditions, maintaining optimal filtering performance on various track grades and avoiding common problems in traditional methods such as filter divergence or tracking hysteresis.

Description

Technical Field

[0001] This invention relates to the field of rail transit technology, and in particular to a method for detecting rail corrugation based on anomaly detection and dynamic adaptation. Background Technology

[0002] Rail corrugation is a common periodic irregularity defect on the surface of high-speed railway tracks. As train speeds increase, the high-frequency interaction between the wheel and rail excited by corrugation generates severe vibrations and noise, not only worsening passenger comfort and accelerating fatigue failure of vehicle bogies and track components, but also, in severe cases, inducing derailment risks and threatening operational safety. Therefore, regular and accurate inspection of rail corrugation is a necessary prerequisite for guiding preventative track maintenance and ensuring the safe operation of high-speed railways.

[0003] Currently, inversion estimation based on axle box acceleration (ABA) signals is the mainstream technical approach for dynamic detection of rail corrugation. In this field, the Kalman filter, with its theoretical advantages in processing linear dynamic systems and suppressing random noise, is widely used to reconstruct rail corrugation waveforms from noisy vibration signals.

[0004] Although traditional Kalman filtering methods perform well under ideal conditions, the inventors have found in practical engineering applications that they strictly rely on the assumptions of a "linear system" and "Gaussian white noise," which fundamentally conflicts with the complex operating conditions of actual power lines, leading to the following insurmountable technical bottlenecks:

[0005] 1. The contradiction between the fixed model parameters and the time-varying nature of the line state leads to a lack of adaptive capability.

[0006] The performance of a standard Kalman filter is highly dependent on the value of the process noise covariance matrix Q, which characterizes the uncertainty of the system model. Existing techniques typically pre-determine a fixed Q matrix based on experience. However, high-speed railway lines and their smoothness exhibit significant spatial and time-varying characteristics: in long-wavelength smooth sections, model predictions are accurate, requiring a smaller Q value to suppress noise; while in severely corrugated sections, model bias increases, necessitating a larger Q value to enhance tracking capability. The fixed-parameter strategy falls into a dilemma: if the Q value is set too small, tracking lag or even filter divergence may occur in defective sections; if the Q value is set too large, unnecessary noise will be introduced in smooth sections, causing drastic fluctuations in detection accuracy across the entire line, resulting in a lack of stability.

[0007] 2. The conflict between the least squares criterion and non-Gaussian impact disturbances leads to insufficient robustness.

[0008] In actual operating lines, strong localized impacts from rail welds, turnouts, and insulation joints are unavoidable. Combined with occasional electrical faults in sensors, this results in measurement noise exhibiting typical non-Gaussian, heavily tailed distribution characteristics. Traditional Kalman filters, based on the mean square error minimization criterion, are extremely sensitive to such outliers deviating from a normal distribution. When a detection vehicle passes through a high-impact point such as a weld, the large measurement residuals are incorrectly accepted by the filter and used for condition correction, leading to non-physical, drastic abrupt changes or false spikes in the wear estimate. This not only causes severe distortion of the detection data but also easily triggers false alarms, misleading subsequent maintenance decisions.

[0009] In summary, overcoming the limitations of traditional Kalman filter algorithms, such as the inability of parameters to dynamically follow track changes and the lack of immunity to non-Gaussian impact interference, and constructing a rail corrugation detection method that combines high adaptability and strong robustness, is a key technical challenge that urgently needs to be solved in this field. Summary of the Invention

[0010] To address the problems existing in the prior art, this invention successfully overcomes the inherent defects of the traditional Kalman filtering method in rail corrugation detection by introducing a dual correction mechanism based on anomaly detection and dynamic adaptation. The specific technical solution includes:

[0011] A rail corrugation detection method based on anomaly detection and dynamic adaptation includes:

[0012] S1. Obtain the axle box acceleration vibration signal of the rail, perform state prediction through Kalman filter model to obtain prior state estimate, and calculate the measurement residual;

[0013] S2. Based on the measured residuals, dynamically adjust the process noise covariance matrix of the Kalman filter model;

[0014] S3. Determine a dynamic threshold based on the measured residual;

[0015] S4. Compare the measurement residual with a dynamic threshold to determine whether the measurement residual is an outlier;

[0016] S5. If so, the prior state estimate is robustly corrected to obtain the posterior state estimate.

[0017] Preferably, step S5 further includes: if not, performing a standard correction on the prior state estimate based on the standard Kalman gain to obtain the posterior state estimate.

[0018] Preferably, the step S1, which involves performing state prediction using a Kalman filter model to obtain a priori state estimates, specifically includes:

[0019] Linear prediction is performed based on the posterior state estimate of the previous time step to obtain an initial prior estimate;

[0020] Calculate a nonlinear compensation term and superimpose the nonlinear compensation term onto the initial prior estimate to obtain the prior state estimate;

[0021] In step S1, the measurement residual is calculated based on the axle box acceleration vibration signal and the prior state estimation.

[0022] Preferably, step S2 specifically includes:

[0023] S21. Calculate the variance of the measurement residuals;

[0024] S22. When the variance of the measurement residual is greater than a preset benchmark value, increase the process noise covariance matrix.

[0025] Preferably, the step of robustly correcting the prior state estimate in step S5 includes:

[0026] S51. Compare a Kalman gain of the Kalman filter model with a preset upper limit of gain, and truncate the Kalman gain to obtain a robust gain.

[0027] Preferably, the step of robustly correcting the prior state estimate further includes:

[0028] S52. Based on the dynamic threshold, the measurement residual is limited to obtain a robust residual.

[0029] Preferably, the robust residual The steps to obtain it include:

[0030] ;in, To measure the residuals; This is a sign function used to preserve the positive and negative directions of the residuals; This is a dynamic threshold.

[0031] Preferably, the dynamic threshold in step S4 The methods for determining this include:

[0032] Where n is the current time number; Let be the variance of the measurement residual; k is a preset coefficient.

[0033] Preferably, the nonlinear compensation term The methods for determining this include:

[0034] ;

[0035] in, For wheel stiffness; For the nonlinear stiffness of the bogie frame; The nonlinear damping coefficient of the bogie frame; This is the posterior state estimate of the rail corrugation displacement at time n-1; n is the current time number. This is the a posteriori state estimate of the rail corrugation speed at time n-1.

[0036] Beneficial effects

[0037] 1. This invention effectively solves the problem that traditional fixed-parameter models cannot accommodate different track conditions by introducing an adaptive adjustment mechanism for the process noise covariance matrix based on the statistical characteristics of measurement residuals. This mechanism enables the filtering model to "sense" changes in track smoothness in real time: when the train is traveling in a smooth section, the model automatically reduces the Q value, increasing confidence in prior predictions, thereby effectively suppressing random noise; when traveling in a severely corrugated section, the model automatically increases the Q value, increasing confidence in new measurements, thereby enhancing the ability to track changes in corrugation amplitude. This dynamic balance ensures that the method maintains optimal filtering performance on track lines of various grades, avoiding the filtering divergence or tracking hysteresis problems common in traditional methods.

[0038] 2. This invention, by establishing a dynamic threshold that fluctuates in real time according to the track condition, can accurately distinguish between signal fluctuations caused by normal track irregularities and abnormal impacts triggered by welds, turnouts, etc., overcoming the shortcomings of fixed thresholds that are prone to missed or misjudged detections. More importantly, this invention employs an innovative dual-path correction strategy, achieving a divide-and-conquer approach to the data: standard Kalman correction is used for signals identified as normal to ensure high accuracy in corrugation inversion; robust correction (such as gain cutoff and residual limiting) is used for impact signals identified as abnormal to effectively absorb and block the contamination of state estimation by high-energy impacts. This strategy successfully avoids non-physical false spikes in the detection results, ensuring the continuity and authenticity of the final corrugation data, and providing a highly reliable decision-making basis for railway maintenance. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating a preferred embodiment of the rail corrugation detection method based on anomaly detection and dynamic adaptation provided by the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments described herein are merely illustrative of the invention and not intended to limit its scope of protection. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within its scope of protection. In the following description, the same reference numerals denote the same or similar parts.

[0041] The method proposed in this invention is typically implemented in a rail corrugation detection system. This system may include a data acquisition subsystem and a data processing subsystem.

[0042] The data acquisition subsystem, typically installed on the test train, may include: at least one axle box acceleration sensor mounted above the axle box of the train bogie, for acquiring vertical vibration acceleration signals during train movement; and a data acquisition unit for amplifying, filtering, analog-to-digital conversion (A / D conversion), and storing the analog signals acquired by the sensor.

[0043] The data processing subsystem can be a computer with sufficient computing power, an embedded system, or a cloud server. This subsystem is configured to execute the method steps disclosed in this invention, process the acquired axle box acceleration vibration signals, and ultimately output rail corrugation status information.

[0044] Example 1

[0045] like Figure 1 As shown, this embodiment provides a complete implementation process for a rail corrugation detection method based on anomaly detection and dynamic adaptation, which aims to achieve the highest detection accuracy and robustness.

[0046] S1. Obtain the axle box acceleration vibration signal of the rail, perform state prediction through Kalman filter model to obtain prior state estimate, and calculate the measurement residual.

[0047] The test train travels on the track under test, and acceleration sensors mounted on the axle boxes collect vertical vibration acceleration signals in real time. After necessary bandpass filtering and resampling, the collected signals are used to obtain a series of discrete axle box acceleration vibration signals. This serves as the input for subsequent processing.

[0048] This embodiment employs a Kalman filter based on a discrete displacement-velocity-acceleration model. The system's state vector x(n) is defined as [d(n), v(n), a(n)]ᵀ, where d(n), v(n), and a(n) are the displacement, velocity, and acceleration at time n, respectively. The state transition matrix F and observation matrix H are defined accordingly. The establishment of these models is a conventional technique in this field and will not be elaborated upon here.

[0049] For each time point n, perform the following recursive calculation:

[0050] 1. State prediction (time update);

[0051] This step includes two sub-steps: linear prediction and nonlinear compensation, to obtain a more accurate prior state estimate.

[0052] Linear prediction:

[0053] Based on the prior state estimation at time n The initial prior state estimate at time n+1 is predicted using the state transition matrix F. .

[0054] Nonlinear compensation:

[0055] Those skilled in the art will recognize that, for computational simplicity, most existing Kalman filter models simplify the vehicle-track system to a purely linear model, neglecting the inherent nonlinear characteristics of components such as the bogie frame and suspension. Clearly, any model simplification introduces systematic errors. The stiffness and damping of the bogie frame exhibit nonlinearity under large vibrations; ignoring this will introduce a persistent, albeit small, bias into the final estimation result.

[0056] Therefore, in order to further improve the detection accuracy, this embodiment introduces an additional nonlinear compensation term based on the initial prior estimate. This is equivalent to refining the linear prediction results and targeting and correcting known errors in the nonlinear model.

[0057] Considering the nonlinear characteristics of the bogie frame, based on the dynamic equations, the nonlinear mapping relationship between corrugation amplitude and velocity, acceleration, frame stiffness, and damping is determined, and the nonlinear compensation term for the prior corrugation value is obtained. The specific concept is as follows:

[0058] Considering only linearity, we express wave grinding from both a dynamic perspective (based on force balance) and a time-displacement perspective (based on kinematic recursion):

[0059] ;in, To incorporate the posterior state estimate of the current measured acceleration; The Kalman gain can be obtained by calculating the weights of prior states and measured data, incorporating common knowledge. To measure the residuals; This is the prior state estimate at time n.

[0060] Decomposing the above equation into three dimensions—displacement, velocity, and acceleration—we obtain the state update equation set:

[0061] ;

[0062] in, , , These are the posterior state estimates of displacement, velocity, and acceleration at time n, respectively. , , These are the predicted values ​​for displacement, velocity, and acceleration, respectively. , , The Kalman gains for displacement, velocity, and acceleration, respectively.

[0063] Under the assumption that the two calculation results are consistent, the linear part of the erosion function can be equivalently replaced:

[0064] ;

[0065] in, , These are the UD decomposition factors of the prediction error covariance matrix, respectively. It is a unit upper triangular matrix. The two are diagonal matrices, and together they represent the uncertainty of the current prediction state. Those skilled in the art should know that dividing the prediction error covariance matrix into UD parts is to prevent computer rounding errors from causing the matrix to no longer be positive definite during program execution (thus causing filter divergence). This is the observation matrix, used to describe the linear relationship between the state (displacement, velocity, acceleration) and the measured values; The covariance matrix of the measurement residuals;

[0066] The nonlinear function of wave wear with time-displacement as the variable is obtained:

[0067] ;

[0068] in, This represents the final estimated value of the wave erosion time series at time n. This is the posterior state estimate of the rail corrugation displacement at time n-1; n is the current time number. The posterior state estimate of the rail corrugation speed at time n-1; For time intervals.

[0069] This allows for the extraction of nonlinear terms; specifically, the nonlinear compensation terms derived according to this embodiment. The calculation formula is:

[0070] ;

[0071] in, For wheel stiffness; For the nonlinear stiffness of the bogie frame; The nonlinear damping coefficient of the bogie frame is given; this coefficient can be obtained in advance through laboratory bench tests or dynamic simulations.

[0072] Final prior state acquisition:

[0073] The nonlinear compensation term is superimposed onto the linear prediction result to obtain the final prior state estimate. The advantage of this approach is that it introduces a correction to the physical model at the very beginning of the filtering loop, ensuring that the measurement residuals calculated subsequently not only include random noise but also eliminate known nonlinear systematic errors, thereby improving the sensitivity of subsequent anomaly detection.

[0074] 2. Measurement residual calculation;

[0075] ;in, The acceleration is estimated a priori; These are the pre-processed axle box acceleration measurements.

[0076] S2. Dynamically adjust the process noise covariance matrix of the Kalman filter model based on the measured residuals.

[0077] Those skilled in the art will recognize that in traditional Kalman filter-based detection methods, the process noise covariance matrix Q is typically a fixed value preset based on experience, remaining constant throughout the detection process. A fixed Q matrix cannot adapt to the dynamic changes in the smoothness of actual track conditions. For example, on a very smooth track, the model's uncertainty is small, and the Q value should be small; while on a severely deteriorated track, the model's uncertainty increases, and the Q value should logically increase. A fixed Q matrix is ​​a one-size-fits-all approach that cannot achieve optimal performance on any track segment.

[0078] Therefore, in this embodiment, the variance of the measurement residual is calculated within a sliding time window. And based on the variance and a preset benchmark value Based on the comparison results, the process noise covariance matrix Q is dynamically adjusted. By dynamically adjusting the Q matrix according to the real-time residual variance, the filtering model acquires adaptive capability. It can perceive the current track smoothness status in real time and automatically adjust the degree of trust in the system model. This enables the present invention to maintain near-optimal filtering performance on various track lines of different grades, significantly improving detection accuracy and universality for different track conditions.

[0079] Furthermore, the preset benchmark value This represents the residual fluctuation level under a well-smooth trajectory. When This means that the nonlinearity of the prior estimation model is enhanced, the uncertainty of the estimated value increases, and it will deviate from reality. Therefore, it needs to be adjusted; otherwise, it is left untreated.

[0080] In some preferred embodiments, update formulas for dynamically adjusting the process noise covariance matrix Q are provided:

[0081] ;

[0082] Optionally, to prevent the Q matrix from changing too rapidly, a smoothing coefficient can be introduced:

[0083] ;

[0084] Where μ is the smoothing coefficient, used to control... The update rate is adjusted to avoid sudden changes caused by transient residual fluctuations; For 1 and The maximum value in the range ensures that the residual variance only exceeds the benchmark. Only increase the size, avoid over-adjustment; It is a natural constant. for of The power is used to smooth the adjustment process and avoid... Non-step transition.

[0085] S3. Determine a dynamic threshold based on the measured residual.

[0086] In existing technologies, outlier removal typically employs a fixed, absolute threshold. For example, simply considering all signal points exceeding a specific acceleration amplitude as outliers fails to effectively distinguish between normal fluctuations and genuine anomalous shocks. For instance, in a severely degraded region, a large residual might be normal; while in a very smooth region, a moderate residual could indicate an anomaly. A fixed threshold leads to underreporting in degraded regions (misclassifying anomalous shocks as normal) and overreporting in smooth regions (misclassifying normal fluctuations as anomalies).

[0087] The dynamic threshold used in this invention is related to the real-time uncertainty of the system (derived from the residual covariance R). e (n) is associated with characterization. It automatically adjusts upwards when track irregularities increase and downwards when the track is smooth. This characteristic enables the invention to intelligently and accurately identify genuine abnormal impacts (such as welds) without being disturbed by normal track irregularities, greatly improving the accuracy and reliability of outlier detection.

[0088] Specifically, the dynamic threshold γ(n) is used to determine whether the measurement residual is an outlier. In a preferred embodiment, this threshold is related to the real-time uncertainty of the measurement residual, and may specifically include:

[0089] S31. Calculate the variance of the measurement residuals. ,in The covariance of the noise is an inherent error of the accelerometer.

[0090] S32. Calculate dynamic threshold ;

[0091] Where k is a preset coefficient, the value of which determines the sensitivity of outlier detection, and is used to ensure that 99.3% of the residuals fall within the noise range. In some other preferred embodiments, the value of k can be 2 to 5, preferably 3, which corresponds to the 3-sigma criterion in statistics, that is, data points falling outside 3 standard deviations are considered outliers.

[0092] S4. Compare the measurement residual with the dynamic threshold to determine whether the measurement residual is an outlier.

[0093] It should be noted that traditional Kalman filtering methods have only a single correction path. Regardless of whether the measurement residual is normal or abnormal, the exact same standard Kalman gain and update formula are used for state correction. Using the same method to process two completely different types of data (normal and abnormal values) is the root cause of the poor performance of traditional methods. When the residual generated by a huge anomalous shock (such as a weld) is indiscriminately used for standard correction, it will inevitably lead to drastic, non-physical abrupt changes in the state estimation results, i.e., data distortion. Therefore, this embodiment determines the correction scheme (i.e., measurement update) by examining whether the measurement residual is abnormal.

[0094] S5. If so, the prior state estimate is robustly corrected to obtain the posterior state estimate.

[0095] At this point, |e(n)|>γ(n) indicates the presence of an abnormal shock interference. A robust correction step is then performed to suppress the abnormal shock interference. In a preferred embodiment, robust correction may include limiting one or more correction parameters.

[0096] S511. Gain Correction: Calculate the standard Kalman gain K(n), and then compare it with a preset upper limit of gain. Comparison to obtain robustness gain . This can be obtained through statistical analysis of normal line data.

[0097] S512. Residual Correction: Limit the measurement residual e(n) to obtain the robust residual eᵣ(n).

[0098] In one specific embodiment, this step can be implemented by the following formula: ;in, As a sign function, this operation essentially forces the absolute value of the residual to be limited to a dynamic threshold. Within, while retaining its original orientation.

[0099] S513. Perform posterior state estimation: .

[0100] S514. Update the error covariance matrix: ; where I is the identity matrix.

[0101] The essence of the above correction is to acknowledge the detection of an impact, but with skepticism about its magnitude, and therefore use only a controlled, discounted amount of information (i.e., the threshold γ(n)) for correction. This effectively suppresses and absorbs the energy of extreme impacts, preventing the state estimation results from being contaminated, thus ensuring the stability and robustness of the detection results.

[0102] If not, meaning |e(n)|≤γ(n), then the state prediction is corrected using standard Kalman gain to obtain the posterior state estimate. In this case, for normal values ​​(|e(n)|≤γ(n)), the standard correction step is performed.

[0103] S521. Calculate the standard Kalman gain. ;in, Represents the inverse of residual covariance and .

[0104] S522. Perform posterior state estimation: .

[0105] S523. Update the error covariance matrix: .

[0106] The estimated corrugated displacement values ​​obtained through the recursive calculations described above are extracted and combined with the real-time speed information of the monitored train to convert them into corrugated data in the spatial domain. This yields a rail corrugation condition map distributed along the track mileage, which can be used for subsequent maintenance and repair decisions. This ensures that, with reliable data, every measurement piece of information is fully utilized to achieve mathematically optimal estimation and the highest accuracy.

[0107] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for rail corrugation detection based on anomaly detection and dynamic adaptation, characterized in that, include: S1. Obtain the axle box acceleration vibration signal of the rail, perform state prediction through Kalman filter model to obtain prior state estimate, and calculate the measurement residual; S2. Based on the measured residuals, dynamically adjust the process noise covariance matrix of the Kalman filter model; S3. Determine a dynamic threshold based on the measured residual; S4. Compare the measurement residual with a dynamic threshold to determine whether the measurement residual is an outlier; S5. If so, the prior state estimate is robustly corrected to obtain the posterior state estimate; The step of robustly correcting the prior state estimate in step S5 includes: S51. Compare a Kalman gain of the Kalman filter model with a preset upper limit of gain, and truncate the Kalman gain to obtain a robust gain; The step of robustly correcting the prior state estimate further includes: S52. Based on the dynamic threshold, the measurement residual is limited to obtain a robust residual; The robust residual The obtaining step comprises: ;in, To measure the residuals; This is a sign function used to preserve the positive and negative directions of the residuals; This is a dynamic threshold.

2. The rail corrugation detection method based on anomaly detection and dynamic adaptation of claim 1, wherein, Step S5 further includes: if not, performing a standard correction on the prior state estimate based on the standard Kalman gain to obtain the posterior state estimate.

3. The rail corrugation detection method based on anomaly detection and dynamic adaptation of claim 1, wherein, The step S1, which involves using a Kalman filter model to predict the state and obtain a priori state estimate, specifically includes: Linear prediction is performed based on the posterior state estimate of the previous time step to obtain an initial prior estimate; Calculate a nonlinear compensation term and superimpose the nonlinear compensation term onto the initial prior estimate to obtain the prior state estimate; In step S1, the measurement residual is calculated based on the axle box acceleration vibration signal and the prior state estimation.

4. The rail corrugation detection method based on anomaly detection and dynamic adaptation as described in claim 1, characterized in that, Step S2 specifically includes: S21. Calculate the variance of the measurement residuals; S22. When the variance of the measurement residual is greater than a preset benchmark value, increase the process noise covariance matrix.

5. The rail corrugation detection method based on anomaly detection and dynamic adaptation as claimed in claim 1, wherein, The dynamic threshold in step S4 The determination method comprises: ; wherein n is a current time index; is a variance of the measurement residual; k is a preset coefficient.

6. The rail corrugation detection method based on anomaly detection and dynamic adaptation as claimed in claim 3, wherein, the non-linear compensation term The determination method comprises: ； in, For wheel stiffness; For the nonlinear stiffness of the bogie frame; The nonlinear damping coefficient of the bogie frame; This is the posterior state estimate of the rail corrugation displacement at time n-1; n is the current time number. This is the a posteriori state estimate of the rail corrugation speed at time n-1.

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