Tqi prediction method for simply supported beam bridge section based on gaussian random process

Abstract

The present application relates to the field of railway operation and maintenance technology, in particular to a simply supported beam bridge section TQI prediction method based on Gaussian random process, which comprises the following steps: step one, data collection and preprocessing of simply supported beam bridge; step two, construction of composite kernel function model suitable for bridge characteristics; step three, adaptive training and optimization of model parameters; step four, probability prediction and uncertainty quantification; step five, calculation of over-limit probability based on reliability theory; step six, residual life prediction and maintenance window generation; the present application can preferably predict the TQI of simply supported beam bridge section.

Description

Technical Field

[0001] This invention relates to the field of railway operation and maintenance technology, and more specifically, to a method for predicting the TQI (Total Quality Index) of a simply supported beam bridge section based on a Gaussian stochastic process. Background Technology

[0002] With the expansion of high-speed railway networks, track smoothness is crucial for operational safety and passenger comfort. Currently, the prediction of the Track Quality Index (TQI) faces the following main problems: existing studies largely rely on linear regression or simple statistical models, which cannot effectively capture the nonlinear characteristics, seasonal periodic fluctuations, and random disturbances in the track degradation process; traditional deterministic models cannot provide confidence intervals or probability distributions for prediction results, leading to a lack of risk assessment basis when setting maintenance thresholds; and the actual inspection frequency of inspection vehicles is affected by operational plans, often resulting in uneven sampling intervals or missing data, making it difficult to directly apply traditional time series models.

[0003] Although existing technologies have made some progress in predicting track irregularities in high-speed railways, mainly focusing on the use of deep learning models and multi-source sensor data fusion, the following significant limitations still exist in practical engineering applications and operation and maintenance decision support: 1) Existing technologies mostly employ deep neural network models. While these models offer high fitting accuracy when data is plentiful, they lack physical interpretability and struggle to intuitively separate long-term trends and seasonal cycles in track degradation. This makes it difficult for maintenance personnel to determine the causes of degradation, and the output is typically a deterministic "point prediction" value, failing to provide confidence intervals or probability distributions for the prediction results. Furthermore, the lack of quantification of prediction uncertainty when setting safety-related maintenance thresholds makes it difficult to assess the actual risk probability of exceeding TQI limits.

[0004] 2) Time-series-based deep learning methods typically assume that the input data is sampled at equal time intervals. In actual railway maintenance operations, the inspection schedule of comprehensive inspection vehicles is affected by operational scheduling, and data collection is often irregular, resulting in uneven time intervals or missing data. Existing technologies often require manual methods such as interpolation to complete the data, which introduces additional error noise.

[0005] 3) Some existing technologies heavily rely on specific, expensive hardware installed on the operating vehicles, which limits their application scenarios. 4) Prediction and maintenance decision-making are disconnected, lacking a closed-loop optimization mechanism. Most solutions stop at the "prediction" stage, that is, only outputting the change value of TQI. The prediction model and the scheduling model are in a "decoupled" state, and cannot form a closed-loop system of "maintenance scheduling guided by state prediction and state prediction corrected by maintenance behavior feedback". Summary of the Invention

[0006] The present invention provides a method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process, which can overcome some or all of the defects of the prior art.

[0007] The TQI prediction method for simply supported beam bridge sections based on Gaussian stochastic processes according to the present invention includes the following steps: Step 1: Data Acquisition and Preprocessing for Simply Supported Beam Bridges By utilizing track geometry data collected by high-speed railway comprehensive inspection trains and combining it with bridge mileage information, inspection data for simply supported beam bridge sections were selected; longitudinal horizontal TQI was calculated using single-span beams or standard management units to construct an observation dataset. ,in For irregularly detected date sequences, These are the TQI observation values ​​for the corresponding bridge sections; Step 2: Construct a composite kernel function model adapted to the bridge characteristics: Define a regression model based on Gaussian processes, where the observed and predicted values ​​follow a joint Gaussian distribution, and construct an additive composite kernel function that includes long-term degradation components, seasonal periodic components, and random perturbation components. Step 3: Adaptive training and optimization of model parameters: Based on historical data, a logarithmic marginal likelihood function is constructed as the objective function for optimization. The objective function is maximized to train and optimize the set of hyperparameters in the additive composite kernel function. Step 4: Probability Prediction and Uncertainty Quantification Using the trained hyperparameters, the Gaussian posterior distribution of the orbital state at any future time point is calculated to obtain the predicted mean and variance of TQI. Step 5: Calculation of the probability of exceeding limits based on reliability theory: Set an operation management threshold for track quality, and calculate the probability of the predicted TQI value exceeding the operation management threshold at each future time based on the predicted mean and variance. Step Six: Remaining Life Prediction and Maintenance Window Generation: Based on the preset recommended maintenance threshold and mandatory maintenance threshold, the corresponding remaining lifespan is calculated, and a graded maintenance window is generated based on the over-limit probability curve.

[0008] As a preferred option, in step two, the regression model based on the Gaussian process is: Let the observed TQI value With time The relationship between them is determined by the latent function and Gaussian white noise Composition, that is ,in Based on the definition of a Gaussian process, the observed and predicted values ​​follow a joint Gaussian distribution: (1.1) in, It follows a normal distribution. The variance of Gaussian white noise is used to measure random errors in the measurement process. Indicates the predicted time series. Represents the identity matrix. The covariance matrix is ​​calculated using the kernel function. These are predicted values.

[0009] Preferably, in step two, the additive composite kernel function for: (1.2) and This indicates any two different testing dates; Long-term degradation components The formula used to capture the monotonically increasing trend of TQI over time, corresponding to the irreversible creep of the beam and the cumulative wear of the track components, is as follows: (1.3) in, It is a hyperparameter that controls the magnitude of the long-term trend variance; Seasonal cyclical components The formula used to capture the periodic fluctuations in TQI (Total Quality Indicator) corresponds to the thermal expansion and contraction deformation of the beam caused by changes in ambient temperature. (1.4) in, For periodic parameters; This is a length scale parameter that controls the smoothness of fluctuations; random perturbation components Used to capture short-term random fluctuations in the data, corresponding to the measurement error of the detection vehicle or small random irregularities in the track, the formula is: (1.5) in, Let Kronecker function be used.

[0010] As a preferred approach, in step three, the maximum likelihood estimation method is used to construct the logarithmic marginal likelihood function as the objective function for optimization. (1.6) Let represent the covariance matrix, which is about the set of hyperparameters; The first term in the formula represents the number of observed samples; the second term is a complexity penalty term, and the third term is a constant.

[0011] Preferably, in step three, the objective function is maximized using the conjugate gradient method or the L-BFGS-B algorithm, and the set of hyperparameters in the additive composite kernel function is obtained. .

[0012] Preferably, in step four, the mean of the Gaussian posterior distribution is... Covariance The calculation is as follows: (1.7) (1.8) The mean is used to show the future trajectory of the TQI, including its upward trend and details of seasonal fluctuations; the variance is used to quantify the confidence level of the forecast.

[0013] Preferably, in step five, for each moment on the future prediction timeline... Calculate the predicted TQI value Exceeding the job management threshold Probability of exceeding the limit: (1.9) in, This is the cumulative distribution function of the standard normal distribution.

[0014] Preferably, in step six, the cost of preventative maintenance is considered. Cost of fault correction Based on the proportional relationship, two key risk thresholds are set: It is recommended to maintain the threshold. At this point, there is a 30% probability that the TQI will exceed the limit, making intervention the most cost-effective option. Forced maintenance threshold At this point, there is an 80% probability that the TQI will exceed the limit, which is a high-risk situation, and large machinery operations must be arranged immediately.

[0015] Preferably, in step six, the corresponding remaining lifetime (RUL) is calculated for both the recommended maintenance threshold and the mandatory maintenance threshold: (1.10) In the remaining lifetime formula, represents the predicted time series points. Indicates the current moment.

[0016] Preferably, in step six, a specific maintenance window is generated for each simply supported beam bridge based on the RUL calculation results: Green or yellow window: When the probability exceeds the limit The recommended maintenance period is when the temperature is between 0.3 and 0.8. During this period, it is recommended to use the sunroof for preventative maintenance. Red window: When the probability exceeds the limit The point at which the value reaches 0.8 and thereafter is a mandatory maintenance period, during which maintenance is required to be completed before this point and is marked as a hard constraint task.

[0017] The beneficial effects of this invention are as follows: 1) Significantly improved the physical interpretability and accuracy of track TQI predictions, especially for bridge sections that are significantly affected by the environment.

[0018] This invention abandons the traditional linear regression model and innovatively constructs a composite kernel function Gaussian process model containing a "long-term trend kernel + periodic kernel + white noise kernel". The model can accurately decouple irreversible settlement (long-term trend) and temperature-induced thermal expansion and contraction deformation (periodic fluctuations) during track degradation. Particularly for simply supported beam bridges, the model successfully captures their annual periodic fluctuation characteristics. Experimental analysis shows that the periodic components extracted by this model exhibit a strong positive correlation with local environmental temperature changes, with a Pearson correlation coefficient reaching 0.767, and the periodic parameters fitted by the model... It is approximately 368 days, close to a calendar year. This proves that the present invention is not merely a numerical fit, but more accurately reflects the physical degradation mechanism, thereby significantly reducing prediction errors.

[0019] 2) It realizes the transformation from "deterministic point prediction" to "probabilistic risk quantification", supporting reliability-based scientific decision-making.

[0020] This invention utilizes a Bayesian inference framework to output the posterior probability distribution of the predicted TQI value and calculates the probability of the TQI exceeding the safety threshold at future times, thus solving the problem that existing deep learning "black box" models cannot assess prediction confidence. By setting dual risk thresholds for suggested and mandatory maintenance, this invention can dynamically generate maintenance windows based on the probability of failure risk. This mechanism effectively avoids over-maintenance due to excessive conservatism and under-maintenance due to insufficient prediction, achieving optimal life-cycle maintenance costs while ensuring driving safety. Attached Figure Description

[0021] Figure 1 This is a flowchart of a TQI prediction method for a simply supported beam bridge section based on a Gaussian random process, as described in this embodiment.

[0022] Figure 2 This is a schematic diagram illustrating the prediction results and uncertainties of a Gaussian stochastic process under a composite kernel function in the embodiment.

[0023] Figure 3This is a schematic diagram illustrating the generation of TQI maintenance suggestions based on a probability model in the example. Detailed Implementation

[0024] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0025] Example like Figure 1 As shown, this embodiment provides a method for predicting the TQI (Total Quality Index) of a simply supported beam bridge section based on a Gaussian stochastic process, which includes the following steps: Step 1: Data Acquisition and Preprocessing for Simply Supported Beam Bridges Using track geometry data collected by high-speed railway comprehensive inspection trains and bridge mileage information from the engineering log, inspection data for all simply supported beam bridge sections were selected. The longitudinal horizontal TQI was calculated using a single-span beam (32m) or a standard management unit (200m) as the unit to construct an observation dataset. ,in For irregularly detected date sequences, The TQI observation values ​​for the corresponding bridge sections are used; the longitudinal horizontal direction is selected as the core indicator because it is most directly affected by beam creep and thermal expansion and contraction deformation.

[0026] This embodiment selects a 32m simply supported beam bridge in a high-speed railway ballastless track line as the specific monitoring object. Because simply supported beam bridges will undergo periodic upward and downward deformation under temperature loads, the degradation law of their track geometry is significantly different from that of the roadbed section, and they have stronger environmental sensitivity.

[0027] Step 2: Construct a composite kernel function model adapted to the bridge characteristics (to accurately decouple the complex physical components mentioned above): Define a regression model based on Gaussian processes, where the observed and predicted values ​​follow a joint Gaussian distribution, and construct an additive composite kernel function that includes long-term degradation components, seasonal periodic components, and random perturbation components. The regression model based on Gaussian processes is as follows: Let the observed TQI value With time The relationship between them is determined by the latent function and Gaussian white noise Composition, that is ,in Based on the definition of a Gaussian process, the observed and predicted values ​​follow a joint Gaussian distribution: (1.1) in, It follows a normal distribution. The variance of Gaussian white noise is used to measure random errors in the measurement process. Indicates the predicted time series. Represents the identity matrix. The covariance matrix is ​​calculated using the kernel function. These are predicted values.

[0028] Additive composite kernel function for: (1.2) and This indicates any two different testing dates; Long-term degradation components Used to capture the monotonically increasing trend of TQI over time, this component physically corresponds to the irreversible creep of the beam and the cumulative wear of the track components, and is formulated as follows: (1.3) in, It is a hyperparameter that controls the magnitude of the long-term trend variance; Seasonal cyclical components Used to capture periodic fluctuations in TQI, this component physically corresponds to the thermal expansion and contraction deformation of the beam caused by changes in ambient temperature, and the formula is: (1.4) in, This is a periodic parameter; in this embodiment, its physical meaning is the number of days in a year. This is a length scale parameter that controls the smoothness of fluctuations; random perturbation components Used to capture short-term random fluctuations in the data, this component physically corresponds to the measurement error of the detection vehicle or small random irregularities in the track, and the formula is: (1.5) in, The Kronecker function (if and only if) (If it is 1, then it is 0).

[0029] Step 3: Adaptive training and optimization of model parameters: Based on historical data, a logarithmic marginal likelihood function is constructed as the objective function for optimization. The objective function is maximized, and the set of hyperparameters in the additive composite kernel function is trained and optimized.

[0030] Using the maximum likelihood estimation method, a log-marginal likelihood function is constructed as the objective function for optimization. (1.6) Let represent the covariance matrix, which is about the set of hyperparameters; The first term in the formula represents the number of observed samples; the second term is a complexity penalty term, and the third term is a constant.

[0031] Maximizing the objective function using the conjugate gradient method or the L-BFGS-B algorithm, the set of hyperparameters in the additive composite kernel function. .

[0032] Step 4: Probability Prediction and Uncertainty Quantification Using the trained hyperparameters, the Gaussian posterior distribution of the orbital state at any future time point is calculated to obtain the predicted mean and variance of TQI.

[0033] Unlike traditional models that output only a single numerical value, this embodiment outputs a predicted value. The complete Gaussian posterior distribution, including the mean. Covariance The calculation is as follows: (1.7) (1.8) The mean is used to show the future trajectory of the TQI, including its upward trend and details of seasonal fluctuations; the variance is used to quantify the confidence level of the forecast. As the forecast period progresses, the variance typically increases gradually, reflecting the uncertainty of long-term forecasts.

[0034] Step 5: Calculation of the probability of exceeding limits based on reliability theory: Set an operation management threshold for track quality, and calculate the probability of the predicted TQI value exceeding the operation management threshold at each future time based on the predicted mean and variance.

[0035] This embodiment, based on the "Maintenance Rules for Ballastless Track Lines of High-Speed ​​Railways," sets the operational management target value for the longitudinal horizontal TQI of the 32m simply supported beam bridge section (e.g., ...). =0.8).

[0036] For every moment on the future prediction timeline Calculate the predicted TQI value Exceeding the job management threshold Probability of exceeding the limit: (1.9) in, This is the cumulative distribution function of the standard normal distribution. This step transforms the numerical TQI prediction into an intuitive failure risk probability curve.

[0037] Step Six: Remaining Life (RUL) Prediction and Maintenance Window Generation: Based on the preset recommended maintenance threshold and mandatory maintenance threshold, the corresponding remaining lifespan is calculated, and a graded maintenance window is generated based on the over-limit probability curve.

[0038] This embodiment proposes a remaining lifetime prediction mechanism based on dual risk thresholds to balance maintenance costs and safety risks.

[0039] Based on preventative maintenance costs Cost of fault correction Based on the proportional relationship, two key risk thresholds are set: It is recommended to maintain the threshold. At this point, there is a 30% probability that the TQI will exceed the limit. Although this does not pose a serious safety hazard, intervention (such as fine-tuning) is the most cost-effective option. Forced maintenance threshold At this point, there is an 80% probability that the TQI will exceed the limit, which is a high-risk situation, and large machinery operations must be arranged immediately.

[0040] Calculate the corresponding Remaining Lifetime (RUL) for both the recommended maintenance threshold and the mandatory maintenance threshold: (1.10) In the remaining lifetime formula, represents the predicted time series points. This indicates the current time. Based on the RUL calculation results, specific maintenance windows are generated for each 32m simply supported beam bridge: Green or yellow window: When the probability exceeds the limit The recommended maintenance period is when the temperature is between 0.3 and 0.8. During this period, it is recommended to use the sunroof for preventative maintenance. Red window: When the probability exceeds the limit The point at which the value reaches 0.8 and thereafter is a mandatory maintenance period, during which maintenance is required to be completed before this point and is marked as a hard constraint task.

[0041] This embodiment decomposes the degradation of track TQI into a long-term trend term, a seasonal periodic term, and a white noise term. It uses Bayesian inference to process irregularly sampled data and outputs the predicted mean and variance of TQI. Furthermore, by calculating the probability of TQI exceeding the safety threshold and combining this with maintenance cost analysis, it dynamically determines the time windows for mandatory and recommended maintenance.

[0042] This embodiment significantly improves the physical interpretability and accuracy of track TQI predictions, especially for bridge sections significantly affected by environmental factors. This embodiment achieves a shift from "deterministic point prediction" to "probabilistic risk quantification," supporting reliability-based scientific decision-making.

[0043] like Figure 2 As shown, this diagram illustrates the prediction results and uncertainties of a Gaussian stochastic process under a composite kernel function. The solid line (orange line) represents the mean trajectory predicted by the TQI, showing the long-term degradation trend of orbit quality over time and the details of seasonal cyclical fluctuations. The shaded area represents the uncertainty interval (confidence interval), which is determined by the prediction variance and is used to quantify the reliability of the prediction.

[0044] like Figure 3 The diagram illustrates the generation of TQI (Total Quality Indicator) maintenance recommendations based on a probabilistic model. Two key risk control lines are defined to guide maintenance decisions: Recommended maintenance threshold (yellow dashed line): set at a 30% probability of exceeding limits. At this point, although the TQI is not severely exceeded, intervention is the most cost-effective approach, belonging to the preventative maintenance stage. Mandatory maintenance threshold (red dashed line): set at an 80% probability of exceeding limits. At this point, the TQI is in a high-risk state, and heavy machinery operations must be immediately arranged to ensure driving safety.

[0045] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for predicting the Time Quality (TQI) of simply supported beam bridge sections based on Gaussian stochastic processes, characterized in that: Includes the following steps: Step 1: Data Acquisition and Preprocessing for Simply Supported Beam Bridges By utilizing track geometry data collected by high-speed railway comprehensive inspection trains and combining it with bridge mileage information, inspection data for simply supported beam bridge sections were selected; longitudinal horizontal TQI was calculated using single-span beams or standard management units to construct an observation dataset. ,in For irregularly detected date sequences, These are the TQI observation values ​​for the corresponding bridge sections; Step 2: Construct a composite kernel function model adapted to the bridge characteristics: Define a regression model based on Gaussian processes, where the observed and predicted values ​​follow a joint Gaussian distribution, and construct an additive composite kernel function that includes long-term degradation components, seasonal periodic components, and random perturbation components. Step 3: Adaptive training and optimization of model parameters: Based on historical data, a logarithmic marginal likelihood function is constructed as the objective function for optimization. The objective function is maximized to train and optimize the set of hyperparameters in the additive composite kernel function. Step 4: Probability Prediction and Uncertainty Quantification Using the trained hyperparameters, the Gaussian posterior distribution of the orbital state at any future time point is calculated to obtain the predicted mean and variance of TQI. Step 5: Calculation of the probability of exceeding limits based on reliability theory: Set an operation management threshold for track quality, and calculate the probability of the predicted TQI value exceeding the operation management threshold at each future time based on the predicted mean and variance. Step Six: Remaining Life Prediction and Maintenance Window Generation: Based on the preset recommended maintenance threshold and mandatory maintenance threshold, the corresponding remaining lifespan is calculated, and a graded maintenance window is generated based on the over-limit probability curve.

2. The method for predicting the TQI of a simply supported beam bridge segment based on a Gaussian stochastic process according to claim 1, characterized in that: In step two, the regression model based on the Gaussian process is as follows: Let the observed TQI value With time The relationship between them is determined by the latent function and Gaussian white noise Composition, that is ,in Based on the definition of a Gaussian process, the observed and predicted values ​​follow a joint Gaussian distribution: （1.1）； in, It follows a normal distribution. The variance of Gaussian white noise is used to measure random errors in the measurement process. Indicates the predicted time series. Represents the identity matrix. The covariance matrix is ​​calculated using the kernel function. These are predicted values.

3. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 2, characterized in that: In step two, the additive composite kernel function for: （1.2）； and This indicates any two different testing dates; Long-term degradation components The formula used to capture the monotonically increasing trend of TQI over time, corresponding to the irreversible creep of the beam and the cumulative wear of the track components, is as follows: （1.3）； in, It is a hyperparameter that controls the magnitude of the long-term trend variance; Seasonal cyclical components The formula used to capture the periodic fluctuations in TQI (Total Quality Indicator) corresponds to the thermal expansion and contraction deformation of the beam caused by changes in ambient temperature. （1.4）； in, For periodic parameters; This is a length scale parameter that controls the smoothness of fluctuations; random perturbation components Used to capture short-term random fluctuations in the data, corresponding to the measurement error of the detection vehicle or small random irregularities in the track, the formula is: （1.5）； in, Let Kronecker function be used.

4. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 3, characterized in that: In step three, the maximum likelihood estimation method is used to construct the log-marginal likelihood function as the objective function for optimization: （1.6）； Let represent the covariance matrix, which is about the set of hyperparameters; The first term in the formula represents the number of observed samples; the second term is a complexity penalty term, and the third term is a constant.

5. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 4, characterized in that: In step three, the objective function is maximized using the conjugate gradient method or the L-BFGS-B algorithm, and the set of hyperparameters in the additive composite kernel function is obtained. .

6. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 5, characterized in that: In step four, the mean of the Gaussian posterior distribution Covariance The calculation is as follows: （1.7）； （1.8）； The mean is used to show the future trajectory of the TQI, including its upward trend and details of seasonal fluctuations; the variance is used to quantify the confidence level of the forecast.

7. The method for predicting the TQI of a simply supported beam bridge segment based on a Gaussian stochastic process according to claim 6, characterized in that: In step five, for each moment on the future prediction timeline... Calculate the predicted TQI value Exceeding the job management threshold Probability of exceeding the limit: （1.9）； in, This is the cumulative distribution function of the standard normal distribution.

8. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 7, characterized in that: In step six, based on preventative maintenance costs... Cost of fault correction Based on the proportional relationship, two key risk thresholds are set: It is recommended to maintain the threshold. At this point, there is a 30% probability that the TQI will exceed the limit, making intervention the most cost-effective option. Forced maintenance threshold At this point, there is an 80% probability that the TQI will exceed the limit, which is a high-risk situation, and large machinery operations must be arranged immediately.

9. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 8, characterized in that: In step six, the corresponding Remaining Lifetime (RUL) is calculated for both the recommended maintenance threshold and the mandatory maintenance threshold: （1.10）； In the remaining lifetime formula, represents the predicted time series points. Indicates the current moment.

10. The method for predicting the TQI of a simply supported beam bridge section based on a Gaussian stochastic process according to claim 9, characterized in that: In step six, based on the RUL calculation results, a specific maintenance window is generated for each simply supported beam bridge: Green or yellow window: When the probability exceeds the limit The recommended maintenance period is when the temperature is between 0.3 and 0.

8. During this period, it is recommended to use the sunroof for preventative maintenance. Red window: When the probability exceeds the limit The point at which the value reaches 0.8 and thereafter is a mandatory maintenance period, during which maintenance is required to be completed before this point and is marked as a hard constraint task.

Images