A monitoring and early warning system for railway foundation settlement in loess areas

Abstract

This invention relates to the field of railway foundation settlement monitoring technology, specifically to a railway foundation settlement monitoring and early warning system in loess areas. The system includes: a data preprocessing module, which assembles settlement data from monitoring points on the railway subgrade at various times into a settlement data sequence; a periodicity judgment module, which determines whether the settlement data sequence is strongly periodic; if so, it uses the period of the settlement data sequence as a lag value to perform a first-order difference on the settlement data sequence to obtain a difference sequence; a difference order optimization module, which, if the settlement data sequence is not strongly periodic, obtains the non-uniformity index of settlement evolution and the degree of data variation disorder, and optimizes the difference order to obtain an optimized difference order, and then performs difference on the settlement data sequence to obtain a difference sequence; and an early warning module, which uses predicted settlement data for the next time moment to issue an early warning. This application can effectively monitor railway foundation settlement.

Description

Technical Field

[0001] This invention relates to the field of railway foundation settlement technology, specifically to a railway foundation settlement monitoring and early warning system in loess areas. Background Technology

[0002] Railway foundation settlement is a significant and long-standing safety issue in railway engineering operations. If settlement changes are not identified and predicted in a timely manner, they may adversely affect track structure safety and train operation smoothness. Therefore, settlement monitoring equipment is typically deployed to continuously collect foundation settlement data over a long period, analyze and predict settlement trends, and provide early warnings of potential risks.

[0003] For railway foundation settlement monitoring data, time series analysis-based prediction methods are commonly used to model and predict settlement trends. Among these, the ARIMA algorithm (Autoregressive Integral Moving Average) is widely used due to its relatively mature structure and well-defined implementation. The ARIMA algorithm weakens the influence of trends by preprocessing the time series data, such as differencing, to ensure the data meets stationarity requirements. It then estimates future foundation settlement changes based on the temporal correlation between historical data. When the prediction result reaches or approaches a preset safety threshold, it can be used as the basis for triggering a railway foundation settlement early warning.

[0004] However, in railway engineering in loess areas, due to the loose soil structure and well-developed pores, the soil is highly sensitive to rainfall infiltration, groundwater changes, and repeated train loads. The evolution of foundation settlement often exhibits significantly different characteristics at different time stages. It may remain in a slow development state for a long time, or it may experience a significant increase in settlement rate under specific conditions. Overall, it shows strong complexity and non-uniformity. Therefore, the monitoring and early warning of railway foundation settlement in this region places higher demands on the prediction methods in terms of the ability to characterize settlement change characteristics, the accuracy of trend prediction, and the ability to reflect risks in advance.

[0005] In traditional methods, the ARIMA algorithm typically uses first-order differencing to eliminate non-stationarity of data during differencing. First-order differencing primarily eliminates a single trend term, meaning it can effectively handle non-stationarity when the original sequence's non-stationarity mainly stems from monotonic or near-monotonic evolution. However, due to factors such as rainfall-evaporation cycles, short-term fluctuations in groundwater levels, and changes in train operating conditions in the Loess region, its settlement data exhibits significant differences across different time scales. First-order differencing struggles to cope with these complex variations. Furthermore, loess structural damage is irreversible; once the structure is damaged, the data permanently changes, completely differing from the previous change model and exhibiting stage-specific differences. Therefore, a fixed differencing order cannot be applied to data change types at any time scale. Summary of the Invention

[0006] To address the aforementioned technical problems, the present invention aims to provide a railway foundation settlement monitoring and early warning system in loess areas. The specific technical solution adopted is as follows:

[0007] One embodiment of the present invention provides a railway foundation settlement monitoring and early warning system in loess areas, the system comprising:

[0008] The data preprocessing module is used to collect vertical displacement data at monitoring points on the railway subgrade at various times and preprocess the data to obtain settlement data at each time point. The settlement data at each time point is then arranged into a settlement data sequence according to time sequence.

[0009] The periodicity determination module is used to obtain the seasonal term and residual term of the settlement data sequence; to obtain the intensity characterization value of the periodic component of the data using the residual term and the timestamps corresponding to each maximum point in the seasonal term; to determine whether the settlement data sequence is strongly periodic using the intensity characterization value of the periodic component of the data; if it is strongly periodic, to perform first-order difference on the settlement data sequence using the period as the lag value to obtain the difference sequence.

[0010] The differential order optimization module is used to: obtain a rate of change sequence based on the difference between every two adjacent settlement data points if the settlement data sequence is non-strongly periodic; analyze the element changes in the rate of change sequence to obtain a settlement evolution non-uniformity index; analyze the changes in the settlement data in the settlement data sequence to obtain the degree of data variation disorder; optimize the differential order based on the settlement evolution non-uniformity index and the degree of data variation disorder to obtain an optimized differential order; and combine the optimized differential order and a preset lag value to perform differential analysis on the settlement data sequence to obtain a differential sequence.

[0011] The early warning module is used to predict the settlement data for the next time step based on the difference sequence corresponding to the settlement data sequence and the ARIMA algorithm; and to issue an early warning using the predicted settlement data for the next time step.

[0012] Preferably, the intensity characterization value of the data periodic component is obtained using the timestamps corresponding to the maximum points in the residual term and the seasonal term, including:

[0013] The cumulative distribution function of the residual term is obtained from the residual term and denoted as the residual cumulative distribution function. The absolute value of the difference between the residual cumulative distribution function and the cumulative distribution function of the standard normal distribution is integrated to obtain the integral result, and the normalized value of the integral result is subtracted from the first preset value to obtain the cumulative distribution function difference term. The difference between the timestamps of the latter and former maxima of two adjacent maxima in the seasonal term is obtained and denoted as the timestamp difference of the latter maxima. Similarly, the timestamp differences of each maxima in the seasonal term are obtained and formed into a timestamp difference sequence according to the time sequence. The difference between the latter and former timestamp differences of each pair of adjacent timestamp differences in the timestamp difference sequence is obtained and summed to obtain the timestamp difference change characteristic value. The timestamp difference term is obtained by subtracting the normalized value of the timestamp difference change characteristic value from the first preset value. The mean value of the cumulative distribution function difference term and the timestamp difference term is obtained to obtain the data periodicity component intensity characterization value.

[0014] Preferably, determining whether a sedimentation data sequence is strongly periodic by using the intensity characterization value of the periodic components of the data includes:

[0015] If the intensity value of the periodic component of the settlement data sequence is greater than or equal to the reference threshold, the settlement data sequence is strongly periodic; if the intensity value of the periodic component of the settlement data sequence is less than the reference threshold, the settlement data sequence is not strongly periodic.

[0016] Preferably, the rate of change sequence is obtained based on the difference between every two adjacent settlement data points in the settlement data sequence, including:

[0017] The absolute value of the difference between the second and first settlement data in two adjacent settlement data in the settlement data sequence is taken as the rate of change of the second settlement data. The rate of change of the other settlement data in the settlement data sequence, except for the rate of change of the first settlement data, is arranged in chronological order to obtain the rate of change sequence.

[0018] Preferably, the analysis of elemental changes in the rate of change sequence to obtain indices of non-uniformity in sedimentation evolution includes:

[0019] The mean of all change rates in the rate of change sequence is obtained and denoted as the average rate of change. The number of change rates in the rate of change sequence whose absolute value of the difference from the average rate of change is less than the average rate of change is obtained and compared with the number of change rates in the rate of change sequence to obtain the stable proportion of settlement rate. The difference between the first preset value and the stable proportion of settlement rate is obtained and denoted as the unstable proportion of settlement rate. The average of the normalized values ​​of the unstable proportion of settlement rate and the variance of all change rates in the rate of change sequence is calculated to obtain the non-uniformity index of settlement evolution.

[0020] Preferably, the calculation model for the degree of data variation disorder is as follows:

[0021] ;

[0022] Where Q represents the degree of data disorder; n represents the number of settlement data in the settlement data sequence; , and These represent the (t-1), t, and t+1th settlement data points in the settlement data sequence, respectively. Indicates an indicator function, when When the value is greater than or equal to 0, the value of the indicator function is 0; when the value is less than 0, the value of the indicator function is 1.

[0023] Preferably, the optimized difference order is obtained by optimizing the difference order based on the non-uniformity index of settlement evolution and the degree of data variation disorder, including:

[0024] Set the lower and upper limits of the differential order interval; obtain the mean values ​​of the non-uniformity index of settlement evolution and the degree of disorder in data changes, and record them as the adjustment coefficient; multiply the difference between the upper and lower limits of the differential order interval by the adjustment coefficient to obtain the adjustment range; add the lower limit of the differential order interval to the adjustment range and then round to obtain the optimized differential order.

[0025] The embodiments of the present invention have at least the following beneficial effects: This application obtains the vertical displacement of monitoring points on the railway foundation as settlement data, and then obtains a settling data sequence; furthermore, it obtains the seasonal term and residual term of the settlement data sequence, and then determines the strength of the periodic component of the settlement data based on the confidence level of the decomposition result from the residual and the seasonal term, that is, it obtains the characteristic value of the strength of the periodic component of the data. If the settlement data sequence is strongly periodic and has reliable periodic components, then first-order difference is used, and the lag value is set to the size of one period to obtain the difference sequence; if the periodic component of the settlement data is not strong, that is, the settlement data sequence is not strongly periodic, then the rate of change is obtained according to the difference between every two adjacent settlement data in the settlement data sequence. The settlement data sequence is analyzed to obtain indices of non-uniformity in settlement evolution and the degree of data disorder. These indices and the degree of data disorder are used to comprehensively characterize the oscillation characteristics of the settlement data sequence. Then, the difference order is optimized based on these indices and the degree of data disorder to obtain an optimized difference order. The settlement data sequence is then differenced using the optimized difference order and a preset lag value to obtain a difference sequence. Finally, the settlement data for the next time step is predicted using the ARIMA algorithm based on the difference sequence, and an early warning is issued. This process allows the difference processing to more effectively eliminate non-stationary structures in the settlement data sequence while avoiding excessive difference that weakens effective information. The resulting difference sequence is statistically more stable, which is beneficial for subsequent autoregressive and moving average models to accurately characterize the settlement evolution pattern, thereby improving the stability and reliability of settlement trend prediction and enabling monitoring and early warning results to reflect potential foundation settlement risks earlier and more accurately. Attached Figure Description

[0026] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a system block diagram of a railway foundation settlement monitoring and early warning system in a loess region, provided as an embodiment of the present invention. Detailed Implementation

[0028] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a railway foundation settlement monitoring and early warning system for loess areas proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0029] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0030] The following description, in conjunction with the accompanying drawings, details the specific scheme of a railway foundation settlement monitoring and early warning system for loess areas provided by this invention.

[0031] In this embodiment, the main application scenario of the present invention is to collect settlement data of railway foundations and then use the ARIMA algorithm to make predictions, so as to enable advanced and accurate monitoring of railway settlement.

[0032] Please see Figure 1 The diagram illustrates a system block diagram of a railway foundation settlement monitoring and early warning system in a loess region, provided by an embodiment of the present invention. The system includes the following modules:

[0033] The data preprocessing module is used to collect vertical displacement data at monitoring points on the railway subgrade at various times and preprocess the data to obtain settlement data at each time point. The settlement data at each time point is then arranged into a settlement data sequence according to time sequence.

[0034] This application uses the location of the foundation directly below the track structure near the centerline of the roadbed along the railway line as the monitoring point. Then, using settlement monitoring equipment such as vertical displacement sensors at the monitoring point, the vertical displacement of the railway foundation and track structure generated during operation is collected continuously over a long period of time. The frequency of data collection needs to be set by the implementer according to the required monitoring accuracy.

[0035] The vertical displacement of the collected monitoring points at each time point was analyzed using statistical methods. Specifically, box plots were used to mark and remove extreme outliers in the vertical displacement. Zero-order interpolation was used to fill in missing data at the removed points, and linear interpolation was also used to fill in missing points. Bandpass filtering was used to perform simple smoothing on the collected vertical displacement data to reduce high-frequency measurement noise. The preprocessed settlement data of each monitoring point at each time point were then arranged into a settlement data sequence according to time sequence. It should be noted that this application uses the settlement data sequence corresponding to a single monitoring point for monitoring and analysis.

[0036] The periodicity determination module is used to perform STL decomposition on the settlement data sequence to obtain the trend term, seasonal term, and residual term; use the timestamps corresponding to the maximum points in the residual term and seasonal term to obtain the intensity characterization value of the periodic component of the data; use the intensity characterization value of the periodic component of the data to determine whether the settlement data sequence is strongly periodic data; if it is strongly periodic data, the period of the settlement data sequence is used as the lag value to perform first-order difference on the settlement data sequence to obtain the difference sequence.

[0037] The settlement of railway foundations in loess areas is influenced by a combination of factors, including soil structure characteristics, rainfall infiltration, and long-term train loads. Its settlement evolution may exhibit a clear long-term trend, or, under the influence of seasonal rainfall or periodic operating conditions, the settlement rate may show certain periodic characteristics. However, the ARIMA algorithm performs poorly when performing differencing on time series, especially for data with strong periodic characteristics. The reason for this is as follows:

[0038] When performing differencing on time series data, the ARIMA algorithm essentially transforms non-stationary sequences into stationary ones, making the processed data sequences statistically more stable to meet the stability requirements of subsequent autoregressive and moving average modeling. However, the model defaults to a lag value of 1 for differencing. This approach is equivalent to a data shift for data with strong periodicity, failing to effectively eliminate non-stationary structures, and the differencing sequence still retains a significant oscillatory structure. Therefore, lag differencing is considered to effectively eliminate the periodic oscillation structure, with the lag value set to be equal to the period value. This is because for data with strong periodicity, the periodic components are highly similar in value and phase at two moments separated by a complete period. Subtracting them can cause the periodic components to cancel each other out, thereby directly weakening or even eliminating the periodic oscillation structure during the differencing stage.

[0039] Based on the above idea, the settlement data sequence is decomposed by STL to obtain three components: trend, seasonal, and residual. The strength of the periodic component of the data is determined by the seasonal component. However, since the STL decomposition inevitably generates the seasonal component during the calculation process, if the decomposition result is unreliable, the seasonal component may be mixed with trend changes or random disturbances, which will lead to the distortion of the periodic analysis results. Therefore, the quality analysis of the STL decomposition results is combined to evaluate the reliability of the decomposition results. Only when the decomposition results are reliable can the strength of the periodic component be further analyzed.

[0040] Therefore, the intensity characterization value of the periodic component of the data is obtained by using the timestamps corresponding to the maximum points in the obtained residual terms and seasonal terms.

[0041] Specifically, the cumulative distribution function of the residual term is obtained based on the residual term, denoted as the residual cumulative distribution function; the absolute value of the difference between the residual cumulative distribution function and the cumulative distribution function of the standard normal distribution is integrated to obtain the integral result, and the normalized value of the integral result is subtracted from the first preset value to obtain the cumulative distribution function difference term; the difference between the timestamps of the latter and former maxima of two adjacent maxima in the seasonal term is obtained, denoted as the timestamp difference of the latter maxima, and similarly the timestamp differences of each maxima in the seasonal term are obtained and formed into a timestamp difference sequence according to the time sequence; the difference between the latter and former timestamp differences of every two adjacent timestamp differences in the timestamp difference sequence is obtained and summed to obtain the timestamp difference change characteristic value; the timestamp difference term is obtained by subtracting the normalized value of the timestamp difference change characteristic value from the first preset value; the mean value of the cumulative distribution function difference term and the timestamp difference term is obtained to obtain the data periodicity component intensity characterization value.

[0042] The specific calculation model for the intensity characterization value of the periodic component of the data is as follows:

[0043] ;

[0044] ;

[0045] Where ρ represents the intensity of the periodic component of the data; Norm represents the normalization function, which restricts the output to [0,1] to ensure that the value range of the intensity of the periodic component of the data is in [0,1]. The larger the value of the intensity of the periodic component of the data, the closer the residual components of the settlement data sequence are to the standard normal distribution. STL decomposition has effectively extracted the main deterministic structure (trend term and / or periodic term) in the settlement data sequence, making the remaining residual closer to random noise. There are indeed stable and identifiable trend or periodic structures in the settlement data sequence, and the seasonal term has obvious periodic characteristics. The more periodic the settlement data sequence, the stronger the periodic component.

[0046] The cumulative distribution function of the residuals, also known as the residual cumulative distribution function, is obtained as follows: After decomposing the settlement data sequence, the resulting residuals are essentially a data sequence. The cumulative distribution function of the residuals can be directly obtained using the empirical cumulative distribution function (ECDF, existing technology). The general steps are: sort the residuals by their numerical values; for any value x, calculate the proportion of residuals that are less than or equal to x. The cumulative distribution function of the standard normal distribution is calculated by integrating the absolute difference between the two distribution curves. This reflects the degree of difference between the residual cumulative distribution function and the standard normal cumulative distribution function. The smaller the integral value, the greater the difference in the cumulative distribution function. The larger the result, the closer the residual term of the settlement data sequence is to the standard normal distribution, and the higher the confidence level of the decomposition result. The first preset value is 1. The integral of the difference between the cumulative distribution function of the residual term and the cumulative function of the standard normal distribution is the range of values ​​of the residual term sequence itself, that is, from the minimum value to the maximum value of the residual term.

[0047] This represents the timestamp difference corresponding to the (u+1)th maximum point in the temporal sequence of the seasonal term. This represents the timestamp difference corresponding to the u-th maximum point in the temporal sequence of the seasonal term; Let be the timestamp corresponding to the u-th maximum point in the temporal sequence of the seasonal term. This is the timestamp corresponding to the (u-1)th maximum point in the time series of the seasonal term. minus To obtain the timestamp difference corresponding to the u-th maximum point, This indicates the number of maximum points in the seasonal term. When performing the summation calculation, the first maximum point in the seasonal term does not have a corresponding timestamp difference, so u starts from 2. When the settlement data has strong periodic characteristics, the local maxima appear stably on the time axis, indicating that the data has some kind of periodic change. Therefore, the difference in time between adjacent maxima is used to measure whether the data has such a stable pattern.

[0048] Finally, a threshold for ρ is set to determine whether the data decomposes reliably and exhibits a clear and strong periodic component. The specific threshold can be set according to different actual needs. It should be noted that setting it too low may lead to misjudging "periodic disturbances" as "stable periods." Since lag difference is a strong intervention operation, it is necessary to ensure that the data has a highly feasible periodic component. Therefore, this application sets a reference threshold of 0.8, which can be adjusted by the implementer based on the actual situation of subsequent predictions. If the intensity of the periodic component of the settlement data sequence is greater than or equal to the reference threshold, the settlement data sequence is considered strongly periodic. If the intensity of the periodic component of the settlement data sequence is less than the reference threshold, the settlement data sequence is considered non-strongly periodic.

[0049] If the settlement data sequence is strongly periodic, it is assumed that the settlement data has a reliable periodic component. In this case, first-order difference is used, and the lag value is set to the size of one period of the settlement data sequence to obtain the difference sequence of the settlement data sequence. One period of the settlement data sequence can be directly obtained through the seasonal term.

[0050] If the settlement data sequence is non-periodic, further analysis is needed to optimize the difference order, and a preset lag value of 1 is used for the difference.

[0051] The differential order optimization module is used to: obtain a rate of change sequence based on the difference between every two adjacent settlement data points if the settlement data sequence is non-strongly periodic; analyze the element changes in the rate of change sequence to obtain a settlement evolution non-uniformity index; analyze the changes in the settlement data in the settlement data sequence to obtain the degree of data variation disorder; optimize the differential order based on the settlement evolution non-uniformity index and the degree of data variation disorder to obtain an optimized differential order; and combine the optimized differential order and a preset lag value to perform differential analysis on the settlement data sequence to obtain a differential sequence.

[0052] The above processing was performed on sedimentation data sequences with strong periodic components. If the sedimentation data sequence does not have strong periodic components, since a uniform difference order is difficult to meet the data with different variation characteristics under different conditions, it is necessary to analyze the sedimentation data sequence to obtain the optimal difference order.

[0053] In addition to the differences in the intensity of subsidence evolution at different time stages, the stability of the foundation subsidence in the loess region in terms of evolution direction also has significant uncertainties. Affected by factors such as rainfall-evaporation cycle, short-term fluctuations in groundwater level and changes in train operation conditions, the subsidence process often manifests as repeated alternations of acceleration and deceleration at local time scales, that is, the subsidence evolution direction frequently switches. This change does not necessarily manifest as drastic fluctuations in subsidence amplitude, but it will cause the subsidence evolution process to exhibit obvious oscillation characteristics in time, making the subsidence development lack a continuous and single evolution direction.

[0054] When the irregularity of settlement data is stronger and the direction of settlement evolution is more unstable, it indicates that there are still many structural change components in the original settlement sequence that have not been eliminated by low-order processing. Its non-stationarity is not only reflected in the amount of settlement but also extends to the evolution rate and its changes. Since the essence of differential operations is to gradually weaken and remove low-frequency, slowly varying, and structural evolutionary components in the time series, there is an inherent correspondence between the degree of instability in the direction of data change and the depth of differential processing required to achieve effective stationarization. Based on this idea, by setting a differential order interval and combining the quantitative analysis results of the data's irregularity and directional instability, mapping and rounding are performed within the differential order interval to determine a differential order that better matches the current settlement data evolution characteristics.

[0055] The specific differential order interval can be set according to actual needs. It should be noted that an excessively high upper limit of the interval will cause severe fluctuations in ARIMA short-term predictions and reduce the reliability of the system. Since railway foundation settlement is a typical cumulative deformation process, the original settlement sequence generally contains trend components. Therefore, the lower limit of the differential order interval is set to 1. Due to the limitations of monitoring sampling frequency and the slow evolution of settlement, the non-stationary structure in settlement data is mainly concentrated at the level of trend and its stage changes. Excessively high differential order will weaken settlement information and affect the stability of subsequent predictions. This scheme recommends setting the upper limit of the differential order interval to 3. The differential order interval is the interval that represents the adjustment of the differential order. The differential order is adjusted within this interval. The minimum value of the differential order is 1, and the maximum value is 3.

[0056] Furthermore, the rate of change sequence is obtained based on the difference between every two adjacent settlement data points in the settlement data sequence; the elemental changes in the rate of change sequence are analyzed to obtain the non-uniformity index of settlement evolution.

[0057] Specifically, the absolute value of the difference between the second and first settlement data in two adjacent settlement data in the settlement data sequence is obtained as the rate of change of the second settlement data; the rate of change of the other settlement data in the settlement data sequence, except for the rate of change of the first settlement data, is arranged in chronological order to obtain the rate of change sequence.

[0058] The specific model for calculating the rate of change is as follows:

[0059] ,

[0060] in, This represents the rate of change of the t-th settlement data point in the settlement data sequence. and These represent the t-th and t-1-th settlement data points in the settlement data sequence, respectively.

[0061] Then, the elemental changes in the rate of change sequence are analyzed to obtain the non-uniformity index of sedimentation evolution.

[0062] Specifically, the mean of all change rates in the rate of change sequence is obtained and denoted as the average rate of change; the number of change rates in the rate of change sequence whose absolute value of the difference from the average rate of change is less than the average rate of change is obtained and compared with the number of change rates in the rate of change sequence to obtain the stable proportion of settlement rate; the difference between the first preset value and the stable proportion of settlement rate is obtained and denoted as the unstable proportion of settlement rate; the mean of the normalized value of the unstable proportion of settlement rate and the variance of all change rates in the rate of change sequence is calculated to obtain the non-uniformity index of settlement evolution.

[0063] The specific calculation model for the non-uniformity index of settlement evolution is as follows:

[0064] ;

[0065] Where P represents the non-uniformity index of settlement evolution, and Norm represents the normalization function used to limit the output results to [0,1]. This represents the variance of all rates of change in the rate of change sequence. This represents the t-th rate of change in the rate of change sequence. A larger variance in the rate of change indicates more significant differences in settlement intensity during the settlement evolution process, and stronger non-uniformity, staged nature, and irregularity of the settlement process. n represents the number of settlement data points in the settlement data sequence, and n-1 represents the number of rates of change in the rate of change sequence. This indicates the number of rate changes in a rate-of-change sequence whose absolute value of the difference from the average rate of change is less than the average rate of change. It represents the stable proportion of settlement rate, used to distinguish between continuous non-uniform changes caused by stage evolution and local abnormal changes caused by individual disturbances, to prevent individual abnormal points from amplifying the variance results, and thus more accurately reflect the stage non-uniformity caused by soil structure differences and water sensitivity characteristics during the settlement evolution of railway foundation in loess areas. This represents the percentage of unstable settlement rates. The larger this value, the more periods deviate from the dominant evolutionary scale during the settlement process, indicating that the settlement process exhibits obvious staged, uneven, or abrupt characteristics.

[0066] Next, the changes in settlement data in the settlement data sequence are analyzed to obtain the degree of data disorder.

[0067] The specific calculation model for the degree of data variation disorder is as follows:

[0068] ;

[0069] Where Q represents the degree of data disorder; n represents the number of settlement data in the settlement data sequence; , and These represent the (t-1), t, and t+1th settlement data points in the settlement data sequence, respectively. Indicates an indicator function, when When the value is greater than or equal to 0, the value of the indicator function is 0; when... When the value is less than 0, the indicator function has a value of 1.

[0070] The higher the value of the disorder of data changes, the higher the frequency of the data evolution direction switching during the settlement process, the stronger the stage and irregularity of the settlement process, and the weaker the overall evolution regularity.

[0071] f() represents an indicator function, where f() is the function's argument. When the value is less than 0, it indicates that the direction of change has reversed once, and the output is 1. When the value is greater than or equal to 0, it indicates that the data change is in one direction, and the output is 0. and The difference between adjacent settlement data is used to retain the direction of settlement rate change by multiplying adjacent differences. If the signs are the same, the result is positive, indicating that the direction of change has not changed. If the signs are opposite, the result is negative, indicating that the direction of change has changed. The system judges whether the change of data in the settlement data sequence has reversed direction and divides by the total number of data changes n-2 to obtain the degree of disorder in the direction of data change.

[0072] The lower and upper limits of the differential order interval are set above. The differential order is then optimized by combining the lower and upper limits of the differential order interval, the non-uniformity index of settlement evolution, and the degree of disorder in data changes.

[0073] Specifically, the mean values ​​of the non-uniformity index of settlement evolution and the degree of disorder in data change are obtained and denoted as the adjustment coefficient; the adjustment range is obtained by multiplying the difference between the upper and lower limits of the differential order interval by the aforementioned adjustment coefficient; the optimized differential order is obtained by adding the lower limit of the differential order interval to the adjustment range and then rounding.

[0074] ;

[0075] In the formula, d represents the order of the optimization difference. , represents the upper and lower limits of the difference order interval, respectively; Q and P represent the degree of data disorder and the non-uniformity index of settlement evolution, respectively. To adjust the range, The adjustment coefficient represents the intensity of the oscillation characteristics of the settlement data. A larger value indicates more significant differences in settlement intensity during the data's settlement evolution, stronger non-uniformity, staged nature, and irregularity of the settlement process, a higher frequency of data evolution direction switching, weaker overall evolution regularity, and a greater need for higher-order differencing to eliminate structural change components. ROUND represents the rounding function, used for rounding to the nearest integer.

[0076] Therefore, when the settlement data sequence is strongly periodic, that is, when it has strong periodicity, the period of the settlement data sequence is used as the lag value to perform first-order difference on the settlement data sequence to obtain the difference sequence. When the settlement data sequence is not strongly periodic, the optimized difference order is obtained, and the lag value is set to the first preset value 1 to perform difference to obtain the difference sequence.

[0077] The early warning module is used to predict the settlement data for the next time step based on the difference sequence corresponding to the settlement data sequence and the ARIMA algorithm; and to issue an early warning using the predicted settlement data for the next time step.

[0078] The above analysis of settlement data sequences explored how to perform differencing on settlement data sequences under two different scenarios, obtaining differencing sequences that meet the stationarity requirements. This allows the differencing process to more effectively eliminate non-stationary structures in the settlement sequence while avoiding excessive differencing that weakens effective information. Furthermore, based on the differencing sequences corresponding to the settlement data sequences and combined with the ARIMA algorithm, AR (Autoregressive Model) and MA (Moving Average Model) are constructed to model the temporal correlation in the sequence, predicting the settlement data for the next time step.

[0079] Based on the predicted settlement data for the next moment, when the predicted settlement data for the next moment shows that the settlement data reaches or exceeds the corresponding safety control threshold, an early warning message is output in advance to prompt maintenance personnel to take corresponding inspection or disposal measures, thereby realizing the early identification and early warning of railway foundation settlement risks.

[0080] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, the above description focuses on specific embodiments of this specification. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0081] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A monitoring and early warning system for railway foundation settlement in loess areas, characterized in that, The system includes: The data preprocessing module is used to collect vertical displacement data at monitoring points on the railway subgrade at various times and preprocess the data to obtain settlement data at each time point. The settlement data at each time point is then arranged into a settlement data sequence according to time sequence. The periodicity determination module is used to obtain the seasonal term and residual term of the settlement data sequence; to obtain the intensity characterization value of the periodic component of the data using the residual term and the timestamps corresponding to each maximum point in the seasonal term; to determine whether the settlement data sequence is strongly periodic using the intensity characterization value of the periodic component of the data; if it is strongly periodic, to perform first-order difference on the settlement data sequence using the period as the lag value to obtain the difference sequence. The differential order optimization module is used to: obtain a rate of change sequence based on the difference between every two adjacent settlement data points if the settlement data sequence is non-strongly periodic; analyze the element changes in the rate of change sequence to obtain a settlement evolution non-uniformity index; analyze the changes in the settlement data in the settlement data sequence to obtain the degree of data variation disorder; optimize the differential order based on the settlement evolution non-uniformity index and the degree of data variation disorder to obtain an optimized differential order; and combine the optimized differential order and a preset lag value to perform differential analysis on the settlement data sequence to obtain a differential sequence. The early warning module is used to predict the settlement data for the next time step based on the difference sequence corresponding to the settlement data sequence and the ARIMA algorithm; and to issue an early warning using the predicted settlement data for the next time step. The step of obtaining the intensity characterization value of the periodic component of the data using the timestamps corresponding to the maximum points in the residual term and the seasonal term includes: The cumulative distribution function of the residual term is obtained from the residual term and denoted as the residual cumulative distribution function. The absolute value of the difference between the residual cumulative distribution function and the cumulative distribution function of the standard normal distribution is integrated to obtain the integral result. The normalized value of the integral result is subtracted from the first preset value to obtain the cumulative distribution function difference term. The difference between the timestamps of the latter and former maxima of two adjacent maxima in the seasonal term is obtained and denoted as the timestamp difference of the latter maxima. Similarly, the timestamp differences of each maxima in the seasonal term are obtained and formed into a timestamp difference sequence according to the time sequence. The difference between the latter and former timestamp differences of each pair of adjacent timestamp differences in the timestamp difference sequence is obtained and summed to obtain the timestamp difference change characteristic value. The timestamp difference term is obtained by subtracting the normalized value of the timestamp difference change characteristic value from the first preset value. The mean value of the cumulative distribution function difference term and the timestamp difference term is obtained to obtain the data periodicity component intensity characterization value. The analysis of elemental changes in the rate of change sequence to obtain indices of non-uniformity in sedimentation evolution includes: The mean of all change rates in the rate of change sequence is obtained and denoted as the average rate of change. The number of change rates in the rate of change sequence whose absolute value of the difference from the average rate of change is less than the average rate of change is obtained and compared with the number of change rates in the rate of change sequence to obtain the stable percentage of settlement rate. The difference between the first preset value and the stable percentage of settlement rate is obtained and denoted as the unstable percentage of settlement rate. The average of the normalized values ​​of the unstable percentage of settlement rate and the variance of all change rates in the rate of change sequence is calculated to obtain the non-uniformity index of settlement evolution. The specific calculation model for the degree of data variation disorder is as follows: ， Where Q represents the degree of data disorder; n represents the number of settlement data in the settlement data sequence; , and These represent the (t-1), t, and t+1th settlement data points in the settlement data sequence, respectively. Indicates an indicator function, when When the value is greater than or equal to 0, the value of the indicator function is 0; when... When the value is less than 0, the indicator function has a value of 1.

2. The railway foundation settlement monitoring and early warning system in loess areas according to claim 1, characterized in that, The step of determining whether a sedimentation data sequence is strongly periodic by utilizing the intensity characterization value of the periodic components of the data includes: If the intensity value of the periodic component of the settlement data sequence is greater than or equal to the reference threshold, the settlement data sequence is strongly periodic; if the intensity value of the periodic component of the settlement data sequence is less than the reference threshold, the settlement data sequence is not strongly periodic.

3. The railway foundation settlement monitoring and early warning system in loess areas according to claim 1, characterized in that, The step of obtaining the rate of change sequence based on the difference between every two adjacent settlement data points in the settlement data sequence includes: The absolute value of the difference between the second and first settlement data in two adjacent settlement data in the settlement data sequence is taken as the rate of change of the second settlement data. The rate of change of the other settlement data in the settlement data sequence, except for the rate of change of the first settlement data, is arranged in chronological order to obtain the rate of change sequence.

4. The railway foundation settlement monitoring and early warning system in loess areas according to claim 1, characterized in that, The process of optimizing the difference order based on the non-uniformity index of settlement evolution and the degree of data variation disorder to obtain the optimized difference order includes: Set the lower and upper limits of the differential order interval; obtain the mean values ​​of the non-uniformity index of settlement evolution and the degree of disorder in data changes, and record them as the adjustment coefficient; multiply the difference between the upper and lower limits of the differential order interval by the adjustment coefficient to obtain the adjustment range; add the lower limit of the differential order interval to the adjustment range and then round to obtain the optimized differential order.

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