A method and system for health monitoring of cable-stayed bridges based on dynamic threshold

Abstract

The application discloses a kind of based on dynamic threshold's cable-stayed bridge health monitoring method, it is related to traffic and transport industry bridge and culvert engineering technical field, including according to generalized Pareto distribution extreme value analysis theory and separated bridge midspan deflection monitoring data, predict reference threshold, and select optimal threshold.SARIMA model is used to temperature effect data separated from deflection signal as training data, the stationarity of sequence after difference is judged using ADF test, and future temperature effect is iteratively predicted using AIC criterion.Temperature correction is performed based on the reference threshold, and dynamic monitoring of the structure is achieved.The application considers temperature correction based on the reference threshold, predicts temperature effect using the seasonal difference autoregressive moving average model, and achieves real-time dynamic early warning during bridge operation.The GPD threshold used is selected based on the threshold-crossing method, which overcomes the disadvantage of not fully utilizing extreme value information.

Description

Technical Field

[0001] This invention relates to the field of bridge and culvert engineering technology in the transportation industry, and in particular to a method and system for health monitoring of cable-stayed bridges based on dynamic thresholds. Background Technology

[0002] As a crucial component of the transportation system, the health and operating environment of long-span bridges are issues of widespread public concern. Research on real-time early warning methods for bridge structures is of great significance for timely detection of structural anomalies, elimination of hazardous factors, and ensuring the normal operation of bridges.

[0003] Current technology utilizes a feedback backpropagation (BP) neural network, training it with the measured natural frequencies of the structure under healthy conditions as input. An alarm is triggered when the frequency change exceeds 2.5%. A new structural damage early warning index has been established using monitoring modal parameters, demonstrating both noise resistance and damage sensitivity. Two warning lines are calculated based on the average and standard deviation at 95% and 99.86% retention rates, respectively, and updated annually during monitoring. By combining a Bayesian model with reliability theory, early warning for bridge expansion joints has been implemented, taking into account uncertainties in the monitoring data. However, static threshold monitoring systems may suffer from false alarms and missed alarms due to the influence of ambient temperature variations on bridge results. Summary of the Invention

[0004] In view of the problems existing in the current dynamic threshold-based health monitoring and system for cable-stayed bridges, this invention is proposed.

[0005] Therefore, the problem to be solved by the present invention is that a fixed threshold monitoring system may have missed or false alarms due to the effect of temperature.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a method for health monitoring of cable-stayed bridges based on dynamic thresholds. This method includes: predicting a baseline threshold and selecting an optimal threshold based on the generalized Pareto distribution extreme value analysis theory and the separated mid-span deflection monitoring data; using the SARIMA model to train temperature effect data separated from the deflection signal; using the ADF test to determine the stationarity of the differencing sequence; and using the AIC criterion to iteratively predict future temperature effects. Temperature correction is then performed based on the baseline threshold to achieve dynamic monitoring of the structure.

[0008] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the prediction of the baseline threshold includes the use of generalized Pareto distribution extreme value analysis theory, wherein the generalized Pareto distribution extreme value analysis theory includes a generalized Pareto distribution and parameter estimation, and the generalized Pareto distribution is assumed to be X1, X2, X3...X... n They are independent random variables and follow the same distribution F(x). Using a fixed, relatively large value u as a threshold, if X... i If the value is greater than u, it is called the threshold, and y = X. i -u represents the corresponding excess quantity, therefore the distribution function of the excess quantity is:

[0009]

[0010] Define e(u) as the average excess function of X,

[0011] e(u)=E(Xu|X>u) (2)

[0012] For a certain threshold u, consider the event {X} exceeding the threshold. i >u}, the recurrence level u(T) in year T, which requires that the average number of times the baseline threshold u(T) is exceeded within the observation period of year T is 1, X i Let the observed value be for year i. Then we have:

[0013] u(T)=F -1 (1-1 / T) (3)

[0014] u(T) is the (1-1 / T) quantile of F(x), given by P(X). i >u(T))=1-F(u(T))=1 / T, where the recurrence level u(T) in year T represents the probability that a certain maximum observed value exceeds u(T) as 1 / T;

[0015] Let τ1 = min{m:X} be the time when the threshold u(T) is first exceeded. m >u(T)}, then the time for the r-th time to exceed the baseline threshold is τ r =min{m>τ r-1 :X m >u(T)},r>1;

[0016]

[0017] Where q = 1 - F(u(T));

[0018] The baseline threshold is derived from the guarantee rate A in year T, and the corresponding quantile is obtained as follows:

[0019] P(τ1≤T)≤1-A (5)

[0020] Where T is the estimated number of years and A is the guarantee rate;

[0021] From equations (2-4), we get:

[0022]

[0023] Substitute equation (5) into equation (6) to obtain q, and obtain the benchmark threshold u(T) from q = 1 / T and equation (3);

[0024] Given that F(x) is unknown, we present the asymptotic distribution of the overthreshold distribution function, i.e., the generalized Pareto distribution:

[0025]

[0026] In the formula, μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter.

[0027] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the parameter estimation is a location parameter of the generalized Pareto distribution GPD, i.e., a threshold. The optimal threshold is selected by establishing a relationship graph between the average excess function e(u) and the threshold u. For data following a generalized Pareto distribution, the average excess function e(u) is expressed as:

[0028]

[0029] Where u is the threshold, ξ is the shape parameter, and σ u Let u be the scale parameter corresponding to the threshold. From equation (7), it can be seen that e(u) has a linear relationship with u. For datasets X1, X2, X3...X n The empirical estimate of e(u) is:

[0030]

[0031] Where, N u This represents the number of data points exceeding the threshold in the dataset.

[0032] For a certain threshold u0, the excess amount approximately follows the shape parameter as follows: The scale parameter is The generalized Pareto distribution shows that when u > u0, the mean excess function fluctuates around a straight line; when u0 > 0, the slope of the mean excess function graph remains approximately unchanged after u > u0, so u0 is selected as the optimal threshold.

[0033] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the SARIMA model is developed based on the Autoregressive Moving Average (ARMA) model. Specifically, the Autoregressive Moving Average (ARMA) model is...

[0034] Suppose {x t Let f(t) = 1, 2, ..., n be a stationary time series with zero mean. Then the observed value x at time t is... t It can be linearly estimated using the observations from its previous p time steps, denoted as AR(p), as shown in the following equation:

[0035]

[0036] in, e is the autoregressive coefficient. t denoted as the residual, and p as the order of the autoregressive model;

[0037] The time series {x t The observed value x at time t for t = 1, 2, ..., n t It can also be expressed as a linear combination of the prediction residuals at the first q time steps, denoted as MA(q):

[0038] x t =e t -θ1e t-1 -θ2e t-2 -…-θ q e t-q (11)

[0039] Where, θ i (i = 1, 2, ..., p) are the moving average coefficients, and q is the order of the autoregressive model;

[0040] The autoregressive moving average (ARMA) combines the AR and MA models, denoted as ARMA(p,q), and can be expressed as:

[0041]

[0042] It can be simply remembered as:

[0043]

[0044] in, θ(B)=1-θ1B-θ2B 2 -…-θ p B p B is the shift operator.

[0045] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the SARIMA model is generally expressed as SARIMA(p,d,q)(P,D,Q,s), where p is the autoregressive order, d is the non-seasonal differencing order, q is the moving average order, P is the seasonal autoregressive order, D is the seasonal differencing order, Q is the seasonal moving average order, and s is the period. The formula is as follows:

[0046]

[0047] Where, x t For non-stationary time series {x t In the table, the observation value at time t is given, s is the length of the seasonal period, and d is the order of the time series stabilization operation. Let Φ represent the D-order seasonal difference operator and the d-order period-by-period difference operator, respectively; P (B s )=1-Φ1B s -Φ2B 2s -…-Φ P B Ps Θ Q (B s )=1-Θ1B s -Θ2B 2s -…-Θ Q B Qs ,

[0048] The AIC criterion is used to select the model order, and its expression is as follows:

[0049]

[0050] Where p is the number of independent parameters in the model, and N is the length of the time series. The variance of the model residuals is denoted by AIC; the optimal order of the model is found when AIC reaches its minimum value.

[0051] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the prediction of the temperature effect includes: using the ADF test to determine the stationarity of the differencing sequence, and using the AIC criterion to find the remaining four parameters in the optimal SARIMA model, denoted as model M; and analyzing its residuals e t1 Perform white noise testing and plot e t1 Time series plots, autocorrelation plots (ACF), and partial autocorrelation plots (PACF) were generated; when 5% of the autocorrelation coefficients and partial autocorrelation coefficients in the residuals exceeded the confidence interval, further analysis of the residuals e was performed. t1 Perform Ljung-Box test; the prediction model needs further optimization, particularly regarding the residuals e. t1Perform secondary prediction; when the ADF test shows that the residual e t1 For stationary time series, the ARMA modeling requirements are met. ARMA is then used to analyze the residuals e. t1 Modeling is performed; the AIC criterion is used to find the optimal ARMA model parameters, denoted as model. Similarly, for the model residual e t2 Perform white noise testing and plot e t2 The time series plots, ACF plots, and PACF plots were analyzed using the Ljung-Box test; the final prediction result P(t) was derived from the prediction result P1(t) of model M and the model... The prediction result P2(t) consists of two parts, namely P(t) = P1(t) + P2(t).

[0052] As a preferred embodiment of the dynamic threshold-based health monitoring method for cable-stayed bridges described in this invention, the dynamic monitoring specifically involves correcting a baseline threshold based on data predicting temperature effects. The specific calculation formula can be expressed as follows:

[0053] D T =D0+D(T,t)

[0054] Where D0 is the threshold baseline value, D(T,t) is the index change caused by temperature T at time t, and D T This is a dynamic threshold.

[0055] Secondly, embodiments of the present invention provide a health monitoring system for cable-stayed bridges based on dynamic thresholds, comprising: an optimal threshold selection module: setting a warning baseline threshold based on the GPD extreme value analysis theory, including selecting the optimal threshold using a generalized Pareto distribution combined with an average excess function; a temperature effect prediction module: using a SARIMA model to iteratively predict future temperature effects using temperature effect data separated from deflection signals as training data; and a threshold dynamic monitoring module: correcting the baseline threshold for temperature effects based on the baseline threshold obtained using the generalized GPD extreme value analysis theory and the temperature effect predicted using the SARIMA model, thereby achieving dynamic threshold health monitoring.

[0056] Thirdly, embodiments of the present invention provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement any step of the above-described method for monitoring the health of cable-stayed bridges based on dynamic thresholds.

[0057] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the above-described method for monitoring the health of cable-stayed bridges based on dynamic thresholds.

[0058] The beneficial effects of this invention are that it performs temperature correction based on a baseline threshold, predicts temperature effects using a seasonal differential autoregressive moving average model, and achieves real-time dynamic early warning during bridge operation. Furthermore, the use of GPD (Gross Damage Distribution) for extreme value selection based on the over-threshold method overcomes the drawback of insufficient utilization of extreme value information. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments 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. Wherein:

[0060] Figure 1 The design intent of this invention's process;

[0061] Figure 2 Deflection measurement point layout for a long-span cable-stayed bridge in Wuhan;

[0062] Figure 3 BD12 deflection monitoring data;

[0063] Figure 4 Deflection monitoring data after temperature effect separation;

[0064] Figure 5 The average deflection at mid-span exceeds the allowable function.

[0065] Figure 6 The correspondence between candidate thresholds and correlation coefficient tests;

[0066] Figure 7 The correspondence between candidate thresholds and the coefficient of determination test;

[0067] Figure 8 The correspondence between candidate thresholds and root mean square error test;

[0068] Figure 9 Cumulative probability density fitting performance test plot;

[0069] Figure 10 .QQ fitting effect test chart;

[0070] Figure 11 Probability density distribution function;

[0071] Figure 12 Temperature effect at BD12 measuring point in June 2021;

[0072] Figure 13 Model M residual e t1 Time series plot;

[0073] Figure 14 Model M residual e t1 ACF diagram;

[0074] Figure 15 Model M residual e t1 PACF plot;

[0075] Figure 16 .Model residual e t2 Time series plot;

[0076] Figure 17 .Model residual e t2 ACF diagram;

[0077] Figure 18 .Model residual e t2 PACF plot;

[0078] Figure 19 .Graph of prediction results of the autoregressive model M;

[0079] Figure 20 .Model The prediction results of the autoregressive model are shown in the figure;

[0080] Figure 21 The final prediction result of the autoregressive model after one error prediction adjustment;

[0081] Figure 22 Dynamic threshold monitoring of the BD12 measuring point on the cable-stayed bridge in July;

[0082] Figure 23 Alarm diagram of BD12 measuring point exceeding threshold on cable-stayed bridge safety service monitoring platform. Detailed Implementation

[0083] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0084] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0085] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0086] Example 1

[0087] Reference Figure 1 This is the first embodiment of the present invention, which provides a method for health monitoring of cable-stayed bridges based on dynamic thresholds, including:

[0088] S1. Based on the generalized Pareto distribution and the isolated bridge mid-span deflection monitoring data, predict the baseline threshold and select the optimal threshold.

[0089] The prediction of the baseline threshold includes the use of generalized Pareto distribution extreme value analysis theory, which comprises a generalized Pareto distribution and parameter estimation. The generalized Pareto distribution is...

[0090] Assume X1, X2, X3...X n They are independent random variables and follow the same distribution F(x). Using a fixed, relatively large value u as a threshold, if X... i If the value is greater than u, it is called the threshold, and y = X. i -u represents the corresponding excess quantity, therefore the distribution function of the excess quantity is:

[0091]

[0092] The probability density function of the excess quantity is,

[0093]

[0094] The distribution function for exceeding the threshold is,

[0095]

[0096] The probability density function for exceeding the threshold is,

[0097]

[0098] Define e(u) as the average excess function of X,

[0099] e(u)=E(Xu|X>u) (5)

[0100] For a certain threshold u, consider the event {X} exceeding the threshold. i >u}, the recurrence level u(T) in year T, which requires that the average number of times the baseline threshold u(T) is exceeded within the observation period of year T is 1, X i Let the observed value be for year i. Then we have:

[0101] u(T)=F -1 (1-1 / T) (6)

[0102] u(T) is the (1-1 / T) quantile of F(x), given by P(X). i >u(T))=1-F(u(T))=1 / T, where the recurrence level u(T) in year T represents the probability that a certain maximum observed value exceeds u(T) as 1 / T;

[0103] Let τ1 = min{m:X} be the time when the threshold u(T) is first exceeded. m >u(T)}, then the time for the r-th time to exceed the baseline threshold is τ r =min{m>τ r-1 :X m >u(T)},r>1;

[0104]

[0105] Where q = 1 - F(u(T));

[0106] The baseline threshold estimated in this paper is the quantile corresponding to a 95% guarantee rate over 100 years, which can be expressed as:

[0107] P(τ1≤100)≤0.05 (8)

[0108] Where T is the estimated number of years and A is the guarantee rate;

[0109] From equation (3-7), we can obtain:

[0110]

[0111] Substituting equation (9) into equation (8) yields q, and from q = 1 / T and equation (6), the baseline threshold u(T) is obtained.

[0112] In practical engineering, random variables X1, X2, X3...X n The distribution function F(x) is generally unknown, therefore its over-threshold distribution function F [u](x) is also unknown. When the threshold is large enough, Pickands gives the asymptotic distribution of the overthreshold distribution function under the condition that F(x) is unknown, which yields the generalized Pareto distribution:

[0113]

[0114] Where μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter;

[0115] The generalized Pareto distribution (GPD) is used to describe the probability distribution of excess or exceeding a threshold by fitting the tail data of a random variable.

[0116] The selection of the optimal threshold includes the fact that the key to estimating the generalized Pareto distribution parameters is the location parameter, i.e., the threshold; the optimal threshold is selected by establishing a relationship between the average excess function e(u) and the threshold u. For data that follows the GPD, its average excess function e(u) can be expressed as:

[0117]

[0118] Where u is the threshold, ξ is the shape parameter, and σ u Let u be the scale parameter corresponding to the threshold. From equation (11), it can be seen that e(u) has a linear relationship with u. For datasets X1, X2, X3...X n The empirical estimate of e(u) is:

[0119]

[0120] Where, N u This represents the number of data points exceeding the threshold in the dataset.

[0121] For a certain threshold u0, the excess amount approximately follows the shape parameter as follows: The scale parameter is For a generalized Pareto distribution, the mean excess function will fluctuate around a straight line for u values ​​greater than u0. Therefore, the principle for threshold selection is: for a certain threshold u0>0, if the slope of the mean excess function graph remains approximately unchanged after u>u0, then u0 is selected as the optimal threshold. However, in practical engineering, the mean excess function graph is rarely perfectly linear, making threshold selection highly subjective. Therefore, an optimal threshold range can be selected, and then the optimal threshold is determined based on three fitting test criteria: root mean square error, correlation coefficient, and coefficient of determination. After determining the optimal threshold, the corresponding shape and scale parameters can be calculated using maximum likelihood estimation.

[0122] S2. Using the SARIMA model, the temperature effect data separated from the deflection signal is used as training data to iteratively predict future temperature effects.

[0123] The SARIMA model is developed based on the Autoregressive Moving Average (ARMA) model. Specifically, the Autoregressive Moving Average (ARMA) model is...

[0124] Suppose {x t Let f(t) = 1, 2, ..., n be a stationary time series with zero mean. Then the observed value x at time t is... t It can be linearly estimated using the observations from its previous p time steps, denoted as AR(p), as shown in the following equation:

[0125]

[0126] in, e is the autoregressive coefficient. t denoted as the residual, and p as the order of the autoregressive model;

[0127] The time series {x t The observed value x at time t for t = 1, 2, ..., n t It can also be expressed as a linear combination of the prediction residuals at the first q time steps, denoted as MA(q):

[0128] x t =e t -θ1e t-1 -θ2e t-2 -…-θ q e t-q (14)

[0129] Where, θ i (i = 1, 2, ..., p) are the moving average coefficients, and q is the order of the autoregressive model;

[0130] The autoregressive moving average (ARMA) combines the AR and MA models, denoted as ARMA(p,q), and can be expressed as:

[0131]

[0132] It can be simply remembered as:

[0133]

[0134] in, θ(B)=1-θ1B-θ2B 2 -…-θ p B p B is the shift operator.

[0135] The SARIMA model is generally represented as SARIMA(p,d,q)(P,D,Q,s), where p is the autoregressive order, d is the non-seasonal differencing order, q is the moving average order, P is the seasonal autoregressive order, D is the seasonal differencing order, Q is the seasonal moving average order, and s is the period. The formula is as follows:

[0136]

[0137] Where, x t For non-stationary time series {x t In the table, the observation value at time t is given, s is the length of the seasonal period, and d is the order of the time series stabilization operation. Let Φ represent the D-order seasonal difference operator and the d-order period-by-period difference operator, respectively; P (B s )=1-Φ1B s -Φ2B 2s -…-Φ P B Ps Θ Q (B s )=1-Θ1B s -Θ2B 2s -…-Θ Q B Qs ,

[0138] The AIC criterion is used to select the model order, and its expression is as follows:

[0139]

[0140] Where p is the number of independent parameters in the model, and N is the length of the time series. Let AIC be the variance of the model residuals. The optimal order of the model is determined when AIC is minimized. The AIC criterion states that increasing the number of free parameters improves the fit, but overfitting should be avoided. Therefore, the model with the smallest AIC value should be prioritized. The AIC criterion method seeks the model that best explains the data while containing the fewest free parameters. The AIC criterion order determination method: Assuming the SARIMA model order is p, the variance of the corresponding SARIMA(p) model residuals can be calculated, and a function is introduced... Each p-value corresponds to a variance of the model residuals. Calculations show that the criterion reaches its minimum at a certain p-value. Here, p represents the number of independent parameters in the model. This represents the variance of the model residuals.

[0141] The ARMA model makes predictions based on the premise that the time series is a stationary random process with zero mean. SARIMA can eliminate the trend and periodicity in the time series through period-by-period differencing and seasonal differencing, transforming non-stationary series into stationary series.

[0142] The prediction of the temperature effect is as follows:

[0143] The stationarity of the differencing sequence is determined by the ADF test, and the remaining four parameters in the optimal SARIMA model are found by the AIC criterion, denoted as model M.

[0144] The residual e of model M t1 Perform white noise testing and plot e t1 Time series plots, autocorrelation plots (ACF), and partial autocorrelation plots (PACF);

[0145] When a large number of autocorrelation coefficients and partial autocorrelation coefficients of order in the residuals exceed the 95% confidence interval, further analysis of the residuals e is needed. t1 Perform the Ljung-Box test; if 5% of the autocorrelation coefficients and partial autocorrelation coefficients exceed the confidence interval, it is considered that a large number of autocorrelation coefficients have exceeded the confidence interval.

[0146] Continue to optimize the prediction model, focusing on the residual e. t1 Perform secondary prediction; when the ADF test shows that the residual e t1 For stationary time series, the ARMA modeling requirements are met. ARMA is then used to analyze the residuals e. t1 Perform modeling;

[0147] The optimal ARMA model parameters are found using the AIC criterion, denoted as model. Similarly, for the model residual e t2 Perform white noise testing and plot e t2 Ljung-Box test was performed on the time series plots, ACF plots, and PACF plots.

[0148] The final prediction result P(t) is composed of the prediction result P1(t) of model M and the prediction result P1(t) of model M. The prediction result P2(t) consists of two parts, namely P(t) = P1(t) + P2(t).

[0149] S3. Temperature correction is performed based on the baseline threshold to achieve dynamic monitoring of the structure.

[0150] Dynamic monitoring uses data predicting temperature effects to adjust a baseline threshold; the specific calculation formula is as follows:

[0151] D T =D0+D(T,t)

[0152] Where D0 is the threshold baseline value, D(T,t) is the index change caused by temperature T at time t, and D T This is a dynamic threshold.

[0153] Furthermore, this embodiment also provides a cable-stayed bridge health monitoring system based on dynamic thresholds, including:

[0154] The optimal threshold selection module sets a warning baseline threshold based on the generalized Pareto distribution (GPD) extreme value analysis theory. This includes using the average excess function in the generalized Pareto distribution and combining it with the recurrence level to select the optimal baseline threshold.

[0155] The temperature effect prediction module uses the SARIMA model to iteratively predict future temperature effects using temperature effect data separated from the deflection signal as training data.

[0156] The threshold dynamic monitoring module uses the benchmark threshold obtained by generalized GPD extreme value analysis theory and the temperature effect predicted by SARIMA model as the basis to correct the benchmark threshold for temperature effect, thereby realizing dynamic threshold health monitoring.

[0157] This embodiment also provides a computer device applicable to the dynamic threshold-based health monitoring method for cable-stayed bridges, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the dynamic threshold-based health monitoring method for cable-stayed bridges as proposed in the above embodiment.

[0158] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0159] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the dynamic threshold-based health monitoring method for cable-stayed bridges as proposed in the above embodiments.

[0160] The storage medium proposed in this embodiment and the data storage method proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0161] Example 2

[0162] Reference Figures 2-23 This is the second embodiment of the present invention, which provides a method for monitoring the health of cable-stayed bridges based on dynamic thresholds. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0163] A case study is conducted using a cross-river bridge in Wuhan. This bridge is a double-tower, double-cable-stayed steel-concrete composite girder bridge with a main span of 618 meters. The bridge utilizes a BeiDou real-time monitoring system, with deflection measuring points deployed at key locations. The layout of these measuring points is detailed below. Figure 2 The effectiveness of the dynamic anomaly early warning method for cable-stayed bridges was verified by selecting mid-span deflection as the early warning indicator.

[0164] This case study uses a full year's worth of data as a sample to set the baseline threshold. However, due to external interference during actual operation, data gaps exist at the monitoring points. To ensure the continuity of the year's data, months with relatively complete monitoring data were selected. Therefore, monitoring data from July 1, 2020 to June 30, 2021 was chosen as the basis for studying the setting of the baseline threshold. Figure 3 The data is the hourly downwind monitoring data of measuring point BD12 from July 1, 2020 to June 30, 2021.

[0165] After separating the temperature effect from the monitoring data using the VMD-SVD method, the baseline threshold was set using GPD extreme value analysis. The deflection monitoring data after temperature effect separation is shown below. Figure 4 As shown.

[0166] 2. Determination of benchmark threshold

[0167] Based on the GPD extreme value analysis theory mentioned above, a warning baseline threshold is set. First, the threshold for the monitored samples is determined, and the average exceedance function graph is shown below. Figure 5 As shown in the figure, when the threshold exceeds 175mm, the average excess amount has a linear relationship with the threshold. However, because the tail data distorts the image, the slope of the graph fluctuates slightly after the threshold reaches 175mm. Therefore, the threshold range [175, 300] is selected. To further determine the optimal threshold, three commonly used test criteria are selected to evaluate the closeness between the distribution curve of the excess data and the theoretical distribution curve: correlation coefficient (PPCC), coefficient of determination (R²), and other parameters. 2 ), Root Mean Square Error (REMS).

[0168]

[0169]

[0170]

[0171] In the formula, x i To monitor the actual value of the sample probability density function, y i The estimated value fitted to GPD, and x i and y i The mean.

[0172] For each candidate threshold, the parameters of the GPD distribution are estimated using maximum likelihood estimation, resulting in an expression for the GPD distribution. These expressions are then applied using PPCC and R... 2 REMS was used to perform a fit test on the GPD distribution for each threshold, and the relationship between the threshold and the test index was obtained as follows: Figures 6-8 As shown:

[0173] In order to comprehensively consider the above three indicators, it is necessary to standardize them first. Formula (4) is used to calculate the positive test index, that is, the larger the value of the test index, the better the fitting effect. Formula (5) is used to calculate the negative test index, that is, the smaller the value of the test index, the better the fitting effect. Then, the correlation matrix of each standardized index is calculated, principal component analysis is performed on the correlation matrix, the first principal component is selected as the comprehensive index, and the index is sorted according to the size of the comprehensive index, and then the optimal threshold is selected [3].

[0174]

[0175]

[0176] In the formula, x ij Let i be the value of the test index, j be the number of thresholds to be tested, and a be the number of test indicators. ij For x ij The corresponding standardized value.

[0177] Table 1. Comprehensive Threshold Test Indicators

[0178]

[0179] Table 1 shows that the first-ranked threshold is the optimal threshold, which is 181. Based on the optimal threshold, maximum likelihood estimation was used to calculate the shape and scale parameters of the GPD, which are 0.0447 and 35.8208, respectively. To more intuitively judge the fitting effect between the over-threshold data and the GPD, cumulative probability density plots and QQ plots were plotted. Figures 9-11As shown.

[0180] Depend on Figure 9 It can be seen that the fitted curve of GPD highly coincides with the cumulative distribution function of the data exceeding the threshold, and the data points in the QQ plot are also evenly distributed around the fitted line, indicating a good fitting effect. Given the shape and scale parameters, the probability density distribution function of GPD is as follows: Figure 11 As shown, the baseline threshold for mid-span deflection, estimated with a 95% guarantee rate over 100 years, is 504.914 mm.

[0181] 3. Temperature effect prediction

[0182] When predicting the temperature effect, 720 data points from the previous month were used as training data to iteratively predict the temperature effect for the next day. The temperature effect (including daily and annual temperature range effects) at the BD12 monitoring point from June 1st to 30th, 2021 is shown below. Figure 12 As shown in the figure, the temperature effect exhibits a clear periodicity, with a 24-hour cycle. Therefore, SARIMA is considered for modeling and prediction. After performing first-order non-seasonal differencing and first-order seasonal differencing on the original data, the ADF test is used to determine the stationarity of the differencing sequence. The output p-value is 0.0122, which is less than 0.05, indicating that the sequence is significantly stationary. The AIC criterion is used to find the remaining four parameters in the optimal SARIMA model. The search results are as follows:

[0183] SARIMA(3,1,3)(0,1,3,24), denoted as model M, has residuals e t1 Perform white noise testing and plot e t1 Time series plots, autocorrelation plots (ACF), and partial autocorrelation plots (PACF), such as... Figures 13-15 As shown.

[0184] Depend on Figures 14-15 It can be seen that a large number of autocorrelation coefficients and partial autocorrelation coefficients of order M exceed the 95% confidence interval in the residuals of model M; further analysis of the residuals e t1 Perform Ljung-Box test, e t1 The white noise statistical result p-value = 0, which is less than 0.05, indicating that the null hypothesis that there is no autocorrelation between the data is rejected, i.e., e t1 Although it is non-white noise, it still contains valuable information, and the prediction model needs to be further optimized, particularly the residual e. t1 Perform a second prediction.

[0185] residual e t1 There is no obvious periodicity or trend; consider using ARMA to analyze the residual e. t1 Modeling was performed, and an ADF test was conducted. The output p-value was 0.001, which is less than 0.05, indicating that the residual et1 For a stationary time series, the model must meet the requirements for ARMA modeling. The AIC criterion is used to find the optimal ARMA model parameters. The optimal result is ARMA(5,10), denoted as model number. Similarly, for the model residual e t2 Perform white noise testing, e t2 Time series plots, ACF plots, and PACF plots, such as Figures 16-18 As shown.

[0186] Depend on Figures 17-18 It can be seen that the residual e t2 Most of the autocorrelation coefficients and partial autocorrelation coefficients are within the confidence interval, although the 10th, 11th, and 15th orders exceed the confidence interval, which may be due to random factors. For the residual e... t2 Perform Ljung-Box test, e t2 The white noise statistical result p-value = 0.2391, which is greater than 0.05, accepting the null hypothesis that there is no autocorrelation among the data, i.e., e t2 White noise indicates model The data e was fitted well. t1 .

[0187] The final prediction result P(t) is composed of the prediction result P1(t) of model M and the prediction result P1(t) of model M. The predicted result P2(t) consists of two parts, namely P(t) = P1(t) + P2(t), as follows: Figures 19-20 As shown. Figure 21 The predicted values ​​and the actual values ​​show the same trend and have similar amplitude ranges, with a relative error of 0.9932.

[0188] 4. Threshold dynamic monitoring

[0189] The above temperature effect prediction results are for the temperature effect at the BD12 measuring point on July 1, 2021. To predict the temperature effect on July 2, data from June 2 to July 1 were used as training data. The above autoregressive analysis was repeated to predict the temperature effect on July 2. This process was iterated to predict the temperature effect for the entire month of July. Based on this, the baseline threshold was dynamically adjusted. Figure 22 This study focuses on dynamic threshold monitoring of the mid-span measuring point of a cable-stayed bridge in July. To facilitate observation, cubic spline interpolation was performed on the temperature effect, and the sampling frequency was adjusted from 1 hour / time to 1 second / time.

[0190] Depend on Figure 22It is evident that using dynamic thresholds to monitor cable-stayed bridges allows for real-time dynamic monitoring based on changes in ambient temperature, offering greater flexibility compared to static threshold monitoring. The cable-stayed bridge safety service monitoring platform, which uses static thresholds, only detected 10 threshold-exceeding warnings around 04:26:26 on July 4, 2021, during the monitoring period. Figure 23 As shown in Table 2, the results of over-threshold monitoring using the dynamic threshold monitoring method presented in this paper show that, in addition to detecting a significant over-threshold alarm at 04:26:26 on 2021-07-04, it can also effectively monitor local mutations in other time periods.

[0191] Table 2 Dynamic Threshold Monitoring Results

[0192]

[0193] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for health monitoring of cable-stayed bridges based on dynamic thresholds, characterized in that: include, Based on the generalized Pareto distribution extreme value analysis theory and the separated bridge mid-span deflection monitoring data, a benchmark threshold is predicted, and the optimal threshold is selected. The SARIMA model was used to train the temperature effect data separated from the deflection signal. The ADF test was used to determine the stationarity of the differenced sequence, and the AIC criterion was used to iteratively predict the future temperature effect. Temperature correction is performed based on a baseline threshold to achieve dynamic monitoring of the structure.

2. The method for monitoring the health of cable-stayed bridges based on dynamic thresholds as described in claim 1, characterized in that: The prediction of the baseline threshold includes the use of generalized Pareto distribution extreme value analysis theory, which comprises a generalized Pareto distribution and parameter estimation, wherein the generalized Pareto distribution is... Assume X1, X2, X3...X n They are independent random variables and follow the same distribution F(x). Using a fixed threshold u, if X... i If the value is greater than u, it is called the threshold, and y = X. i -u represents the corresponding excess quantity, therefore the distribution function of the excess quantity is: Define e(u) as the average excess function of X, e(u)=E(Xu|X>u) (2) For a certain threshold u, consider the event {X} exceeding the threshold. i >u}, the recurrence level u(T) in year T, which requires that the average number of times the baseline threshold u(T) is exceeded within the observation period of year T is 1, X i Let the observed value be for year i. Then we have: u(T)=F -1 (1-1 / T) (3) u(T) is the (1-1 / T) quantile of F(x), given by P(X). i >u(T))=1-F(u(T))=1 / T, where the recurrence level u(T) in year T represents the probability that a certain maximum observed value exceeds u(T) as 1 / T; Let τ1 = min{m:X} be the time when the threshold u(T) is first exceeded. m >u(T)}, then the time for the r-th time to exceed the baseline threshold is τ r =min{m>τ r-1 :X m >u(T)},r>1; Where q = 1 - F(u(T)); The baseline threshold is derived from the guarantee rate A in year T, and the corresponding quantile is obtained as follows: P(τ1≤T)≤1-A (5) Where T is the estimated number of years and A is the guarantee rate; From equations (2) to (4), we get: Substitute equation (5) into equation (6) to obtain q, and obtain the benchmark threshold u(T) from q = 1 / T and equation (3); Given that F(x) is unknown, we present the asymptotic distribution of the overthreshold distribution function, i.e., the generalized Pareto distribution: In the formula, μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter.

3. The method for monitoring the health of cable-stayed bridges based on dynamic thresholds as described in claim 2, characterized in that: The parameter estimates are location parameters of the generalized Pareto distribution (GPD), i.e., the threshold. The optimal threshold is selected by establishing a graph showing the relationship between the average excess function e(u) and the threshold u. For data following a generalized Pareto distribution, the average excess function e(u) is expressed as follows: Where u is the threshold, ξ is the shape parameter, and σ u Let u be the scale parameter corresponding to the threshold. From equation (7), we can see that e(u) has a linear relationship with u. For datasets X1, X2, X3...X n The empirical estimate of e(u) is, Where, N u This represents the number of data points exceeding the threshold in the dataset. For a certain threshold u0, the excess amount approximately follows the shape parameter as follows: The scale parameter is The generalized Pareto distribution shows that when u > u0, the mean excess function fluctuates around a straight line; when u0 > 0, the slope of the mean excess function graph remains approximately unchanged after u > u0, so u0 is selected as the optimal threshold.

4. The method for health monitoring of cable-stayed bridges based on dynamic thresholds as described in claim 1, characterized in that: The SARIMA model is an improvement upon the Autoregressive Moving Average (ARMA) model. Specifically, the Autoregressive Moving Average (ARMA) model is... Suppose {x t If}, t=1,2,…,n is a stationary time series with zero mean, then the observed value x at time t is... t A linear estimate is performed using the observations from the previous p time steps, denoted as AR(p), as shown in the following equation. in, e is the autoregressive coefficient. t denoted as the residual, and p as the order of the autoregressive model; The time series {x t The observed value x at time t for t = 1, 2, ..., n t Let MA(q) be the linear combination of the predicted residuals at the first q time steps. x t =e t -θ1e t-1 -θ2e t-2 -…-θ q e t-q (10) Where, θ i (i = 1, 2, ..., p) are the moving average coefficients, and q is the order of the autoregressive model; The autoregressive moving average (ARMA) model combines the AR and MA models, denoted as ARMA(p,q), and expressed as follows: In short, in, B is the shift operator.

5. The method for monitoring the health of cable-stayed bridges based on dynamic thresholds as described in claim 4, characterized in that: The SARIMA model is represented as SARIMA(p,d,q)(P,D,Q,s), where p is the autoregressive order, d is the non-seasonal differencing order, q is the moving average order, P is the seasonal autoregressive order, D is the seasonal differencing order, Q is the seasonal moving average order, and s is the period. The formula is as follows. Where, x t For non-stationary time series {x t In the table, the observation value at time t is given, s is the length of the seasonal period, and d is the order of the time series stabilization operation. Let Φ represent the D-order seasonal difference operator and the d-order period-by-period difference operator, respectively; P (B s )=1-Φ1B s -Φ2B 2s -…-Φ P B Ps Θ Q (B s )=1-Θ1B s -Θ2B 2s -…-Θ Q B Qs , The AIC criterion is used to select the model order, as shown in the following formula. Where p is the number of independent parameters in the model, and N is the length of the time series. The variance of the model residuals is denoted by AIC; the optimal order of the model is found when AIC reaches its minimum value.

6. The method for health monitoring of cable-stayed bridges based on dynamic thresholds as described in claim 1, characterized in that: The prediction of the temperature effect includes, The stationarity of the differencing sequence is determined by the ADF test, and the remaining four parameters in the optimal SARIMA model are found by the AIC criterion, denoted as model M. The residual e of model M t1 Perform white noise testing and plot e t1 Time series plots, autocorrelation plots (ACF), and partial autocorrelation plots (PACF); When 5% of the autocorrelation coefficients and partial autocorrelation coefficients in the residuals exceed the confidence interval, further analysis of the residuals e is needed. t1 Perform the Ljung-Box test; Continue to optimize the prediction model, focusing on the residual e. t1 Perform secondary prediction; When the ADF test shows that the residual e t1 For stationary time series, the ARMA modeling requirements are met. ARMA is then used to analyze the residuals e. t1 Perform modeling; The optimal ARMA model parameters are found using the AIC criterion, denoted as model. Similarly, for the model residual e t2 Perform white noise testing and plot e t2 Ljung-Box test was performed on the time series plots, ACF plots, and PACF plots. The final prediction result P(t) is composed of the prediction result P1(t) of model M and the prediction result of model M. The prediction result P2(t) consists of two parts, namely P(t) = P1(t) + P2(t).

7. The method for health monitoring of cable-stayed bridges based on dynamic thresholds as described in claim 1, characterized in that: The dynamic monitoring is based on data predicting temperature effects, and the baseline threshold is adjusted accordingly. The specific calculation formula is as follows: D T =D0+D(T,t) Where D0 is the threshold baseline value, D(T,t) is the index change caused by temperature T at time t, and D T This is a dynamic threshold.

8. A cable-stayed bridge health monitoring system based on dynamic thresholds, based on the cable-stayed bridge health monitoring method based on dynamic thresholds according to any one of claims 1 to 7, characterized in that: include, The optimal threshold selection module sets the warning baseline threshold based on the extreme value analysis theory of the generalized Pareto distribution (GPD). This includes using the average excess function in the generalized Pareto distribution and combining it with the recurrence level to select the optimal baseline threshold. The temperature effect prediction module uses the SARIMA model to iteratively predict future temperature effects using temperature effect data separated from the deflection signal as training data. The threshold dynamic monitoring module uses the benchmark threshold obtained by generalized GPD extreme value analysis theory and the temperature effect predicted by SARIMA model as the basis to correct the benchmark threshold for temperature effect, thereby realizing dynamic threshold health monitoring.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the cable-stayed bridge health monitoring method based on dynamic thresholds as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the cable-stayed bridge health monitoring method based on dynamic thresholds as described in any one of claims 1 to 7.

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