Method for predicting residual life of bridge support sliding plate based on monitoring and detection data combined drive

Abstract

The invention discloses a method for predicting the residual life of a bridge support sliding plate based on monitoring and detection data combined drive. The method comprises the following steps: S1, estimating the wear thickness of the support sliding plate; s2, constructing a support sliding plate residual life prediction model; and S3, dynamic prediction of the residual life of the support sliding plate: based on an Archard wear model, considering the influence of the support pressure and the sliding speed, and establishing a quantitative relation between the support displacement and the wear thickness of the sliding plate. The influence of lubrication conditions and displacement measurement distortion caused by low sampling frequency of a sensor are eliminated by using detection data of the wear thickness of the sliding plate. Then, considering the uncertainty and the time-varying property of the sliding plate wear process, and establishing a support sliding plate residual life prediction model based on the inverse Gaussian random process; based on a Bayesian algorithm and an expectation maximization (EM) algorithm, model parameters are updated by using monitoring data of the wear thickness of the sliding plate, and dynamic prediction of the residual life of the support is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of performance monitoring and evaluation of key restraint devices for bridge structures, and particularly relates to a method for predicting the remaining life of a bridge bearing sliding plate driven by joint monitoring and detection data. Background Technique

[0002] As a key restraint device for bridges, the bearing is a vulnerable component connecting the upper and lower structures of the bridge. The commonly used bearing types in long-span bridges are pot rubber bearings and spherical steel bearings. Although there are differences in their structural forms, they both satisfy the longitudinal expansion and contraction of the main girder through the relative sliding between the stainless steel plate and the polytetrafluoroethylene sliding plate. During the long-term service of the bearing, the repeated sliding of the bearing sliding plate under high-frequency loads leads to wear of the sliding plate and loss of the sliding function of the bearing, which in turn changes the structural boundary conditions and affects the safe operation of the bridge. Therefore, before the bridge bearing sliding plate is severely worn, the bridge maintenance department needs to replace the sliding plate. However, due to the influence of factors such as its own lubrication conditions, external environment, and load changes on the wear of the bearing sliding plate, its wear process has significant uncertainty, resulting in the lack of a clear basis for the bridge maintenance department to determine the replacement time of the bearing sliding plate. Therefore, conducting research on predicting the remaining life of the bearing sliding plate has great engineering significance.

[0003] With the development of health monitoring technology, structural health monitoring systems are increasingly applied to long-span bridges. These systems monitor the service status of structural components by deploying high-precision sensors at key positions on the bridges. At the same time, many scholars have carried out early warning and evaluation of key bridge restraint devices such as bearings based on the monitoring data collected by structural health monitoring systems. Yang established a correlation model between temperature and thermally induced displacement of bearings considering the time-delay effect, and realized the wear detection of bridge sliding bearings (Wear Detection of Bridge Sliding Bearing Based on Temporal Variation of Thermally Induced Daily Displacement Amplitude). Wang analyzed the cumulative displacement of bearings under the action of train loads and proposed a method for evaluating the wear life of bearings based on reliability indices (Safety Evaluation of the Wear Life of High-Speed Railway Bridge Bearings by Monitoring Train-Induced Dynamic Displacements). Wu considered the problem of low sampling frequency of displacement sensors, calculated the cumulative displacement of bearings based on acceleration data, and predicted the sliding life of bearings (Sliding life prediction of sliding bearings using dynamic monitoring data of bridges). Wei considered the wear of the sliding plate due to the cumulative displacement of bearings under the action of both temperature and vehicle loads, and predicted the bearing life based on reliability analysis (Wear Life Prediction of Sliding Bearings Based on Multitype Monitoring Data of Bridges). So far, although some scholars have carried out research on predicting the remaining life of bearing sliding plates, none of them have considered the influence of changes in the movement characteristics of the beam end on the wear law of bearings, resulting in inaccurate prediction of the remaining life of bearings. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the remaining life of a bridge bearing sliding plate driven by combined monitoring data to solve the problems raised in the above background technology.

[0005] To achieve the above purpose, the present invention provides the following technical solution: A method for predicting the remaining life of a bridge bearing sliding plate driven by combined monitoring data, comprising the following steps:

[0006] S1. Estimation of the wear thickness of the bearing sliding plate:

[0007] (1.1) Construct a wear model of the bearing slide plate considering the changes in external conditions. Based on the Archard wear model and combined with the actual situation of the bridge bearing, obtain a wear model expressed by the wear thickness, determine the calculation method of the bearing sliding distance, and construct the functional relationship between the wear coefficient and the bearing pressure and the bearing sliding speed;

[0008] (1.2) Introduce the regular inspection information of the bearing slide plate to correct the calculation of the wear thickness of the slide plate. Use the comparison between the measured thickness and the calculated thickness to introduce a correction coefficient and establish a mathematical model of the dynamic wear of the bearing slide plate;

[0009] S2. Construction of the remaining life prediction model of the bearing slide plate: Use the inverse Gaussian stochastic process to characterize the wear process of the bearing slide plate, define the relevant characteristics of the inverse Gaussian process, set the wear threshold of the bearing slide plate as a specific value, and define the time when the wear threshold is exceeded for the first time as the remaining life of the bearing, and establish a remaining life prediction model of the bearing based on the stochastic process.

[0010] S3. Dynamic prediction of the remaining life of the bearing slide plate: Based on the inverse Gaussian process, determine the joint distribution of the wear data set of the bearing slide plate at the new monitoring time point, use the Bayesian theory to update the posterior distribution of the stochastic parameters, use the expectation maximization (EM) algorithm to estimate the model parameters, and update the prediction model parameters through the displacement monitoring data of the bearing obtained in real time to realize the dynamic prediction of the remaining life of the bearing slide plate.

[0011] Preferably, in step (1.1), the bridge bearing slides through a friction pair composed of a polytetrafluoroethylene slide plate and a stainless steel plate. When the polytetrafluoroethylene slide plate wears, debris is formed and it is adhesive wear. The adhesive wear calculation model is the Archard wear model. The Archard wear model is that two mutually contacting objects are uneven. When the object is subjected to a normal load, the high micro-protrusions will come into contact first, resulting in local stress concentration. When the stress exceeds the yield strength of the bridge bearing material itself, the micro-protrusions will undergo plastic deformation. The formula of the Archard wear model is expressed as:

[0012] V = KWL / H

[0013] In the formula, V represents the volume of the micro-protrusions shed during material wear; K represents the wear coefficient; W represents the normal load; L represents the sliding distance; H represents the material hardness.

[0014] Preferably, the products after the wear of the bridge bearing slide plate are mostly sheet-like and small granular, so that the wear volume of the slide plate can be accurately measured, and the wear thickness is used as an index to evaluate the wear condition of the bearing slide plate. Therefore, based on the formula of the Archard wear model, the wear model of the bearing slide plate is expressed as:

[0015] V = Ah plate

[0016] W = AP bear

[0017] h plate = KP bear L / H

[0018] Wherein, A represents the area of the contact surface between the bearing slide plate and the stainless steel plate; h plate represents the worn thickness of the bearing slide plate, that is, the wear index of the bearing slide plate; P bear represents the pressure exerted by the main beam on the bearing;

[0019] In the bridge health monitoring system, a displacement sensor is installed at the beam end to monitor the longitudinal sliding of the bearing. Therefore, the sliding distance L bear (t) of the bearing is calculated by the following formula:

[0020]

[0021] Wherein, N represents the number of sampling points of the bearing displacement sensor at time t; l n-1 , l n respectively represent the bearing displacement values of the (n - 1)-th sampling point and the n-th sampling point.

[0022] Preferably, the characteristics of the polytetrafluoroethylene slide plate are that its wear coefficient is affected by the surface pressure and the sliding speed. Tests show that the wear coefficient of the bearing slide plate is inversely proportional to the surface pressure and directly proportional to the sliding speed. Therefore, a functional relationship between the wear coefficient and the bearing pressure and the bearing sliding speed is constructed to map the change of the wear coefficient of the bearing slide plate under different surface pressures and sliding speeds, as shown in the following formula:

[0023]

[0024]

[0025] Wherein, K dwc represents the dynamic wear coefficient of the bearing slide plate; v bear (n) represents the sliding speed of the bearing at the n-th sampling point; a, b represent power exponents; c, d represent constant coefficients; f bear represents the sampling frequency of the bearing displacement data.

[0026] Preferably, in step (1.2), for the correction of the wear model based on the detection data, the regular detection information of the support slide plate is introduced to correct the calculation of the wear thickness of the slide plate. That is, the regular detection thickness of the support slide plate is compared with the wear thickness of the slide plate calculated based on the monitoring data during this period, and a correction coefficient is introduced to calculate the wear thickness of the support slide plate jointly driven by the monitoring and detection data. Based on the wear model formula of the support slide plate, the support sliding distance formula, the formula for the change of the wear coefficient under pressure and sliding speed, and the correction parameter α obtained from the regular detection of the support, a mathematical model for the dynamic wear of the support slide plate is established:

[0027] h plate =αK dwc P bear L bear (t) / H

[0028] Preferably, in step 2, an independent and monotonic inverse Gaussian stochastic process is used to characterize the wear process of the support slide plate. The independent increment property of the stochastic process is applied to the remaining life prediction and reliability modeling of structural components. The inverse Gaussian process is as follows:

[0029] (2.1) At t = 0, the wear thickness h of the support slide plate plate (0) = 0;

[0030] (2.2) h plate (t) is an independent increment process;

[0031] (2.3) The increment Δh plate (t) follows an inverse Gaussian distribution, that is, Δh plate (t) ~ IG(αΔΛ, λΔΛ 2 );

[0032] In the formula, Δh plate (t) = h plate (t + Δt) - h plate (t), ΔΛ = Λ(t + Δt) - Λ(t).

[0033] Therefore, the wear process of the support slide plate can be expressed as h plate (t) ~ IG(αΔΛ(t), λΔΛ(t) 2 ), and its probability density function can be expressed as:

[0034]

[0035] In the formula, α represents the drift parameter, which reflects the change trend of the slide plate wear over time; λ represents the scale parameter; Λ(t) represents the shape function, which is a non - negative right - continuous and monotonically increasing function and Λ(0) = 0.

[0036] Preferably, the wear process of the bearing slide plate is mainly affected by α. Regarding α as a random parameter, modeling is carried out. At the same time, it is assumed that the prior distribution of 1 / α follows a normal distribution. The wear threshold of the bearing slide plate is set as ω, and the service life T of the bearing slide plate is defined as the time when h plate (t) exceeds the wear threshold ω.

[0037] Preferably, when the prediction model of the remaining life of the bearing is modeled as a first passage time based on a stochastic process, it is assumed that there are discrete monitoring time points t1, t2, … t j , and denote H j = [h1, …, h j as the historical bearing slide plate wear data set up to time t j . h j = h plate (t j ) represents the wear amount of the bearing slide plate at time t j . The remaining life R j of the bearing slide plate at the current time t j can be expressed as:

[0038] R j = inf{r j : H(t j + r j ) ≥ ω|H j}

[0039] In the formula, H j represents the historical bearing slide plate wear data set up to time t j ; r j represents the predicted value of the remaining life of the bearing at time t j .

[0040] It can be obtained that under the condition of known H j , the probability density function of the remaining life R j of the bearing at time t j , that is, the remaining life prediction model of the bearing: That is, the remaining life prediction model of the bearing:

[0041]

[0042] In the formula, Φ(·) represents the cumulative distribution function of the standard normal distribution; φ(·) represents the probability density function of the standard normal distribution; μ α represents the mean value of α; σ α represents the standard deviation of α.

[0043] Preferably, according to step 3, for the prediction of the remaining life of the bridge bearing slide plate, there are new discrete monitoring time points t1, t2, …, t i , … t k, the wear data of the bearing slide plate corresponding to each time point is h i = h plate (t i ), i = j + 1, …, k, denote H k = [h1, …, h i , …, h k as the bearing slide plate wear data set up to time t k . Let Δh i = h i - h i-1 be the wear increment of the slide plate from time t i-1 to t i , Δt i = t i - t i-1 . Based on the inverse Gaussian process, the joint distribution of the bearing slide plate wear data set H k under the determination of parameter α is:

[0044]

[0045] To reflect the dynamic update of the prediction model with the wear data, redefine the unknown parameters μ α , λ as μ α,k , λ k . The prior distribution of the random parameter 1 / α follows a normal distribution which is conjugate to the sampling distribution p(H k |α). The posterior distribution of 1 / α under the condition of p(H k |α) is still a normal distribution. Therefore, the posterior distribution of 1 / α is calculated and updated through the following formula:

[0046]

[0047] In the formula, μ 0,k , respectively represent the mean and standard deviation of the posterior distribution of 1 / α.

[0048] Preferably, the random parameter 1 / α according to the parameter contains latent variables and cannot be directly obtained through observation. Instead, the expectation maximization (EM) algorithm is used to estimate the model parameters. The core idea of the EM algorithm is to estimate the latent variable 1 / α according to the conditional expectation of the observed data. The update of the bearing slide plate remaining life prediction model parameters depends on the historical wear data H k obtained at time t k . To reflect the characteristic that the model parameters can be continuously updated through the wear data, represent the model parameters as Assume that the estimated value of the model parameters at the j-th iteration of the EM algorithm If it is considered that the random parameter 1 / α is observed, the corresponding log-likelihood function is expressed as:

[0049]

[0050] At the known time t k the historical wear data H k and the estimated value of the model parameter under the condition, the expectation of the log-likelihood function of the latent variable 1 / α is obtained based on the EM algorithm:

[0051]

[0052] In the maximization step, the expectation obtained in the expectation step is maximized. Let the updated estimated value of the model parameter can be obtained

[0053]

[0054] Based on the formula, the updated formula for the estimated value of the model parameter is obtained, and the prediction model parameter is updated through the support displacement monitoring data obtained in real time for the dynamic prediction of the remaining life of the support slide plate.

[0055] Compared with the prior art, the technical effects and advantages of the present invention: The method for predicting the remaining life of the bridge support slide plate driven by the joint detection data

[0056] 1. The wear model of the support slide plate constructed in the present invention can consider the influence of the support pressure and the slip speed, and establish a quantitative relationship between the wear thickness of the slide plate and the longitudinal displacement of the support.

[0057] 2. The wear model correction method based on the detection data proposed in the present invention can eliminate the influence of the lubrication condition and the low sampling frequency of the sensor, and improve the calculation accuracy of the wear thickness of the slide plate.

[0058] 3. The dynamic prediction method for the remaining life of the support slide plate proposed in the present invention can consider the change of the beam end motion characteristics caused by the traffic volume increase, damper leakage, etc., and provide guidance for the bridge maintenance department to formulate the maintenance and replacement strategy of the support. Brief Description of the Drawings

[0059] Figure 1 is the flow chart of the method of the present invention;

[0060] Figure 2 is the drawing of the wear thickness of the support slide plate of the upstream support of the east tower;

[0061] Figure 3 is the drawing of the wear thickness of the support slide plate of the upstream support of the west tower;

[0062] Figure 4Diagram of the upstream bearings of the east tower for predicting the remaining life of the bearings

[0063] Figure 5 Diagram of the upstream bearings of the west tower for predicting the remaining life of the bearings Specific implementation manner

[0064] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0065] Please refer to Figures 1-5 , the present invention provides a technical solution: a method for predicting the remaining life of the sliding plate of a bridge bearing driven by combined monitoring data, including the following steps:

[0066] S1. Estimation of the wear thickness of the bearing sliding plate: Construct a wear model of the bearing sliding plate considering changes in external conditions. Based on the Archard wear model and combined with the actual situation of the bridge bearing, obtain a wear model expressed by the wear thickness, determine the calculation method of the bearing sliding distance, and construct the functional relationship between the wear coefficient and the bearing pressure and the bearing sliding speed;

[0067] (1.1) Construction of the wear model of the bearing sliding plate. The wear law of the bearing sliding plate will be affected by changes in external conditions. For example, changes in factors such as bearing pressure, sliding speed, and service environment will all affect bearing wear. Therefore, in order to accurately evaluate the wear thickness of the bearing sliding plate and ensure the safe operation of the bridge, the present invention constructs a wear model of the bearing sliding plate that can consider changes in external conditions.

[0068] For a bridge bearing, its sliding function is realized through a friction pair composed of a polytetrafluoroethylene sliding plate and a stainless steel plate. When the polytetrafluoroethylene sliding plate wears, a large amount of debris will be formed. According to different wear mechanisms, it belongs to adhesive wear. The commonly used calculation model for adhesive wear is the Archard wear model. The Archard wear model microscopically assumes that two mutually contacting objects are uneven. When the object is subjected to a normal load, the high micro-protrusions will come into contact first, resulting in local stress concentration. When the stress exceeds the yield strength of the material itself, the micro-protrusions will undergo plastic deformation. The expression formula used in the Archard wear model is:

[0069] V = KWL / H (1)

[0070] In the formula, V represents the volume of the micro-protrusions peeled off during material wear; K represents the wear coefficient; W represents the normal load; L represents the sliding distance; H represents the material hardness.

[0071] Since the products of the wear of the bridge bearing slide plate are mostly flaky and small granular, it is difficult to accurately measure the volume of the wear of the slide plate. In actual engineering, the wear thickness is used as an index to evaluate the wear condition of the bearing slide plate. Therefore, based on formula (1), the wear model of the bearing slide plate can be expressed as:

[0072] V = Ah plate (2)

[0073] W = AP bear (3)

[0074] h plate = KP bear L / H (4)

[0075] In the formula, A represents the contact area between the bearing slide plate and the stainless steel plate; h plate represents the wear thickness of the bearing slide plate, that is, the wear index of the bearing slide plate; P bear represents the pressure exerted by the main beam on the bearing;

[0076] In the bridge health monitoring system, displacement sensors are usually installed at the beam ends to monitor the longitudinal sliding of the bearings. Therefore, the sliding distance L bear (t) of the bearing can be calculated by the following formula:

[0077]

[0078] In the formula, N represents the number of sampling points of the bearing displacement sensor at time t; l n-1 , l n respectively represent the bearing displacement values of the (n - 1)-th sampling point and the n-th sampling point. According to the characteristics of the polytetrafluoroethylene slide plate material, its wear coefficient is affected by the surface pressure and the sliding speed. Relevant experiments show that the wear coefficient of the bearing slide plate is inversely proportional to the surface pressure and directly proportional to the sliding speed. And the changes of the surface pressure and the sliding speed have a great influence on the wear coefficient of the slide plate. Therefore, in this paper, the functional relationship between the wear coefficient and the bearing pressure and the bearing sliding speed is constructed to accurately map the change of the wear coefficient of the bearing slide plate under different surface pressures and sliding speeds, as shown in the following formula: In the formula, K dwc represents the dynamic wear coefficient of the bearing slide plate; v bear (n) represents the sliding speed of the bearing at the n-th sampling point; a, b represent the power exponents; c, d represent the constant coefficients; f beardenotes the sampling frequency of the bearing displacement data; (1.2) Introduce the regular inspection information of the bearing slide plate to correct the calculation of the wear thickness of the slide plate. Use the comparison between the detected thickness and the calculated thickness to introduce a correction coefficient, and establish a mathematical model for the dynamic wear of the bearing slide plate. Based on the correction of the wear model using the detection data, relevant research shows that the sampling frequency of displacement sensors in the bridge health monitoring system is relatively low, and it is impossible to accurately obtain high-frequency displacements caused by vehicle loads and other factors, which affects the calculation accuracy of the wear thickness of the slide plate. At the same time, during the long-term service of bridge bearings, the lubrication conditions of the slide plate and changes in the external environment will also affect the wear law of the bearing slide plate. However, the change information of these external factors cannot be obtained from the monitoring data. Therefore, this study introduces the regular inspection information of the bearing slide plate to correct the calculation of the wear thickness of the slide plate. That is, use the regularly detected thickness of the bearing slide plate to compare with the wear thickness of the slide plate calculated based on the monitoring data during this period, and then introduce a correction coefficient to realize the calculation of the wear thickness of the bearing slide plate jointly driven by the monitoring and detection data. Finally, based on formulas (4)-(7) and the correction parameter α obtained from the regular inspection of the bearing, establish a mathematical model for the dynamic wear of the bearing slide plate: h plate = αK dwc P bear L bear (t) / H (8) S2. Construction of the remaining life prediction model for the bearing slide plate: Use the inverse Gaussian stochastic process to characterize the wear process of the bearing slide plate, define the relevant characteristics of the inverse Gaussian process, set the wear threshold of the bearing slide plate as a specific value, and define the time when the wear threshold is exceeded for the first time as the remaining life of the bearing, and establish a remaining life prediction model for the bearing based on the stochastic process; In the failure analysis of the bearing slide plate, the most crucial thing is to establish a reasonable remaining life prediction model for the slide plate, which should be able to comprehensively consider the influence of various factors on the wear law of the slide plate. And based on the life information implied by the wear data of the bearing slide plate, predict the remaining life of the bearing slide plate. Due to the randomness of the external environment and load acting on the bearing slide plate, the wear process of the bearing slide plate has uncertainty and time variability. If a deterministic function is used to describe the wear process of the bearing slide plate, a large error will occur. Therefore, the present invention uses an inverse Gaussian stochastic process with independence and monotonicity to characterize the wear process of the bearing slide plate. The stochastic process has the property of independent increments and is widely used in the remaining life prediction and reliability modeling of structural components. The inverse Gaussian process is a stochastic process with independent increments and is suitable for modeling structural components with monotonic degradation characteristics. The present invention defines a stochastic process with the following characteristics as the inverse Gaussian process. (2.1) At t = 0, the wear thickness h plate (0) = 0; (2.2) h plate (t) is an independent increment process; (2.3) The increment Δh plate (t) follows an inverse Gaussian distribution, that is, Δh plate (t) ~ IG(αΔΛ, λΔΛ2 ); where, Δh plate (t) = h plate (t + Δt) - h plate (t), ΔΛ = Λ(t + Δt) - Λ(t). Therefore, the wear process of the bearing slide plate can be expressed as h plate (t) ~ IG(αΔΛ(t), λΔΛ(t) 2 ), and its probability density function can be expressed as: Where, α represents the drift parameter, which reflects the change trend of the slide plate wear with time; λ represents the scale parameter; Λ(t) represents the shape function, which is a non - negative right - continuous and monotonically increasing function and Λ(0) = 0. Since the wear process of the bearing slide plate is mainly affected by α, in this study, α is regarded as a random parameter. And for the convenience of subsequent modeling work, the present invention assumes that the prior distribution of 1 / α follows a normal distribution. Set the wear threshold of the bearing slide plate as ω, and the service life T of the bearing slide plate is defined as the time when h plate (t) exceeds the wear threshold ω. The present invention uses the concept of first passage time to define the time when the wear process of the bearing slide plate first exceeds the wear threshold ω as the remaining life of the bearing. Therefore, the modeling of the bearing remaining life prediction model based on the stochastic process can also be called first passage time modeling. Assume that there are discrete monitoring time points t1, t2,... t j , and denote H j = [h1,..., h j as the historical bearing slide plate wear data set up to time t j , h j = h plate (t j ) represents the wear amount of the bearing slide plate at time t j . The remaining life R j of the bearing slide plate at the current time t j can be expressed as:

[0079] R j = inf{r j : H(t j + r j ) ≥ ω|H j} (10)

[0080] Where, H j represents the historical bearing slide plate wear data set up to time t j ; r j represents the predicted value of the bearing remaining life at time t j .

[0081] It can be obtained that under the condition of known H j , the probability density function of the bearing remaining life R j at time t j ​ That is, the remaining life prediction model of the bearing:

[0082]

[0083] In the formula, Φ(·) represents the cumulative distribution function of the standard normal distribution; φ(·) represents the probability density function of the standard normal distribution; μ α represents the mean of α; σ α represents the standard deviation of α.

[0084] S3. Dynamic prediction of the remaining life of the bearing slide plate: Based on the inverse Gaussian process, determine the joint distribution of the bearing slide plate wear data set at the new monitoring time point, update the posterior distribution of the random parameters using Bayesian theory, estimate the model parameters using the Expectation-Maximization (EM) algorithm, and update the prediction model parameters through the displacement monitoring data of the bearing obtained in real time to achieve the dynamic prediction of the remaining life of the bearing slide plate;

[0085] Assume that after predicting the remaining life of the bridge bearing slide plate, there are new discrete monitoring time points t1, t2, …, t i , … t k , and the bearing slide plate wear data corresponding to each time point is h i = h plate (t i ), i = j + 1, …, k. Denote H k = [h1, …, h i , …, h k as the bearing slide plate wear data set up to time t k . Let Δh i = h i - h i-1 be the slide plate wear increment from time t i-1 to t i , and Δt i = t i - t i-1 . Based on the inverse Gaussian process, when the parameter α is determined, the joint distribution of the bearing slide plate wear data set H k is: To reflect the dynamic update of the prediction model with the wear data, redefine the unknown parameters μ α , λ as μ α,k , λ k . As mentioned above, the prior distribution of the random parameter 1 / α follows a normal distribution which is conjugate to the sampling distribution p(H k |α). Based on Bayesian theory, at p(H kThe posterior distribution of 1 / α under the condition of |α) is still a normal distribution. Therefore, the posterior distribution of 1 / α can be updated by the following formula: where μ 0,k , respectively represent the mean and standard deviation of the posterior distribution of 1 / α. Since the parameter 1 / α is a random parameter containing latent variables and cannot be directly obtained through observation, the maximum likelihood estimation method cannot be used. Therefore, the present invention uses the expectation maximization (EM) algorithm to estimate the model parameters. The core idea of the EM algorithm is to estimate the latent variable 1 / α according to the conditional expectation of the observable data, which consists of an expectation step and a maximization step, and the calculation is repeated alternately in two steps until the convergence criterion is reached. The EM algorithm can effectively estimate the model parameters and optimize the log-likelihood function. The update of the remaining life prediction model parameters of the bearing slide plate depends on the historical wear data H k obtained at time t k . To reflect the characteristic that the model parameters can be continuously updated through the wear data, the model parameters are represented as Θ k =(μ α,k , σ α 2 ,k , λ k ). Assume that the estimated value of the model parameters at the j-th iteration of the EM algorithm is If the random parameter 1 / α is considered observable, the corresponding log-likelihood function can be expressed as: Given the historical wear data H k at time t k and the estimated value of the model parameters , the expectation of the log-likelihood function of the latent variable 1 / α is calculated based on the EM algorithm: to obtain the updated estimated value of the model parameters Based on formulas (19)-(21), the prediction model parameters are updated using the real-time obtained bearing displacement monitoring data to achieve the dynamic prediction of the remaining life of the bearing slide plate. In summary, by combining the monitoring and detection data of the bearing slide plate, the method proposed in the present invention realizes the dynamic prediction of the remaining life of the bearing slide plate. This method can reduce the uncertainty of the remaining life prediction of the bearing slide plate and improve the prediction accuracy. The method for dynamically predicting the remaining life of the bearing slide plate of the present invention is divided into three steps: "estimating the wear thickness of the bearing slide plate", "constructing the remaining life prediction model of the bearing slide plate" and "dynamically predicting the remaining life of the bearing slide plate", and the method implementation process is as Figure 1As shown. In a specific numerical example, the monitoring and detection data of the bearings of an in-service suspension bridge in China are used for verification. First, the estimated wear thickness of the sliding plates is calculated based on the displacement monitoring data of the bearings according to step (1.1). Then, according to step (1.2), the wear model of the sliding plates is corrected using the detection data of the wear thickness of the bearing sliding plates, and the wear thickness of the bearing sliding plates at each position is obtained, as Figures 2-3 shown. Finally, the dynamic prediction of the remaining life of the bearing sliding plates is realized according to steps 2 and 3. To verify the effectiveness of the dynamic prediction method for the remaining life of the bearing sliding plates proposed in the present invention, the dynamic prediction results of the remaining life of the sliding plates obtained in the present invention are compared with the wear thickness of the sliding plates. The average wear thickness of the bearing sliding plates calculated in step 1 for 60 days is evenly divided into 6 groups of bearing sliding plate wear data sets. By dynamically updating the prediction model parameters through the bearing sliding plate wear data sets, the prediction results of the remaining life of the sliding plates at the upstream of the west tower and the upstream of the east tower at different prediction times are obtained, as Figures 4-5 shown. It can be seen from the figure that the method proposed in the present invention can update the prediction results according to the changes in data characteristics, and with the increase of the bearing sliding plate wear data sets, the prediction error of the remaining life of the sliding plates tends to be stable, and it is all within 10%. In summary, the dynamic prediction method for the remaining life of the bearing sliding plates driven by the combination of monitoring and detection proposed in this study has a high prediction accuracy, which can provide guidance for the bridge management and maintenance department to formulate the replacement strategy for the bearing sliding plates. Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data, characterized in that: The steps include: S1. Estimation of wear thickness of bearing slide: (1.1) Construct a bearing slide wear model that takes into account changes in external conditions. Based on the Archard wear model and combined with the actual situation of bridge bearings, a wear model expressed in wear thickness is obtained, the calculation method of bearing sliding distance is determined, and the functional relationship between the wear coefficient and bearing pressure and bearing sliding speed is constructed; (1.2) Introduce the periodic inspection information of the support slide to correct the calculation of the slide wear thickness, introduce the correction coefficient by comparing the inspection thickness with the calculated thickness, and establish the mathematical model of the dynamic wear of the support slide; S2. Construction of the prediction model for the remaining life of the bearing slide: The inverse Gaussian random process is used to characterize the wear process of the bearing slide, the relevant characteristics of the inverse Gaussian process are defined, the wear threshold of the bearing slide is set to a specific value, the time when the wear threshold is exceeded for the first time is defined as the remaining life of the bearing, and a prediction model for the remaining life of the bearing based on the random process is established; S3. Dynamic prediction of the remaining life of the bearing slide: Based on the inverse Gaussian process, the joint distribution of the bearing slide wear data set at the new monitoring time point is determined, the posterior distribution of the random parameters is updated using the Bayesian theory, the model parameters are estimated using the expectation maximization algorithm, and the prediction model parameters are updated through the real-time bearing displacement monitoring data to achieve dynamic prediction of the remaining life of the bearing slide.

2. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 1 is characterized by: In step (1.1), the bridge bearing slides by forming a friction pair with a polytetrafluoroethylene plate and a stainless steel plate. When the polytetrafluoroethylene plate is worn, debris is formed, and it is adhesive wear. The adhesive wear calculation model is the Archard wear model. The Archard wear model is that two objects in contact with each other are uneven. When the objects are subjected to normal loads, the high micro-convex bodies will come into contact first, resulting in local stress concentration. When the stress exceeds the yield strength of the bridge bearing material itself, the micro-convex bodies undergo plastic deformation. The Archard wear model formula is expressed as: V=KWL / H Where V represents the volume of micro-convex bodies that fall off when the material wears; K represents the wear coefficient; W represents the normal load; L represents the sliding distance; and H represents the hardness of the material.

3. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 2 is characterized by: The products of the bridge bearing slide after wear are in the form of flakes and small particles, which makes it difficult to accurately measure the volume of the slide wear. The wear thickness is used as an indicator to evaluate the wear condition of the bearing slide, and based on the Archard wear model formula, the wear model of the bearing slide is expressed as: V=Ah plate W=AP bear h plate =KP bear L / H Where A represents the contact area between the support slide and the stainless steel plate; h plate Indicates the wear thickness of the bearing slide, that is, the wear index of the bearing slide; P bear Indicates the pressure exerted by the main beam on the support; In the bridge health monitoring system, displacement sensors are installed at the beam ends to monitor the longitudinal sliding of the bearings and the sliding distance L of the bearings. bear (t) is calculated by the following formula: Where N is the number of sampling points of the support displacement sensor at time t; n-1 , l n They represent the support displacement values ​​of the n-1th sampling point and the nth sampling point respectively.

4. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 2 is characterized by: The characteristics of the polytetrafluoroethylene slide plate are that its wear coefficient is affected by the surface pressure and the sliding speed. The test shows that the wear coefficient of the support slide plate is inversely proportional to the surface pressure and proportional to the sliding speed. The functional relationship between the wear coefficient and the support pressure and the support sliding speed is constructed to map the wear coefficient changes of the support slide plate under different surface pressures and sliding speeds, as shown in the following formula: In the formula, K dwc The dynamic wear coefficient of the bearing slide; v bear (n) represents the sliding velocity of the support at the nth sampling point; a and b represent power exponents; c and d represent constant coefficients; f bear Indicates the support displacement data sampling frequency.

5. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 4 is characterized by: In step (1.2), the wear model correction based on the detection data introduces the periodic detection information of the support slide to correct the calculation of the slide wear thickness, that is, the periodic detection thickness of the support slide is compared with the slide wear thickness calculated based on the monitoring data during the period, and a correction coefficient is introduced to calculate the wear thickness of the support slide driven by the monitoring data. Based on the wear model formula of the support slide, the support sliding distance formula, the wear coefficient change formula under pressure and sliding speed, and the correction parameter α obtained by the periodic detection of the support, a mathematical model of dynamic wear of the support slide is established: h plate =αK dwc P bear L bear (t) / H。 6. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 1 is characterized by: In step 2, an independent, monotonic inverse Gaussian random process is used to characterize the wear process of the bearing slide. The inverse Gaussian process is: (2.1) At t = 0, the wear thickness of the bearing slide h plate (0) = 0; (2.2)h plate (t) is an independent incremental process; (2.3) Increment Δh plate (t) obeys the inverse Gaussian distribution, that is, Δh plate (t)~IG(αΔΛ,λΔΛ 2 ); where Δh plate (t) = h plate (t + Δt) - h plate (t), ΔΛ = Λ(t + Δt) - Λ(t); The wear process of the bearing slide can be expressed as h plate (t)~IG(αΔΛ(t),λΔΛ(t) 2 ), its probability density function is expressed as: Wherein, α is the drift parameter, which is used to reflect the change trend of the slide wear over time; λ is the scale parameter; Λ(t) is the shape function, which is a non-negative right-continuous monotonically increasing function and Λ(0)=0.

7. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 6 is characterized by: The wear process of the bearing slide is mainly affected by α, which is regarded as a random parameter and modeled. At the same time, it is assumed that the prior distribution of 1 / α obeys the normal distribution, the wear threshold of the bearing slide is set to ω, and the service life T of the bearing slide is defined as h plate (t) The time when the wear threshold ω is exceeded.

8. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 7 is characterized by: The residual life prediction model of the bearing based on random process is modeled as the first arrival model, assuming that the bridge bearing has discrete monitoring time points t1, t2, …t during its service life. j , note H j =[h1,…,h j ] is the time t j The historical bearing slide wear dataset, h j =h plate (t j ) represents the time t j The wear amount of the support slide at the current time is t j The remaining life of the support slide is R j It is expressed as: R j =inf{r j :H(t j +r j )≥ω|H j } In the formula, H j Indicates that at time t j Historical bearing slide wear dataset; r j Indicates that at time t j The predicted value of the remaining life of the bearing; It can be concluded that H j Under the condition, at time t j The remaining life of the bearing is R j The probability density function of That is, the remaining life prediction model of the bearing: In the formula, Φ(·) represents the cumulative distribution function of the standard normal distribution; φ(·) represents the probability density function of the standard normal distribution; μ α represents the mean of α; σ α represents the standard deviation of α.

9. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 1 is characterized by: According to step 3, the remaining life of the bridge bearing slide is predicted with new discrete monitoring time points t1, t2, ..., t i ,…t k , the wear data of the support slide corresponding to each time point is h i =h plate (t i ), i=j+1,…,k, record H k =[h1,…,h i ,…,h k ] is the time t k The wear data set of the bearing slide, assuming Δh i =h i -h i-1 is time t i-1 to i The wear increment of the slide plate, Δt i =t i -t i-1 Based on the inverse Gaussian process, the wear data set H of the bearing slide is determined by the parameter α. k The joint distribution of is: The unknown parameter μ α , λ is redefined as μ α,k , λ k , the prior distribution of the random parameter 1 / α follows a normal distribution It is related to the sampling distribution p(H k |α) conjugation, in p(H k |α) is still a normal distribution, and the posterior distribution of 1 / α is updated by the following formula: In the formula, μ 0,k , They represent the mean and standard deviation of the 1 / α posterior distribution respectively.

10. The method for predicting the remaining life of a bridge bearing slide plate driven by monitoring and testing data according to claim 9 is characterized in that: The parameter 1 / α is a random parameter containing hidden variables, and the expectation maximization algorithm is used to estimate the model parameters. The expectation maximization algorithm estimates the hidden variable 1 / α according to the conditional expectation of the observed data. The update of the remaining life prediction model parameters of the support slide depends on the time t k The historical wear data H k , the model parameters are expressed as Assume that the estimated value of the model parameters at the jth iteration of the EM algorithm is If the random parameter 1 / α is considered to be observed, the corresponding log-likelihood function is expressed as: At a known time t k Historical wear data H k and model parameter estimates Under the condition of , the expectation of the log-likelihood function of the latent variable 1 / α is calculated based on the EM algorithm: In the maximization step, the expectation obtained in the expectation step is maximized, and Find the updated model parameter estimates The updated model parameter estimation formula is obtained based on the formula, and the prediction model parameters are updated through the obtained bearing displacement monitoring data to dynamically predict the remaining life of the bearing slide.

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