A concrete dam deformation monitoring method based on OLS-SW

Abstract

The application discloses a kind of concrete dam deformation monitoring methods based on OLS-SW, comprising the following steps: step one, acquisition monitoring data forms training set;Step two, based on the general regression model of general horizontal displacement of concrete dam displacement deformation model is constructed;Step three, for the general regression model of total horizontal displacement, least square method with constraint condition is converted into nonlinear programming problem, to form short-term detection model;Step four, the regression model obtained in step three is applied to sliding window algorithm to realize long-term automatic monitoring.The application can not only realize real-time monitoring, high precision and strong timeliness according to the data in the past to predict the future data situation, and can realize long-term high-precision monitoring purpose.

Description

Technical Field

[0001] The present invention belongs to the technical field of concrete monitoring, and in particular to a concrete dam deformation monitoring method based on OLS-SW. Background Art

[0002] my country, with its vast territory and numerous rivers, holds vast hydropower resources. Dams are among the most important engineering structures for regulating the spatial and temporal distribution of water resources and for their rational redistribution. However, due to insufficient understanding of hydrogeological conditions and dam characteristics, dam construction presents numerous safety risks. Furthermore, over the years of operation, some dams experience degradation of material properties, foundation leakage, and structural deterioration, all of which can easily lead to dam failures. Dam safety monitoring is a crucial tool for mitigating project risks and reducing the likelihood of accidents. While the causes of dam failures vary, the vast majority stem from a failure to accurately and timely assess the actual operational performance of dams and the evolving trends in their safety status. Therefore, dam safety monitoring relies on the accuracy and analysis of monitoring data, which is then used to assess operational performance, issue early warnings and forecasts when necessary, and recommend emergency measures.

[0003] Relying on the long-term operation monitoring data of concrete dams, a model construction study on the deformation prediction of concrete dams is carried out to establish a reasonable model to more objectively reflect the operation status of concrete dams. At present, the more mature concrete dam deformation monitoring models mainly include statistical models, deterministic models and hybrid models. The basic feature of these models is to generalize the influencing factors (independent variables) of the deformation (dependent variable) of any point on the concrete dam at time t into three parts: upstream and downstream water levels (water pressure), temperature and time effect (aging). Therefore, the lateral deformation of the concrete dam δ Y The monitoring model is mainly composed of the water pressure component δ H , temperature component δ T and the time-dependent component δ θ Taking the statistical model as an example, the general expression of the deformation monitoring model is:

[0004] δ Y =δ H +δ T +δ θ

[0005] Currently, mainstream concrete dam deformation monitoring models only provide real-time monitoring. Data prediction is prone to overfitting, resulting in unreliable predictions with poor accuracy and timeliness. Furthermore, during long-term monitoring, the data exhibits errors due to periodic, seasonal, and random characteristics, leading to poor accuracy. Summary of the Invention

[0006] The purpose of the present invention is to provide a concrete dam deformation monitoring method based on OLS-SW, which is used to solve the technical problems of the existing monitoring methods, such as insufficient reliability of prediction results, poor accuracy and timeliness, and poor accuracy of long-term monitoring.

[0007] The OLS-SW-based concrete dam deformation monitoring method comprises the following steps:

[0008] Step 1: Collect monitoring data to form a training set;

[0009] Step 2: construct a general regression model of the total horizontal displacement based on the general model of concrete dam displacement and deformation;

[0010] Step 3: For the general regression model of the total horizontal displacement, the constrained least squares method is transformed into a nonlinear programming problem to form a short-term detection model;

[0011] Step 4: Apply the regression model obtained in step 3 to the sliding window algorithm to achieve long-term automatic monitoring.

[0012] Preferably, in step 1, the monitoring data include horizontal displacement of the earth dam (Y(t)), water temperature (T w (t)), temperature (T n (t)), upstream water level (H 上 (t)) and downstream water level (H 下 (t)), where t represents the time of data collection; based on the first day’s data, calculate the corresponding changes in earth dam horizontal displacement, water temperature, air temperature, upstream water level, and downstream water level relative to the first day’s data: ΔY(t), ΔT w (t), ΔT n (t), ΔH 上 (t) and ΔH 下 (t).

[0013] Preferably, in step 2, taking a number of consecutive days of monitoring as a cycle, the general regression model of the total horizontal displacement is:

[0014] Y t =α1ΔH 上游 +α2ΔH 下游 +β1ΔT w +β2ΔT n +γ1θ+γ2ln(θ)+C,

[0015] Among them, C is a constant term, Y t is the observed displacement, that is, the total horizontal displacement; θ = t / 100, t is the number of days of observation, α i , β i and γ iFor statistical coefficient, i = 1, 2; ΔT w , ΔT n , ΔH 上游 and ΔH 下游 are the change amounts of water temperature, air temperature, upstream water level and downstream water level respectively compared with the corresponding data of the first day of the period.

[0016] Preferably, in the step three, converting the constrained least square method into a nonlinear programming problem specifically includes the following steps:

[0017] (1) constructing an objective function, the least square method requires the error square sum Q to reach a minimum value, the actual measured earth dam transverse displacement is Y i , then:

[0018]

[0019] wherein n is the total number of data in the period;

[0020] (2) constructing inequality constraints, by first and second order derivation on the general model of time-dependent component, the regression model is given a constraint;

[0021] (3) constructing equality constraints, the least square method requires the error square sum Q to reach a minimum to estimate the unknown parameters of the regression model, the partial derivatives of the seven unknown parameters are set to zero as the equality conditions of the nonlinear programming problem.

[0022] Preferably, in the step (2), by first and second order derivation on the general model of time-dependent component, the regression model is given a constraint:

[0023]

[0024] and thus the constraint conditions 1 and 2 are obtained:

[0025]

[0026] wherein, the time-dependent component y t is slowly increasing and greater than or equal to 0, since the first order derivative value is greater than or equal to 0, as long as y t is greater than or equal to 0 at t = 1, there is:

[0027] when t = 1,

[0028] and thus the constraint condition 3 is obtained:

[0029] Preferably, in the step (3), the unknown parameters include alpha1, alpha2, beta1, beta2, gamma1, gamma2 and C, partial derivatives of the seven unknown parameters are calculated respectively, and the partial derivative values are set to zero to obtain a 7-order linear equation set with a unique solution; since the value range of gamma1 and gamma2 is restricted, the result is an empty set;

[0030] Q is respectively taken as the partial derivative of parameters alpha1, alpha2, beta1, beta2 and C, and the corresponding partial derivative values are set to zero as the equality condition of the nonlinear programming problem, and there are:

[0031]

[0032] Wherein, DeltaT wi , DeltaT ni , DeltaH 上游i and DeltaH 下游i respectively represent the water temperature change value, the air temperature change value, the upstream water level change value and the downstream water level change value of the data collected every day in a period compared with the data of the first day of the period, theta i =t i / 100, t i is the cumulative number of days from the first day of the period to the date of data collection, and t i =i.

[0033] Preferably, in the step four, a short-term displacement monitoring regression model is constructed by using the data in the period forming the training set, a sliding window width w is set, the current time is t current , the current window is defined as currentWindow=time(t current -w, t current ), the sliding window is a time interval with a width of w, the left boundary of the sliding window is t l , and the right boundary of the sliding window is t r , t l =t current -w, t r =t current ; the regression model obtained in the step three is applied to the sliding window algorithm to realize long-term automatic monitoring.

[0034] The present application has the following advantages:

[0035] 1. The present application predicts future data conditions according to past data, solves the limitation that the past detection equipment can only monitor in real time and cannot predict data, and can not only monitor in real time with high precision, but also has strong timeliness.

[0036] 2. The present application modifies the popular statistical model, designs an algorithm, solves the least square parameter estimation problem with constraints, and effectively realizes accurate prediction within a certain period.

[0037] 3. The present invention first constructs a short-term earth dam displacement monitoring model, then applies the short-term monitoring model to the sliding window algorithm, dynamically corrects the model parameters, and achieves the purpose of long-term high-precision monitoring.

[0038] 4. The present invention has a wide range of applications. It not only solves the classic problem of the least squares method with constraints, but also avoids the influence of the periodicity, seasonality, and randomness of the data itself on the statistical model, realizes high-precision long-term automatic monitoring, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a concrete dam deformation monitoring method based on OLS-SW of the present invention.

[0040] Figure 2 It is a curve diagram showing the expression of the aging component in the present invention.

[0041] Figure 3 Schematic diagram of the sliding window in the present invention.

[0042] Figure 4 Schematic diagram of the sliding window model of data stream in the present invention. DETAILED DESCRIPTION

[0043] The specific implementation methods of the present invention will be further explained in detail below through the description of embodiments with reference to the accompanying drawings, so as to help those skilled in the art to have a more complete, accurate and in-depth understanding of the inventive concept and technical solution of the present invention.

[0044] The meanings of the parameter symbols in this article are shown in Table 1.

[0045] Table 1: Meaning of the parameters in this article

[0046]

[0047]

[0048] like Figure 1 As shown, the present invention provides a concrete dam deformation monitoring method based on OLS-SW, which includes the following steps.

[0049] Step 1: Collect monitoring data to form a training set.

[0050] Install monitoring equipment, such as Beidou, thermometers and water level gauges, and collect monitoring data at 24:00 every day as a training set, including the horizontal displacement of the earth dam Y(t), water temperature T w (t), temperature T n (t), upstream water level H 上 (t) and downstream water level H 下(t), where t represents the time of data collection; calculate ΔY(t), ΔT w (t), ΔT n (t), ΔH 上 (t), ΔH 下 (t). ΔY(t), ΔT w (t), ΔT n (t), ΔH 上 (t) and ΔH 下 (t) are the change values of the corresponding earth dam horizontal displacement, water temperature, air temperature, upstream water level and downstream water level relative to the first day data.

[0051] Step two, construct a general regression model of the total horizontal displacement based on the general model of concrete dam displacement deformation.

[0052] This embodiment takes monitoring from the first day to the 60th day as a cycle, and the general model of concrete dam displacement deformation is:

[0053] δ Y = δ H + δ T + δ θ .

[0054] Among them, the water pressure deformation caused by water depth change is the water pressure component δ H The general model is:

[0055]

[0056] The temperature deformation caused by temperature change is the temperature component δ T The general model is:

[0057]

[0058] The time-dependent deformation caused by its own structure and material is the time-dependent component δ θ The general model is:

[0059] δ θ = γ1θ + γ2ln(θ).

[0060] Among them, H represents the upstream and downstream water level, ΔH i , i = 1, 2 respectively represent the upstream and downstream water level change values, that is, ΔH1 = ΔH 上游 , ΔH2 = ΔH 下游 ; ΔT i , i = 1, 2 represent two temperatures related to the temperature component δ T , that is, ΔT1 = ΔT w , ΔT2 = ΔT n ; θ = t / 100, t is the number of observation days, and αi , β i and γ i is the statistical coefficient, i = 1, 2. The general regression model of the total horizontal displacement is:

[0061] Y t =α1ΔH 上游 +α2ΔH 下游 +β1ΔT w +β2ΔT n +γ1θ+γ2ln(θ)+C,

[0062] Among them, C is a constant term, Y t is the observed displacement (i.e. the total horizontal displacement).

[0063] Step 3: For the general regression model of the total horizontal displacement, the constrained least squares method (OLS) is transformed into a nonlinear programming problem to form a short-term detection model.

[0064] Converting the constrained least squares method into a nonlinear programming problem specifically includes the following steps.

[0065] (1) Construct the objective function.

[0066] The least squares method requires that the sum of squared errors Q reaches a minimum value. The actual measured lateral displacement of the earth dam is Yi, then:

[0067]

[0068] Wherein n is the total number of data in a period. In this embodiment, one period has 60 days, that is, n=60.

[0069] (2) Construct inequality constraints.

[0070] Time-dependent component δ θ It is the time-dependent deformation caused by the structure and material of the concrete dam itself and is irreversible. Figure 2 As shown, the aging component δ θ It increases or becomes flat over time. According to its physical meaning, by taking the first-order and second-order derivatives of the general model of the time-dependent component, constraints 1 and 2 are given for the regression model:

[0071]

[0072] Among them, the time-sensitive component y t (with the time-dependent component δ θ Same) slowly increases and is greater than or equal to 0. Since the first-order derivative value is greater than or equal to 0, as long as the first day (t = 1) y t Greater than or equal to 0, there are:

[0073] When t=1,

[0074] Then we get constraint 3:

[0075] (3) Construct equality constraints.

[0076] The least squares method requires that the sum of squared errors Q be minimized to estimate the unknown parameters of the regression model, that is, when the unknown parameters α1, α2, β1, β2, γ1, γ2 and C are equal, the Q value is minimized. Taking partial derivatives of these seven unknown parameters and making them zero will result in a 7th-order linear equation system with a unique solution. Since the range of γ1 and γ2 is constrained and not between (-∞, +∞) by default, the result is an empty set. Taking partial derivatives of Q with respect to the parameters α1, α2, β1, β2, C and making the corresponding partial derivatives zero as the equality conditions for the nonlinear programming problem, we have:

[0077]

[0078] Where, ΔT wi , ΔT ni , ΔH 上游i and ΔH 下游i They represent the water temperature change, air temperature change, upstream water level change, and downstream water level change values ​​of the data collected daily during a 60-day cycle compared to the data on the first day of the cycle, respectively. i =t i / 100,t i The cumulative number of days from the first day of the cycle to the day of data collection, t i =i.

[0079] Based on the above constraints, the constrained least squares method is transformed into a nonlinear programming problem, thus forming a short-term monitoring model - a regression model for universal concrete dam deformation monitoring.

[0080] Step 4: Apply the regression model obtained in step 3 to the sliding window algorithm to achieve long-term automatic monitoring.

[0081] like Figure 3 As shown in the figure, a short-term displacement monitoring regression model is constructed with 60 days of training data, and a sliding window (SW) width of w = 5 days is set to slide to achieve long-term automatic monitoring.

[0082] like Figure 4 As shown, in the data stream, let the current time be t current , the sliding window width is w, then the current window is defined as currentWindow=time(t curpent -w,t current). The sliding window is a time interval with a width of w = 5 days. In the sliding window, each t current A new element will arrive at time t current +w leaves the window, which is called expired data. For the convenience of description, the left boundary of the sliding window is t l , the right boundary is t r Obviously, t l =t current -w,t r =t current Applying the regression model to the above sliding window can achieve high-precision long-term automatic monitoring of concrete dams and has broad application prospects.

[0083] The present invention is described above by way of example in conjunction with the accompanying drawings. It is obvious that the specific implementation of the present invention is not limited to the above-mentioned method. As long as various non-substantial improvements are made using the inventive concept and technical solution of the present invention, or the inventive concept and technical solution are directly applied to other occasions without improvement, they are all within the scope of protection of the present invention.

Claims

1. A method for monitoring deformation of concrete dams based on OLS-SW, characterized by: The following steps are involved: Step 1: Collect monitoring data to form a training set; Step 2: construct a general regression model of the total horizontal displacement based on the general model of concrete dam displacement and deformation; Step 3: For the general regression model of the total horizontal displacement, the constrained least squares method is transformed into a nonlinear programming problem to form a short-term detection model; Step 4: Apply the regression model obtained in step 3 to the sliding window algorithm to achieve long-term automatic monitoring; In the step 1, the monitoring data include the horizontal displacement Y(t) of the earth dam, the water temperature T w (t), temperature T n (t), upstream water level H 上 (t) and downstream water level H 下 (t), where t represents the time of data collection; based on the first day’s data, calculate the corresponding changes in earth dam horizontal displacement, water temperature, air temperature, upstream water level, and downstream water level relative to the first day’s data: ΔY(t), ΔT w (t), ΔT n (t), ΔH 上 (t) and ΔH 下 (t); In step 2, taking a number of consecutive days of monitoring as a cycle, the general regression model of the total horizontal displacement is: Y t =α1ΔH 上游 +α2ΔH 下游 +β1ΔT w +β2ΔT n +γ1θ+γ2ln(θ)+C, Among them, C is a constant term, Y t is the observed displacement, that is, the total horizontal displacement; θ = t / 100, t is the number of days of observation, α i , β i and γ i is the statistical coefficient, i = 1, 2; ΔT w , ΔT n , ΔH 上游 and ΔH 下游 are the changes in water temperature, air temperature, upstream water level and downstream water level compared with the corresponding data on the first day of the cycle; In step 3, converting the constrained least squares method into a nonlinear programming problem specifically includes the following steps: (1) Construct the objective function. The least square method requires that the sum of squared errors Q reaches the minimum value. The actual measured lateral displacement of the earth dam is Y i , then: Where n is the total number of data in the cycle; (2) Construct inequality constraints and give constraints to the regression model by taking first-order and second-order derivatives of the general model of the time-effect component: And thus we get constraints 1 and 2: Among them, the time-sensitive component y t Slowly increasing and greater than or equal to 0, since the first-order derivative value is greater than or equal to 0, as long as it is guaranteed that y t Greater than or equal to 0, there are: When t=1, Then we get constraint 3: (3) Constructing the equality constraint condition, the least square method requires that the sum of squared errors Q is minimized to estimate the unknown parameters of the regression model. The unknown parameters include α1, α2, β1, β2, γ1, γ2 and C. The partial derivatives of these seven unknown parameters are calculated to make the partial derivatives zero, and a 7th-order linear equation system is obtained with a unique solution. Due to the constraints on the range of γ1 and γ2, the result is an empty set. Take the partial derivatives of Q with respect to the parameters α1, α2, β1, β2, and C respectively, and make the corresponding partial derivatives zero as the equality conditions of the nonlinear programming problem: Where, ΔT wi , ΔT ni , ΔH 上游i and ΔH 下游i They represent the water temperature change, air temperature change, upstream water level change, and downstream water level change values ​​of the data collected daily in a cycle compared to the first day of the cycle, θ i =t i / 100,t i The cumulative number of days from the first day of the cycle to the day of data collection, t i =i.

2. The method for monitoring deformation of a concrete dam based on OLS-SW according to claim 1, characterized in that: In the fourth step, a short-term displacement monitoring regression model is constructed using the data within the period of the training set, and the sliding window width w is set, and the current time is set to t current , the current window is defined as currentWindow=time(t current -w,t current ), the sliding window is a time interval with a width of w, and the left boundary of the sliding window is t l , the right boundary is t r , there are t l =t current -w,t r =t current ; Apply the regression model obtained in step 3 to the sliding window algorithm to achieve long-term automatic monitoring.

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