Method for predicting confidence interval of displacement of concrete dam by measured temperature

Abstract

The present application relates to a kind of method for predicting concrete dam displacement confidence interval using measured temperature, comprising: from the measured temperature time series of all effective temperature measuring points of dam body, selecting the measured temperature time series with characteristic;Orthogonal test design is carried out to all the measured temperature time series with characteristic, obtain multiple measured temperature factor combinations;Each measured temperature factor combination is combined with water pressure component and time effect component to establish SVM model respectively;Based on the distribution law of the displacement prediction value of multiple SVM models at each time, according to the required guarantee rate, calculate eigenvalue;According to eigenvalue, the displacement prediction confidence interval of concrete dam under the influence of measured temperature load representation uncertainty is obtained.The present application selects the measured temperature time series with characteristic, establishes machine learning model based on SVM orthogonal test sampling, the distribution law of multiple model prediction value under the uncertainty of measured temperature deformation factor is counted, and the prediction result is more in line with the causal mechanism of displacement confidence interval.

Description

Technical Field

[0001] This invention relates to the field of concrete dam safety monitoring, and specifically to a method for predicting the confidence interval of concrete dam displacement using measured temperature. Background Technology

[0002] my country has constructed numerous arch dams, including super-high arch dams, such as the Jinping I Arch Dam, which boasts a maximum height of 305 meters, making it the world's tallest completed concrete arch dam. However, the construction and safety management of high dams still face many significant problems and challenges, making structural health monitoring throughout their entire life cycle indispensable for ensuring their safe operation. Therefore, the primary goal of structural health monitoring should be the establishment of high-precision mathematical monitoring models.

[0003] Among numerous monitoring parameters, displacement is the most direct reflection of the structural behavior of concrete dams. The most classic existing concrete dam displacement monitoring model is the Hydraulic-seasonal-time (HST) model, which uses a three-causal relationship modeling factor of water pressure, periodic temperature, and aging. However, the periodic harmonic temperature factor in the HST model is actually an idealized description of the air temperature at the dam site, making it difficult to reflect the influence of extreme climates and the differences in temperature evolution patterns across different parts of the high concrete dam body. From a mechanical point of view, directly using thermometer measurements of the dam concrete and foundation rock as temperature deformation factors to construct the Hydraulic-temperature-time (HTT) model is the most reasonable approach. However, extracting a small amount of the most representative and effective information from massive temperature monitoring data remains a problem that needs further investigation in current research. High concrete dams have hundreds or even thousands of temperature measurement points. When constructing the temperature deformation factor for arch dam displacement using measured dam temperatures, it is difficult to determine the most reasonable representation form. Therefore, it is necessary to consider the impact of the uncertainty of measured temperature loads on the prediction of high arch dam displacement.

[0004] Furthermore, existing mathematical monitoring models primarily perform deterministic point value predictions under fixed combinations of input factors and determine fixed confidence intervals based on model fitting errors, without considering the uncertainty of input factors or the dynamic changes in the causal relationships of deformation behavior during periodic load cycles. In addition, traditional linear regression (MLR) models treat effect sizes as linear explicit functions of relevant influencing factors, leading to difficulties in further improving prediction accuracy due to interference from nonlinear causal relationships and the correlation of influencing factors. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the defects of the prior art and provide a method for predicting the displacement confidence interval of concrete dams using measured temperature. It selects representative measured temperature time series of dam bodies, establishes a machine learning model of orthogonal experimental sampling based on SVM, statistically analyzes the distribution law of multi-model predicted values ​​under the uncertainty of measured temperature deformation factor, and formulates dynamically changing displacement confidence intervals accordingly. The modeling efficiency is high and the prediction results are more consistent with the causal mechanism of displacement confidence intervals.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is: a method for predicting the confidence interval of concrete dam displacement using measured temperature, comprising:

[0007] Select representative measured temperature time series from all effective temperature measuring points on the dam body;

[0008] Orthogonal experimental design was performed on all characteristic measured temperature time series to obtain multiple combinations of measured temperature factors;

[0009] By combining the measured temperature factors with the water pressure component and the aging component respectively, an SVM model is established to obtain multiple SVM models.

[0010] Based on the distribution pattern of displacement prediction values ​​from multiple SVM models at each time point, the characteristic values ​​are calculated according to the required guarantee rate.

[0011] Based on the aforementioned feature values, the confidence interval for predicting the displacement of concrete dams under the influence of uncertainties in measured temperature loads is obtained.

[0012] Furthermore, the selection of representative measured temperature time series from all effective temperature measuring points on the dam body includes:

[0013] Using the measured temperature time series of all effective temperature measuring points in the dam body as input, the similarity distance between any two measured temperature time series is calculated based on DTW.

[0014] Based on all the aforementioned similarity distances, measured temperature time series that are not representative are discarded.

[0015] Furthermore, the step of eliminating non-characteristic measured temperature time series based on all the aforementioned similarity distances includes:

[0016] All the aforementioned similarity distances are normalized, and a threshold is determined;

[0017] If the normalized similarity distance between two measured temperature time series is less than the threshold, the corresponding measured temperature time series is removed according to the removal rules.

[0018] Furthermore, the exclusion rules include:

[0019] If the similarity distance between the selected measured temperature time series A and at least two other measured temperature time series is less than the threshold, then measured temperature time series A is removed, and the at least two other measured temperature time series are retained.

[0020] If the selected measured temperature time series A has a similarity distance of less than a threshold with only one measured temperature time series B, then if measured temperature time series B is removed in the previous or subsequent periods, then A is retained; otherwise, B is retained. If neither measured temperature time series A nor B can be removed in the previous or subsequent periods, then A is retained and B is removed.

[0021] Furthermore, the proposed threshold includes:

[0022] A quantitative relationship is established between the number of retained measured temperature time series and a threshold. Based on the representativeness of the retained measured temperature time series and the required number of models, the threshold is determined.

[0023] Furthermore, in the case of a concrete gravity dam, the dam body is the dam section where the displacement monitoring point is located; in the case of a concrete arch dam, the dam body is the arch crown beam dam section.

[0024] Furthermore, the feature values ​​include the mean, maximum, and minimum values.

[0025] Furthermore, when determining the confidence intervals for the secondary and tertiary monitoring indicators, the corresponding guarantee rates are 95% and 99%, respectively.

[0026] By adopting the above technical solution, the present invention has the following beneficial effects:

[0027] (1) This invention can extract a small amount of the most representative effective information from massive temperature monitoring data and use it to construct a temperature deformation factor, overcoming the defect that the traditional harmonic function temperature factor is difficult to accurately reflect the temperature deformation effect of high concrete dams.

[0028] (2) The present invention can take into account the uncertainty of causal factors and the dynamic changes of causal relationships during the periodic cycle of load, and replace the traditional static confidence interval with a dynamic confidence interval.

[0029] (3) The present invention uses orthogonal experimental design to combine uncertain measured temperature factors, which can significantly reduce the modeling workload and shorten the modeling time. Attached Figure Description

[0030] Figure 1 This is a flowchart of a method for predicting the confidence interval of concrete dam displacement using measured temperature, according to an embodiment of the present invention.

[0031] Figure 2A schematic diagram illustrating the classification and selection of temperature measuring points for arch crown beam dam sections;

[0032] Figure 3 The variation of the temperature factor retention number with the similarity distance threshold is shown.

[0033] Figure 4 The measured temperature time series of the temperature measurement points with the lowest similarity;

[0034] Figure 5 The distribution pattern of multi-model displacement predictions for the full model group and orthogonal test group on August 8, 2018;

[0035] Figure 6 The distribution patterns of multi-model displacement predictions for the full model group and orthogonal test group as of December 31, 2018;

[0036] Figure 7 The predicted mean values ​​for the full model group and the orthogonal experimental group;

[0037] Figure 8 This represents the minimum predicted value for the full model group and the orthogonal experimental group at a 95% guarantee rate.

[0038] Figure 9 This represents the maximum predicted value for the full model group and the orthogonal experimental group at a 95% guarantee rate.

[0039] Figure 10 An orthogonal experimental model that is closest to the predicted mean at each time point in the prediction phase;

[0040] Figure 11 The number of times the temperature factor is selected during the prediction phase;

[0041] Figure 12 Predicted mean and confidence interval of radial displacement interval for the 23-factor orthogonal test group at PL13-1 measuring point;

[0042] Figure 13 The predicted values ​​and confidence intervals for the radial displacement interval of the HST model at the PL13-1 measuring point are given. Detailed Implementation

[0043] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0044] like Figure 1 As shown, a method for predicting the confidence interval of concrete dam displacement using measured temperature includes:

[0045] S1, Select a representative measured temperature time series from all effective temperature measuring points of the dam body;

[0046] S2, orthogonal experimental design is performed on all characteristic measured temperature time series to obtain multiple combinations of measured temperature factors;

[0047] S3, combine each measured temperature factor combination with water pressure component and aging component to establish SVM model, and obtain multiple SVM models;

[0048] S4. Based on the distribution pattern of displacement prediction values ​​of multiple SVM models at each time point, calculate the characteristic values ​​according to the required guarantee rate.

[0049] S5. Based on the characteristic values, obtain the confidence interval for predicting the displacement of the concrete dam under the uncertainty of the measured temperature load.

[0050] The original temperature time series contain a large number of temperature time series with certain similarities. If we do not remove those with excessive similarity and directly conduct orthogonal experimental design on all temperature time series, the resulting single measured temperature factor combination will contain multiple temperature time series with basically repeated functions. This will cause the temperature time series combination obtained by the orthogonal experimental design to not have the best characterization ability, and the constructed part of the model will be invalid. The displacement distribution law obtained from this will also be incorrect.

[0051] Theoretically, the distribution of displacement predictions from multiple SVM models at various time points should conform to a normal distribution. Therefore, we consider selecting their normal distribution characteristic values, namely the mean, maximum, and minimum values. According to dam safety monitoring theory, the confidence intervals corresponding to the secondary and tertiary monitoring indicators are determined with corresponding guarantee rates of 95% and 99%, respectively.

[0052] In this embodiment, S1 specifically includes:

[0053] S11, take the measured temperature time series (a total of p) of all effective temperature measuring points in the dam body as input, calculate the similarity distance between any two measured temperature time series based on DTW, and obtain a p×p similarity distance matrix;

[0054] Based on DTW calculation, any two temperature time series Z = (z1, z2, ..., z...) can be calculated. n ) and O=(o1,o2,…o m The similarity distance between them can be determined by the following steps:

[0055] (1) Construct an n×m distance matrix D, where the element at (i,j) is the sequence value z. i and o j The squared distance d(z) between i ,o j )=(z i -o j ) 2 ;

[0056] (2) The goal of DTW is to find the optimal path from the top left corner to the bottom right corner in the distance matrix D, such that the sum of the values ​​of the elements traversed is minimized. To achieve this, k twisted curves must first be constructed. in, h is composed of a series of points in matrix D. z (t) and v o (t) represents the row number and column number, respectively. When constructing a twisted curve, the row number and column number of two adjacent points can be increased by 1 simultaneously or individually. According to this rule, all possible routes from the top left corner to the bottom right corner of the matrix must be constructed as twisted curves.

[0057] (3) Each draft Then, the cumulative distance between the two time series can be calculated. And finally find an optimal twist curve that minimizes the cumulative distance, as shown in equations (1) and (2);

[0058]

[0059]

[0060] In the formula, m k Let be the total number of points traversed by the k-th twisted curve in the distance matrix D;

[0061] Compared to methods like Euclidean distance that require establishing a one-to-one correspondence, the biggest advantage of DTW is that it can establish one-to-many or many-to-one matching relationships, thereby minimizing the total distance between the two. High arch dams are massive in volume, and the lag effect of air temperature and upstream reservoir water temperature on the dam's temperature field is exceptionally complex. The lag and attenuation phenomena of temperature changes within the dam body vary significantly across different parts. Therefore, using DTW to construct a non-one-to-one correspondence between two temperature time series can effectively incorporate the impact of these local differences on the overall similarity of the temperature time series.

[0062] S12, Based on the similarity distance matrix, remove measured temperature time series that are not representative.

[0063] In this embodiment, S12 specifically includes:

[0064] S121, normalize the similarity distance matrix and determine thresholds in stages between 0 and 1;

[0065] S122, if the normalized similarity distance between two measured temperature time series is less than the threshold, the corresponding measured temperature time series is removed according to the removal rules.

[0066] The rejection rules include:

[0067] If the similarity distance between the selected measured temperature time series A and at least two other measured temperature time series is less than the threshold, then measured temperature time series A is removed, and the at least two other measured temperature time series are retained.

[0068] If the selected measured temperature time series A has a similarity distance of less than a threshold with only one measured temperature time series B, then if measured temperature time series B is removed in the previous or subsequent periods, then A is retained; otherwise, B is retained. If neither measured temperature time series A nor B can be removed in the previous or subsequent periods, then A is retained and B is removed.

[0069] This elimination rule ensures that nothing is missed, and also prevents the deletion of unintended factors. For example, if we consider the measured temperature time series A to be iterative, directly deleting B and C, whose similarity distance to A is less than the threshold, could lead to incorrect deletions. This is because A, B, and C are similar, and it's reasonable to assume that deleting any two of them would be acceptable. However, since B and C haven't been iterated over yet, their importance to other factors cannot be determined. Therefore, A should be deleted first.

[0070] In this embodiment, the proposed threshold includes:

[0071] A quantitative relationship is established between the number of retained measured temperature time series and a threshold. Based on the representativeness of the retained measured temperature time series and the required number of models, the threshold is determined. The retained measured temperature time series are then considered optimal.

[0072] In this embodiment, when the concrete dam is a concrete gravity dam, the dam body is the dam section where the displacement monitoring point is located.

[0073] For concrete arch dams, the measured temperature field of the arch-capped beam dam section is the most representative. Therefore, in the case of a concrete arch dam, the dam body described is the arch-capped beam dam section.

[0074] An effective temperature measurement point refers to a measurement point whose measured temperature time series has good integrity, and whose few missing values ​​can be filled in by conventional simple interpolation methods.

[0075] The technical solutions involved in the above embodiments will be described below with reference to an optional embodiment.

[0076] A 305m high concrete double-curvature arch dam, located in Liangshan Prefecture, Sichuan Province, is the world's highest existing arch dam. In November 2013, the joints were grouted to an elevation of 1885m at the dam crest. In August of the following year, water was impounded to the normal water level of 1880m. Subsequently, the upstream reservoir water level cyclically fluctuated between the dead water level of 1800m and the normal impoundment level of 1880m. Downstream, a second dam was constructed, and the reservoir water level remained at 1645m for an extended period.

[0077] This study takes the PL13-1 temperature measuring point on the crest of the arched beam dam as an example to establish an interval prediction model for its radial displacement under uncertain measured temperature load. Temperature measuring points in the arched beam dam section are the most representative and are typically used to characterize the measured temperature field of arch dams. The No. 13 arched beam section of this dam contains 140 usable temperature measuring points. The monitoring data used in this study covers the period from September 1, 2015 to December 31, 2018. With May 28, 2018 as the dividing line, the first 1000 sets of data were used for model training, and the last 218 sets were used for model prediction performance testing.

[0078] (1) Optimization of dam body measured temperature factor based on DTW

[0079] A total of 140 measured temperature factors are available. This large number of factors would require a huge computational workload for direct modeling. Therefore, the first step is to calculate the pairwise time series similarity between each of the 140 measured temperature factors using Time-of-Warping (DTW). Factors with excessively high similarity are then eliminated, thereby reducing the factor size and improving computational efficiency, especially for the full model group without replacement sampling. Based on the shape characteristics of the measured temperature time series and the hysteresis mechanism of the dam's temperature field evolution, the 140 embedded temperature measuring points can be divided into six categories, such as... Figure 2 As shown. Therefore, when reducing the modeling factor based on DTW similarity distance, the shape partitioning of the measured temperature field of the dam body should also be taken into account.

[0080] By calculating the similarity distance between 140 temperature factors using DTW, it can be found that... Figure 2 The temperature time series within the same category, as shown, exhibit relatively small similarity distances due to their generally consistent fluctuation patterns. This is especially true for the second and third categories, whose evolution patterns largely conform to periodic harmonic factors. In contrast, the similarity distances between temperature measurement points in the fourth category are significantly larger. This is because the measured temperature evolution patterns in the dam area where the fourth category measurement points are located are the most complex. The variation of the temperature factor retention number with the similarity distance threshold is as follows: Figure 3 As shown in Table 1, under the premise of ensuring that each category has a measured temperature factor selected, in order to minimize the number of retained temperature factors, the proposed similarity distance threshold is 0.0041, and the number of retained temperature factors is 23.

[0081] Table 1. Temperature measuring points of the minimum similarity dam body selected by DTW

[0082]

[0083] The locations of the 23 selected temperature measuring points on the dam body are as follows: Figure 2 As shown, the measured temperature process lines at the measuring points are mainly located at the upstream and downstream boundaries of the dam body, especially in areas significantly affected by reservoir water level changes. Figure 4 As shown. From Figure 4 It can be seen from this:

[0084] 1. The measured temperature time series of the first type of temperature measuring points generally showed a downward trend, with T13-5, T13-10 and T13-43 showing rapid decline, steady decline and fluctuating decline, respectively;

[0085] 2. The measured temperature evolution patterns of the second and third types of temperature measuring points are basically consistent with the patterns shown by the annual periodic harmonic factor. The annual temperature variation has been significantly weakened relative to the air temperature. However, the annual variation of the second type is significantly smaller than that of the third type. Therefore, only T13-136 and T13-53 are retained in these two types of temperature measuring points, respectively.

[0086] 3. The fourth type of temperature measuring points are greatly affected by the rise and fall of the reservoir water level. This is mainly because the water level of the upstream reservoir of the arch dam is low during the annual temperature rise phase of the air temperature cycle, so the dam body heats up faster. As a result, the different temperature time series of the fourth type of temperature measuring points are similar in the whole but have large differences in details. Therefore, more measuring points were retained.

[0087] 4. The fifth type of temperature measuring points are located on the downstream face and top of the dam, which are directly affected by solar radiation. The three measuring points selected on the downstream face of the dam are located at different elevations. The reason is that the lower the elevation, the more obvious the shading effect of the canyon slope on the dam at this point, which causes slight differences in temperature along the elevation of the downstream face of the dam.

[0088] 5. The selected sixth type of temperature measuring points are relatively evenly distributed in the three sub-regions of the sixth zone of the dam body temperature field.

[0089] In summary, after DTW similarity distance calculation, according to the minimum similarity elimination rule of temperature time series proposed in this invention, the temperature factors that are finally retained can reflect the evolution law of the measured temperature field of the arch dam, and the degree of aggregation is low, which can maximize the characterization ability of the measured temperature deformation factor and the efficiency of modeling.

[0090] (2) Construction of modeling factors in the prediction model

[0091] The HTT model used for causal explanation and prediction of displacement in high arch dams includes a water pressure component δ. H The temperature component δ, characterized by measured temperature T and time-dependent component δ θ Its mathematical expression is as follows:

[0092]

[0093] In the formula, H is the upstream reservoir water depth on that day; T j The measured temperature value of the j-th dam body temperature measuring point obtained after DTW similarity analysis is given on the current day, where N is the total number of selected temperature measuring points; θ = t / 100, where t is the cumulative number of days from the displacement monitoring day to the starting monitoring day; a i bj c1 and c2 are the fitting coefficients.

[0094] (3) Displacement interval prediction model

[0095] In the HTT model, the uncertainties of the water pressure component and the time-aging component are not considered. Therefore, each model includes the four water pressure factors and two time-aging factors shown in Equation (1). The 23 measured temperature factors selected are used to account for their uncertainties through sampling without replacement and orthogonal experimental sampling. For the full model group with sampling without replacement, the number of SVM models to be established is 2. 23 =8388608; Table 2 shows the 23-factor, 2-level orthogonal experimental design for 23 measured temperature factors. A total of 32 SVM models need to be established, which is far fewer than the full model group. Regarding modeling time, the full model group with 23 factors takes approximately 65 hours to run using MATLAB quad-core parallel computation, while the orthogonal experimental group with 23 factors only takes about 2 seconds using MATLAB conventional computation, significantly reducing modeling time. Therefore, the prediction results of the two need to be compared to verify the rationality of the orthogonal experimental design. Furthermore, to verify the necessity of selecting the minimum similarity temperature factor, an orthogonal experimental group with 140 factors was also set up, corresponding to 148 models.

[0096] Table 2.23 Orthogonal Experimental Design Table for Temperature Factor 32 (2 23 )

[0097]

[0098] Note: In the table, "1" and "0" represent selecting and not selecting the factor, respectively; L q (t) p In the orthogonal array, q represents the total number of rows (i.e., the number of combinations), p represents the number of factors, and t represents the level of each factor.

[0099] After establishing a specified number of SVM models for both the full model group and the orthogonal experimental design group, statistical analysis of the predicted values ​​from multiple models revealed that the distribution of predicted displacements at each time point conformed to a normal distribution. The results obtained by randomly selecting two time points during the prediction phase are shown below. Figure 5 and Figure 6 As shown, the distribution pattern at other times is similar. From Figure 5 and Figure 6It can be seen that the displacement distribution patterns and means obtained by the full model group with 23 factors and the orthogonal experimental design group are basically consistent, thus verifying the rationality of the factor combination used in the latter. However, the number of models in the latter is much less than that in the former, so there is a slight difference in frequency between the two. The probability density of the mean in the 23-factor orthogonal experimental group is slightly less than that in the full model group. However, without minimum similarity optimization of the measured temperature factors, since the initial 140 temperature factors contain a large number of similar factors, the 148 models built according to the orthogonal experimental design are not representative. They show significant deviations from the full model group with 23 factors and the orthogonal experimental design group in terms of displacement prediction mean and distribution range. The displacement prediction range is significantly increased. The reason for this is that the number of models is too small and does not reflect the optimal combination of input factors.

[0100] To further verify the rationality of using orthogonal experimental design for the minimum similarity temperature factor, the predicted mean values ​​at each time point and the minimum and maximum values ​​at a 95% guarantee rate for the full model group and orthogonal experimental design group of the 23 factors in the prediction stage are as follows: Figures 7 to 9 As shown in the figure. A comparison reveals that the characteristic values ​​obtained by the two methods at various times are basically consistent with each other, with small deviations. The maximum deviation of the predicted mean is 0.066 mm, only 0.52% of the predicted mean of the entire model group at that time. Larger deviations mainly occur during the brief period when the reservoir water level drops to the dead water level of 1800 m and during periods of sudden changes in reservoir water level. This is because sudden changes in reservoir water level directly lead to sudden changes in the boundary of the dam's temperature field, causing short-term fluctuations in the measured temperature process line. The orthogonal experimental group, due to its very small number of models, cannot reflect this subtle influence. Overall, the orthogonal experimental group can reflect the results of the entire model group and can be used to construct the displacement prediction interval.

[0101] By comparing each of the 218 predicted displacement values ​​from the 32 models in the orthogonal experimental group with its predicted mean, the model that best matches the predicted displacement mean at each time step can be identified. Figure 10 As shown, it is evident that the closest model differs at different times, meaning the optimal temperature factor is not entirely the same at each time. This indicates that the causal relationship of the temperature deformation effect of high arch dams during periodic load cycles is dynamically changing. This is also the initial intention behind using different combinations of measured temperature factors to construct the displacement interval prediction model in this embodiment. Figure 11 It can be observed that among the 218 predicted values, the number of times each temperature factor was selected ranged between 79 and 166. Among these, T13-102, T13-114, and T13-41 were selected significantly more frequently than other temperature factors. Combined with... Figure 2 It can be seen that these three temperature measuring points are located on the upstream face of the dam body, the middle of the dam body, and the downstream face of the dam body, respectively, near the dead water level of 1800m. They are the most representative of the reservoir water temperature boundary and air temperature boundary of the dam body, and are therefore more suitable for showing the overall evolution law of the measured temperature load on the dam body.

[0102] (4) Comparative analysis with the traditional HST model

[0103] In the field of dam safety monitoring, the fitting and prediction accuracy of a model is mainly measured by the root mean square error (RMSE), maximum absolute error (ME), and multiple correlation coefficient (R2). The smaller the first two and the larger the latter, the higher the model accuracy.

[0104]

[0105]

[0106]

[0107] In the formula, and These represent the fitted (predicted) values ​​for the fitted (predicted) period, respectively. and monitoring value δ t The average values ​​of each; n is the number of samples within the fitting (prediction) period.

[0108] Table 3 shows the statistical results of model performance evaluation during the prediction phase. For the 23-factor full model group and orthogonal experimental group, the predicted mean was used as the calculation basis, while the HST model adopted a stepwise regression modeling method. A comparison in Table 3 reveals that the RMSE and R² of the 23-factor orthogonal experimental group and the full model group are the same. However, the ME of the former is significantly higher than that of the full model group and the HST model. Furthermore, the predicted RMSE of the HST model is significantly lower than that of the interval prediction model. This is because the latter is calculated using the mean, not the prediction result of a single model under the optimal combination of input factors.

[0109] Table 3. Performance Evaluation Indicators of the Prediction Phase

[0110]

[0111] To account for the impact of various uncertainties on displacement diagnosis results, traditional methods, when formulating confidence intervals based on mathematical monitoring models, add or subtract a fixed multiple of the model standard deviation on both sides of the predicted value. For example, with a guarantee rate of 95%, a 2S confidence interval can be formed (actually 1.96S, where S is the RMSE during the modeling stage). The displacement prediction values ​​and confidence intervals obtained by the method in this embodiment and the HST model are as follows... Figure 12 and Figure 13 As shown. Comparison Figure 12 and Figure 13It can be observed that the predicted values ​​obtained by both models are quite close to the monitored values. The displacement confidence interval obtained by the method of this invention varies in size at different times, and is in a dynamic process of change. In contrast, the displacement confidence interval established by the traditional method for the HST model is static and does not consider the dynamic changes in causal relationships during the periodic cycle of the load. This is one of the reasons why this invention establishes a displacement interval prediction model under uncertain measured temperature load. The traditional HST model predicts fixed values, and the manually added confidence interval is obtained from a statistical perspective based on the model fitting error, without a strict causal mechanism. The method in this embodiment is used to predict displacement confidence intervals, tracing the root cause of displacement uncertainty and having a clear causal mechanism. Therefore, the traditional HST model is not suitable for this embodiment.

[0112] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1.A method for predicting a displacement confidence interval of a concrete dam using measured temperature, comprising: selecting characteristic measured temperature time series from measured temperature time series of all effective temperature measuring points of a dam body; performing orthogonal test design on all characteristic measured temperature time series to obtain a plurality of measured temperature factor combinations; establishing a plurality of SVM models by combining each measured temperature factor combination with a water pressure component and an aging component; calculating characteristic values including mean value, maximum value and minimum value based on normal distribution of displacement prediction values of the plurality of SVM models at each time according to a required assurance rate; and obtaining a displacement prediction confidence interval of the concrete dam under the influence of characteristic measured temperature load uncertainty according to the characteristic values. 2.The method according to claim 1, wherein the step of eliminating non-characteristic measured temperature time series based on all the similarity distances comprises: normalizing all the similarity distances and setting a threshold value; and eliminating a corresponding measured temperature time series according to an elimination rule if the normalized similarity distance between two measured temperature time series is less than the threshold value. 3.The method according to claim 2, wherein the elimination rule comprises: if the similarity distance between the selected measured temperature time series A and at least two measured temperature time series is less than the threshold value, eliminating the measured temperature time series A and retaining the at least two measured temperature time series; if the similarity distance between the selected measured temperature time series A and only one measured temperature time series B is less than the threshold value, retaining A if measured temperature time series B is eliminated in the previous or subsequent step, retaining B otherwise, retaining A and eliminating B if both A and B cannot be eliminated in the previous or subsequent step. 4.The method according to claim 2, wherein the step of setting a threshold value comprises: establishing a quantitative relationship between the number of retained measured temperature time series and the threshold value, and setting the threshold value based on the representativeness of the retained measured temperature time series and the required number of modeling. 5.The method according to claim 1, wherein in the case of a concrete gravity dam, the dam body is a dam section where displacement monitoring points are located; and in the case of a concrete arch dam, the dam body is a crown beam section. 6.The method according to claim 1, wherein ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ When determining the confidence intervals for the secondary and tertiary monitoring indicators, the corresponding guarantee rates are 95% and 99%, respectively.

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