Method for filling in missing values in arch dam temperature field monitoring data based on causality and proximity influence

Abstract

This invention relates to a method for interpolating missing values ​​in arch dam temperature field monitoring data based on causal and proximity effects. The method includes: distinguishing between complete temperature time series and temperature time series to be interpolated; determining whether each missing value segment of each temperature time series to be interpolated meets the linear interpolation criteria based on the location and relative change amplitude of the missing value segments; if it meets the criteria, performing linear interpolation; if it does not meet the criteria, establishing a prediction model that considers both causal mechanisms and proximity effects, and performing machine learning interpolation based on a multi-measuring-point stratification standard and a same-layer priority criterion. This invention can achieve efficient and accurate interpolation of missing values ​​in arch dam temperature field monitoring data.

Description

Technical Field

[0001] This invention relates to the field of dam temperature field monitoring, and specifically to a method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects. Background Technology

[0002] Among existing concrete dam displacement monitoring models, the Hydraulic-Seasonal-Time (HST) model is widely used due to its simplicity and convenience, requiring only reservoir water level as the external factor input. However, the periodic harmonic temperature factor in the HST model is actually an idealized description of the air temperature at the dam site, which is difficult to reflect the influence of extreme climate and the differences in temperature evolution patterns in different parts of the high arch dam body. Therefore, using measured temperature data of the dam body to establish a temperature deformation factor is one of the effective methods to improve the interpretability and prediction accuracy of concrete dam displacement monitoring models. However, due to dam monitoring instrument malfunctions or instability of automated monitoring systems, some temperature measurement points have missing data, and the missing values ​​from multiple measurement points often appear in close time periods. Therefore, reasonable interpolation of missing values ​​in the arch dam temperature field monitoring data is very important.

[0003] To interpolate missing values ​​in monitoring data, Wang Bin et al. proposed a Bayesian model weighted average method, Pandif et al. proposed a Kalman filter method, Zhang et al. proposed a recursive formaldehyde least squares method and a maximum likelihood estimation method, Huang Chengzhang et al. proposed a method for interpolating concrete dam deformation monitoring data considering both time and cross-sectional dimensions, and Shao et al. proposed using image processing to directly interpolate missing values ​​from the measured process line. Furthermore, machine learning models integrating artificial intelligence algorithms, such as maximum likelihood estimation (EM), backpropagation neural networks, extreme learning machines (ELM), and random forests (RF), possess powerful nonlinear data mining capabilities and are therefore widely used for interpolating missing values ​​in monitoring data. Essentially, this involves using established machine learning models to predict missing value segments.

[0004] The summary found that current methods for interpolating missing values ​​in monitoring data are mainly for single measuring points. However, there are hundreds or even thousands of temperature measuring points set up on high arch dams. Directly using existing single-point interpolation methods will result in low overall interpolation efficiency, lack of judgment criteria for the interpolation order of multiple measuring points, and failure to fully utilize the proximity influence relationship between temperature time series of multiple measuring points during the interpolation process. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects. This method can achieve efficient and accurate interpolation of missing values ​​in arch dam temperature field monitoring data.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is: a method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects, comprising:

[0007] Distinguish between complete temperature time series and temperature time series to be interpolated;

[0008] Based on the location and relative change amplitude of the missing value segment, determine whether each missing value segment of the temperature time series to be interpolated meets the linear interpolation standard;

[0009] If the conditions are met, linear interpolation is performed; otherwise, a prediction model that takes into account both causal mechanisms and proximity effects is established, and machine learning interpolation is performed based on multi-point hierarchical standards and same-level priority criteria.

[0010] Furthermore, the linear interpolation criterion satisfies either case A or case B; wherein,

[0011] Case A: The missing value segment is a discontinuous missing value, and the number of missing value dates does not exceed the preset number of dates;

[0012] Case B: The missing value segment is a continuous missing value segment, located in the rising or falling segment of a periodic cycle, and the relative change amplitude is less than the preset threshold.

[0013] Furthermore, the formula for calculating the relative change amplitude is as follows:

[0014]

[0015] In the formula, T u and T d The temperature measurements, T, are the first and last temperatures of the continuous missing value segment, respectively. max and T min These are the annual maximum and minimum values ​​for the temperature time series, respectively.

[0016] Furthermore, the multi-point stratification standard is as follows:

[0017] Step SA involves dividing all temperature time series to be interpolated that meet the similarity distance threshold with the complete temperature time series into layers to be interpolated; wherein, the complete temperature time series in this step includes the complete temperature time series before linear interpolation and the complete temperature time series formed by linear interpolation;

[0018] Step SB: After interpolation of the layer to be interpolated is completed by SVM modeling, all temperature time series in the layer to be interpolated become a complete temperature time series; wherein, the neighboring temperature factor, upstream reservoir water level and dam site air temperature are used as modeling factors when the layer to be interpolated is modeled by SVM.

[0019] In step SC, among the remaining temperature time series to be interpolated, those that meet the similarity distance threshold with the complete temperature time series interpolated by the previous interpolation layer are classified as new interpolation layers, and the process returns to step SB until all remaining temperature time series to be interpolated do not meet the similarity distance threshold requirement with the complete temperature time series interpolated by the previous layer.

[0020] Step SD: All remaining temperature time series to be interpolated are taken as the remaining layer; wherein, the temperature time series to be interpolated in the remaining layer shall use at least the upstream reservoir water level and the dam site air temperature as modeling factors when establishing the SVM interpolation prediction model.

[0021] Furthermore, the proximity temperature factor is selected from complete temperature time series that meet a similar distance threshold with the temperature time series to be interpolated.

[0022] Furthermore, in the process of dividing the layers to be interpolated, the similarity distance threshold is larger for later layers.

[0023] Furthermore, the same-level priority criterion is as follows:

[0024] For temperature time series to be interpolated that are divided into the same interpolation layer, the sum of similarity distances between the temperature time series to be interpolated and all complete temperature time series in the previous layer is calculated one by one. The smaller the sum of similarity distances, the higher the interpolation priority of the corresponding measurement point in the same layer.

[0025] Furthermore, the same-level priority criterion also includes:

[0026] For the remaining layers, the similarity distance between each temperature time series to be interpolated and all complete temperature time series is calculated. The smaller the sum of similarity distances, the higher the priority for interpolation in this layer. When the temperature time series interpolated first in this layer and the temperature time series to be interpolated later meet the similarity distance threshold, the former is used as the neighboring temperature factor of the latter. The temperature time series interpolated first in this layer and the temperature time series interpolated later without neighboring temperature factors only use the upstream reservoir water level and the air temperature at the dam site as modeling factors. Other temperature time series use the neighboring temperature factor, the upstream reservoir water level, and the air temperature at the dam site as modeling factors.

[0027] Furthermore, the same-level priority criterion also includes:

[0028] In the same interpolation layer, if the temperature time series that has been interpolated previously meets the similarity distance threshold with the temperature time series that is to be interpolated later, it is used as the neighboring temperature factor of the temperature time series that is to be interpolated later.

[0029] Furthermore, if the total number of neighboring temperature factors exceeds 5, the top 5 with the smallest similarity distance are selected.

[0030] By adopting the above technical solution, this invention uses the location of missing values ​​and the relative change amplitude as the selection criteria for the temperature time series missing value interpolation method, which can reasonably take into account the characteristics of the missing value segment. Compared with the traditional disordered interpolation method, this invention uses multi-measurement point layered interpolation and considers the interpolation priority of the same layer, which can effectively realize the systematic interpolation of the temperature time series of all measurement points in the arch dam temperature field, and considers the influence of the adjacent temperature time series for as many measurement points as possible, making the maximum use of the spatial correlation between multiple measurement points in the arch dam temperature field, thereby realizing efficient and accurate interpolation of missing values ​​of all measurement points in the temperature field, and is easy to implement. Attached Figure Description

[0031] Figure 1 This is a flowchart of the method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects according to the present invention.

[0032] Figure 2 This is a schematic diagram illustrating different missing data scenarios in the temperature time series.

[0033] Figure 3 This is a schematic diagram of the time series correspondence in DTW;

[0034] Figure 4 The measured temperature time series at measuring points T13-155, T13-146, and T13-105;

[0035] Figure 5 Statistical chart of relative variation amplitude of missing values ​​at all measuring points on the dam body;

[0036] Figure 6 The interpolation results for missing temperature time series values ​​in dam section 13 and the priority map of the same layer;

[0037] Figure 7 The process for completing the machine learning interpolation segment of T13-155;

[0038] Figure 8 The temperature time series after T13-155 interpolation;

[0039] Figure 9 This is the temperature time series after T13-146 interpolation;

[0040] Figure 10 This is the temperature time series after T13-105 interpolation. Detailed Implementation

[0041] 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.

[0042] like Figure 1 As shown, a method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects includes:

[0043] Distinguish between complete temperature time series and temperature time series to be interpolated;

[0044] Based on the location and relative change amplitude of the missing value segment, determine whether each missing value segment of the temperature time series to be interpolated meets the linear interpolation standard;

[0045] If the conditions are met, linear interpolation is performed; otherwise, a prediction model that takes into account both causal mechanisms and proximity effects is established, and machine learning interpolation is performed based on multi-point hierarchical standards and same-level priority criteria.

[0046] Data loss in arch dam temperature monitoring data can generally be categorized into two situations: one is the presence of one or more discontinuous measurements with a relatively small number of missing dates within a certain time period; the other is the continuous loss of all measurements within a certain time period. For the first situation, linear interpolation is usually sufficient. Therefore, the selection of the temperature time series interpolation method in this embodiment primarily considers the position of the missing value in the original time series and its relative magnitude of change. The relative magnitude of change is calculated as follows:

[0047]

[0048] In the formula, T u and T d These are the temperature measurements at the beginning and end of the missing value segment, T. max and T min These are the annual maximum and minimum values ​​for the temperature time series, respectively.

[0049] For continuous missing value segments, there are mainly two situations in the measured temperature time series of arch dams: the first situation is that the missing value segment is located at a peak or trough; the second situation is that the missing value segment is located in the rising or falling segment of the annual periodic cycle, such as... Figure 2 As shown.

[0050] In Case 1, the missing value segment is located at the peak or trough. If linear interpolation is used for interpolation, the overall trend will be a single linear upward or downward trend. After the initial stage of water storage operation, the temperature field of the arch dam gradually becomes stable, and the overall evolution law of the peak or trough is parabolic. Linear interpolation will result in a large deviation between the completed temperature time series and the actual situation. Therefore, the embodiment establishes a machine learning model for predictive interpolation. In Case 2, the missing value segment is not at the peak or trough. It is necessary to judge based on the relative change amplitude of the missing value segment: (1) If the relative change amplitude is large, it means that the degree of change of the missing value segment is relatively large compared with the fluctuation of the overall temperature time series. There may be one or more slope changes in the missing value segment, so machine learning interpolation is required; (2) If the relative change amplitude is small, it indicates that the evolution law of the missing value segment is relatively close to that before and after it. Linear interpolation can basically reflect its change law. In addition, for the missing value case of a single date, considering the continuity and stability of the heat conduction of the dam concrete, linear interpolation can be used regardless of its relative amplitude.

[0051] Therefore, the linear interpolation standard in this embodiment can be, but is not limited to, being formulated to satisfy either case A or case B; wherein,

[0052] Case A: The missing value segment is a discontinuous missing value, and the number of missing value dates does not exceed the preset number of dates;

[0053] Case B: The missing value segment is a continuous missing value segment, located in the rising or falling segment of a periodic cycle, and the relative change amplitude is less than the preset threshold.

[0054] Considering the differences in missing values ​​in the temperature time series of multiple measuring points of the arch dam, and to include the neighboring temperature factor in the interpolation prediction model for more measuring points, this embodiment adopts a layered interpolation mode for the multiple measuring points of the dam body. The layered index for multiple measuring points can be defined as follows:

[0055] Step SA involves dividing all temperature time series to be interpolated that meet the similarity distance threshold with the complete temperature time series into layers to be interpolated; wherein, the complete temperature time series in this step includes the complete temperature time series before linear interpolation and the complete temperature time series formed by linear interpolation;

[0056] Step SB: After the interpolation of the layer to be interpolated is completed by SVM modeling, all temperature time series in the layer to be interpolated become complete temperature time series. In the SVM modeling of the layer to be interpolated, the neighboring temperature factor, the upstream reservoir water level and the air temperature at the dam site are used as modeling factors. The neighboring temperature factor is selected from complete temperature time series that meet the similar distance threshold with the temperature time series to be interpolated.

[0057] In step SC, among the remaining temperature time series to be interpolated, those that meet the similarity distance threshold with the complete temperature time series interpolated by the previous interpolation layer are classified as new interpolation layers, and the process returns to step SB until all remaining temperature time series to be interpolated do not meet the similarity distance threshold requirement with the complete temperature time series interpolated by the previous layer.

[0058] Step SD: All remaining temperature time series to be interpolated are taken as the remaining layer; wherein, the temperature time series to be interpolated in the remaining layer shall use at least the upstream reservoir water level and the dam site air temperature as modeling factors when establishing the SVM interpolation prediction model.

[0059] It should be noted that, in order to allow more interpolation measurement points to use the adjacent temperature deformation factor, the similarity distance threshold can be gradually increased when dividing the interpolation layers later in the division sequence.

[0060] For temperature time series to be interpolated within the same interpolation layer, first calculate the sum of similarity distances between each temperature time series and all complete temperature time series in the previous layer. The smaller this value, the higher the overall similarity with the previous layer, and the corresponding measurement points should be interpolated preferentially within the same layer. Based on this, if previously interpolated temperature time series within the same interpolation layer also meet the similarity distance threshold with subsequent temperature time series to be interpolated, they should also be used as neighboring temperature factors for the same layer's temperature time series. This is because, within the same layer, the later the interpolation order of the interpolated sequence, the lower its overall similarity with the temperature time series in the previous layer. Therefore, using the temperature time series with preferential interpolation within the same layer as its input factor helps improve the accuracy of subsequent interpolation.

[0061] For the remaining layers, the similarity distance between each temperature time series to be interpolated and all complete temperature time series is calculated. The smaller the sum of similarity distances, the higher the priority for interpolation in this layer. When the temperature time series interpolated first in this layer and the temperature time series to be interpolated later meet the similarity distance threshold, the former is used as the neighboring temperature factor of the latter. The temperature time series interpolated first in this layer and the temperature time series interpolated later without neighboring temperature factors only use the upstream reservoir water level and the air temperature at the dam site as modeling factors. Other temperature time series use the neighboring temperature factor, the upstream reservoir water level, and the air temperature at the dam site as modeling factors.

[0062] If the total number of neighboring temperature factors exceeds 5, then the top 5 with the smallest similarity distance should be selected. The reason for setting the maximum number of neighboring temperature factors to 5 here is that when the number of modeling factors is greater than 7, the model is prone to ill-conditioned problems, and the model in this embodiment also needs to include two causal factors: upstream reservoir water level and dam site air temperature.

[0063] In this embodiment, SVM is used as the prediction model. SVM regression fitting essentially involves finding an optimal classification surface to separate the two groups of samples, thereby obtaining the optimal training model. For the training set {(x... i ,y i ), i = 1, 2, ..., n (n is the total number of samples), where It contains l input factors, y i If ∈R is the output of the model, then the linear regression model established in the high-dimensional feature space is:

[0064] f(x) = wφ(x) + b

[0065] In the formula, φ(x) is a nonlinear mapping function; w is the weight; and b is a constant.

[0066] To mitigate overfitting, SVM lowers the model training requirements. When the error between the model output and the measured value is less than a threshold ε, the fitting is considered lossless. The defined linearly insensitive loss function L is:

[0067]

[0068] By introducing the Lagrange function, the above regression problem can be further transformed into a coupled optimization problem:

[0069]

[0070] In the formula, K(x) i ,x j )=φ(x i )φ(x j ) is the kernel function; C is the penalty factor; α i ≥0 and It is a Lagrange multiplier.

[0071] Solving for the optimal Lagrange multiplier α = [α1, α2, ..., α], we obtain the optimal Lagrange multiplier α = [α1, α2, ..., α]. i ], Then, the above regression function can be expressed as:

[0072]

[0073] Arch dams are massive, and the temperature evolution patterns obtained from widely spaced measuring points vary significantly. If weakly correlated temperature time series are used as neighboring temperature factors, and a machine learning model is built based on this for interpolation, the prediction results will be highly biased. Therefore, when using machine learning modeling for missing value interpolation, the selected neighboring temperature time series should have strong similarity to the temperature time series to be interpolated, thus ensuring the rationality of the model and the accuracy of the prediction results.

[0074] In this embodiment, Dynamic Time Warping (DTW) is used to calculate the similarity distance between two temperature time series. DTW measures the similarity between two time series according to the principle of minimizing nonlinear distance. Compared to methods such as 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, such as... Figure 3 As shown, 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 changes in ambient temperature within the dam body also exhibit more pronounced differences across different parts. Therefore, using DTW to construct a non-one-to-one correspondence between two temperature time series can better incorporate the influence of the aforementioned local differences on the overall similarity of the temperature time series.

[0075] DTW uses a time warping function that satisfies certain conditions to describe the temporal correspondence between the test sequence and the reference sequence, and then solves for the warping function corresponding to the minimum cumulative distance during the matching process of the two time series. Given two time series Z = (z1, z2, ..., z... n ) and O=(o1,o2,…o m The similarity distance calculation steps based on DTW are as follows:

[0076] (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 .

[0077] (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. h z (t)∈[1:n],v o (t)∈[1:m],t∈[1:k], where, 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 upper left corner to the lower right corner of the matrix must be constructed as twisted curves.

[0078] (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 the following formula.

[0079]

[0080]

[0081] In the formula, m k Let be the total number of points that the k-th twisted curve passes through in the distance matrix D.

[0082] Based on the above-mentioned multi-point stratification criteria and same-level priority criteria, such as Figure 1 As shown, the specific process of the method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects is as follows:

[0083] S1 takes all available temperature time series of the dam body (a total of p) as input and calculates the similarity distance between any two temperature time series using DTW, thus obtaining a p×p similarity distance matrix.

[0084] S2, calculate the relative amplitude of each consecutive missing value segment. Based on the relative amplitude of all missing value segments at each measuring point, and considering both the interpolation workload and accuracy requirements, determine the relative amplitude threshold for machine learning interpolation. In engineering, a commonly used accuracy guarantee rate is 95.00%, therefore, the maximum relative amplitude threshold that can be determined here is 5.00%.

[0085] S3. For each measurement point, select an interpolation method for continuous missing value segments. If the missing value segment is not located at the peak or trough of the temperature time series and the relative change amplitude is less than the threshold, then linear interpolation is used to complete it. If the missing value segment is located at the peak or trough, or although it is not located at the peak or trough, but the relative change amplitude is greater than the threshold, then machine learning interpolation is required. The temperature time series for which all missing value segments have been completed by linear interpolation is also classified as a complete temperature time series.

[0086] S4, divide all temperature time series to be interpolated that meet the similarity distance threshold with the complete temperature time series into layers to be interpolated;

[0087] S5. The upstream reservoir water level and dam site air temperature, two causal factors, and the selected neighboring temperature factors are used as input factors to establish an SVM model. After the SVM model completes the interpolation of the interpolation layer, all temperature time series in the interpolation layer become a complete temperature time series.

[0088] S6. In the remaining temperature time series to be interpolated, those that meet the similarity distance threshold with the complete temperature time series interpolated by the previous interpolation layer are classified as new interpolation layers, and the process returns to step S5 until all remaining temperature time series to be interpolated do not meet the similarity distance threshold requirement with the complete temperature time series interpolated by the previous layer.

[0089] In this process, the temperature time series to be interpolated in each layer is selected from all complete temperature time series prior to the start of interpolation for that layer, choosing neighboring temperature factors. Furthermore, if a previously interpolated temperature time series in the same layer also meets a similarity distance threshold with a subsequent temperature time series to be interpolated, it should also be considered a neighboring temperature factor for that layer's temperature time series. However, the total number of neighboring temperature factors cannot exceed five. If it exceeds five, the five with the smallest similarity distance are selected.

[0090] S7. All remaining temperature time series to be interpolated are treated as the remaining layer. First, the similarity distance between each remaining temperature time series to be interpolated and all complete temperature time series is calculated. Interpolation starts from the temperature time series with the smallest sum of similarity distances. If there is no already interpolated complete temperature time series in this layer that meets the similarity distance threshold, the upstream reservoir water level and dam site air temperature are used as input factors to establish an SVM model. After completion, a complete temperature time series is formed. If there is an already interpolated complete temperature time series in the remaining layer that meets the similarity distance threshold, the latter should be used as its neighboring temperature factor. Together with the upstream reservoir water level and dam site air temperature, it should be used as input factors to establish an SVM model. Similarly, the total number of neighboring temperature factors cannot exceed 5, thereby completing the interpolation of all missing temperature time series segments in the dam body temperature field.

[0091] The technical solutions involved in the above embodiments will be described in detail below with reference to specific examples.

[0092] A certain high arch dam has a maximum height of 305m. Its arch crown beam section currently has 142 usable thermometers, but all measured temperature time series have varying degrees of missing values. This embodiment aims to interpolate the missing values ​​of all measured temperature time series, and details the interpolation process using T13-155, T13-146, and T13-105 as examples. The measured temperature time series process lines are as follows: Figure 4 As shown, based on the stratification results, T13-155 and T13-146 are the measurement points of the fourth and first layers to be interpolated in SVM interpolation, respectively. T13-105 is a measurement point without adjacent temperature factors, therefore the selected measurement point has good representativeness. The upstream reservoir water level and dam site air temperature are measured daily; therefore, when selecting the modeling data period, the continuity of the input and output temperature time series is mainly considered. This study selects the time period where all modeling factors coexist, which can completely reflect the curve's changing trend. The prediction stage is the continuous missing value segment that does not meet the requirements of linear interpolation.

[0093] 1. Selection of interpolation method for missing value segments at single measurement points

[0094] Statistics on the relative change amplitude of all missing values ​​at 142 temperature measuring points on the dam body are as follows: Figure 5 As shown. By Figure 5 It can be seen that the relative change amplitude of most missing value segments is within 5.00%. Therefore, 5.00% can be selected as the dividing threshold between linear interpolation and SVM modeling interpolation. At this point, the workload of SVM modeling interpolation is minimized, and it meets the 95.00% guarantee rate requirement commonly used in engineering. In T13-155, except for the missing value segment from October 5, 2016 to January 3, 2017, which is located at the peak and requires SVM modeling interpolation, the remaining missing value segments can be directly linearly interpolated. In T13-146, there are three segments that require SVM interpolation: the segment from November 5, 2016 to January 3, 2017, which is located at the peak; the rising segment from July 20, 2017 to September 11, 2017; and the segment from November 24, 2017 to July 1, 2018, which is missing more than half a cycle. The relative change amplitude of these two segments is greater than 5.00%. Although the missing value segment of T13-105 from November 5, 2016 to December 31, 2016 is located in the decreasing segment of the annual cycle of the temperature time series, its relative change amplitude of 41.39% is much greater than 5.00%, therefore SVM modeling and interpolation are also required. The other missing value segments meet the requirements of linear interpolation. The statistics of the missing value segments requiring SVM interpolation in T13-155, T13-146, and T13-105 are shown in Table 1.

[0095] Table 1. Statistics of missing value segments requiring SVM imputation in T13-155, T13-146, and T13-105

[0096]

[0097] 2. Layered interpolation and interpolation priority of all measuring points on the dam body

[0098] After calculating the similarity distances between 142 temperature time series using DTW, a similarity distance matrix among all temperature time series can be obtained. To ensure that most temperature time series have a certain number of neighboring temperature time series similar to them, thus facilitating the establishment of the SVM model, this paper normalizes the similarity distance matrix for this arch dam, and uses a fixed similarity distance threshold of 0.005 for each layer. Interpolation sequence analysis was performed on the 142 temperature measurement points, and the results are as follows... Figure 6 As shown. There are a total of 33 linearly interpolable measurement points and 58 SVM interpolation measurement points with adjacent temperature factors. Among them, the interpolation with adjacent temperature factors is carried out in 5 layers, and the number of measurement points decreases as the number of layers increases. There are a total of 51 measurement points in the remaining layers, of which 13 measurement points have adjacent temperature factors and 38 measurement points do not.

[0099] 3. Interpolation process and results

[0100] Taking the T13-155 temperature time series as an example, firstly, the missing value segments except for the missing value segment from October 5, 2016 to January 3, 2017 are linearly interpolated. Then, an SVM model is established to complete the missing value segment from October 5, 2016 to January 3, 2017. The directly input neighboring temperature factors are T13-148 and T13-149. The specific process is as follows: Figure 7 As shown. Through similarity distance analysis, T13-90, which is completed by linear interpolation, is first used as a neighboring temperature factor to complete T13-135. Before completing T13-135, T13-100, T13-89, T13-55, T13-80, T13-120, T13-85, T13-69, T13-39, T13-29, T13-25, and T13-74, which meet the similarity distance threshold, have all been preferentially interpolated in the first layer of SVM interpolation. However, since the total number of neighboring temperature factors should not exceed 5, the neighboring temperature factors used for T13-135 are only T13-90, T13-100, T13-89, T13-55, and T13-80. In the first layer after interpolation, temperature time series that meet the similarity distance threshold with T13-148 in the second layer are searched. Finally, using T13-135, T13-143, T13-146, T13-145, and T13-100 as neighboring input factors, an SVM model is built to interpolate T13-148 in the second layer. This process is repeated until T13-149 in the third layer is interpolated, finally completing the interpolation of T13-155 in the fourth layer.

[0101] Using causal factors and neighboring temperature factors as input factors, SVM modeling was used to impute missing data from November 5, 2016 to January 3, 2017 for T13-155 and three consecutive missing data segments for T13-146. The temperature time series process lines for T13-155 and T13-146 are as follows: Figure 8 and 9 As shown. The results generally conform to the overall evolution of the temperature time series, and are similar to the fluctuations of the preceding and following curves. However, the junction of T13-155 with the original curve in the descending segment is not very smooth, showing a slight abrupt change. This error may be due to the fluctuations in the modeling data segment and the small number of adjacent temperature factors used for T13-155, resulting in subtle differences. The interpolation effect using only the upstream reservoir water level and dam site air temperature as two causal factors showed a significant deviation. This is because the measured process lines of both the upstream reservoir water level and the dam site air temperature exhibit significant fluctuations, especially the dam site air temperature. The SVM model is sensitive to such fluctuations, making it prone to overfitting.

[0102] For the T13-105 temperature time series, the missing values ​​except for the period from November 5, 2016 to December 31, 2016 were first linearly interpolated, and then the missing value segment from November 5, 2016 to December 31, 2016 was modeled and interpolated using SVM. Figure 6 As shown in the stratification results, T13-105 has no neighboring temperature factors within the selected similarity distance threshold range. Therefore, when establishing an SVM interpolation prediction model for it, the input factors are only the dam site air temperature and the upstream reservoir water level. The interpolated temperature time series of T13-105 is as follows: Figure 10 As shown, the missing data from November 5, 2016 to December 31, 2016, after being imputed using SVM modeling, showed a similar evolution pattern to the overall temperature time series, indicating that its overall prediction accuracy was high.

[0103] 4. Quantitative evaluation of interpolation effect

[0104] To effectively evaluate the interpolation effect of temperature time series, this embodiment uses the Person correlation coefficient to characterize it. The Person correlation coefficients of the temperature time series before and after interpolation with the air temperature at the dam site are calculated respectively. If the absolute value of the Person correlation coefficient after interpolation is greater than that before interpolation, it indicates that the interpolation effect is better.

[0105]

[0106] In the formula, and Temperature time series and dam site temperature δ t Their respective average values.

[0107] During the interpolation to the fifth layer T13-150, a total of 25 temperature time series had to be layered and successively subjected to SVM prediction interpolation. This embodiment statistically analyzed the changes in the Person correlation coefficients of the 25 temperature time series before and after interpolation, and the specific statistical results are shown in Table 2. Table 2 shows that among the 25 temperature time series, the absolute values ​​of the Person correlation coefficients increased to varying degrees after interpolation for 21 of them. Among them, the increase for T13-69 reached 165.06%, while a few temperature time series with an increase of less than 100% exhibited strong volatility. This verifies the necessity and rationality of combining causal mechanisms and proximity effects for interpolating missing values ​​in temperature time series.

[0108] Table 2. Absolute values ​​of Person correlation coefficients for temperature time series obtained by interpolation based on causal mechanisms and proximity effects.

[0109]

[0110]

[0111] Comprehensive analysis results show that the method combining linear interpolation and SVM modeling interpolation in this embodiment can effectively complete the interpolation of missing data in the arch dam temperature field monitoring data. Furthermore, the interpolation modeling strategy that combines causal mechanisms and proximity influences can better reflect the evolution of the measured temperature time series at a single measuring point. In addition, when performing hierarchical interpolation according to the criteria constructed in this paper, the influence of the temperature evolution of neighboring measuring points can be considered for as many measuring points as possible, thereby achieving efficient and accurate interpolation of missing data in the arch dam temperature field monitoring data.

[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 interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects, characterized in that, include: Distinguish between complete temperature time series and temperature time series to be interpolated; Based on the location and relative change amplitude of the missing value segment, determine whether each missing value segment of the temperature time series to be interpolated meets the linear interpolation standard; If the conditions are met, linear interpolation is performed; if not, a prediction model that takes into account both causal mechanisms and proximity effects is established, and machine learning interpolation is performed based on multi-point hierarchical standards and same-level priority criteria. The multi-point stratification standard is as follows: Step SA involves dividing all temperature time series to be interpolated that meet the similarity distance threshold with the complete temperature time series into layers to be interpolated; wherein, the complete temperature time series in this step includes the complete temperature time series before linear interpolation and the complete temperature time series formed by linear interpolation; Step SB: After interpolation of the layer to be interpolated is completed by SVM modeling, all temperature time series in the layer to be interpolated become a complete temperature time series; wherein, the neighboring temperature factor, upstream reservoir water level and dam site air temperature are used as modeling factors when the layer to be interpolated is modeled by SVM. In step SC, among the remaining temperature time series to be interpolated, those that meet the similarity distance threshold with the complete temperature time series interpolated by the previous interpolation layer are classified as new interpolation layers, and the process returns to step SB until all remaining temperature time series to be interpolated do not meet the similarity distance threshold requirement with the complete temperature time series interpolated by the previous layer. Step SD: All remaining temperature time series to be interpolated are taken as the remaining layer; wherein, the temperature time series to be interpolated in the remaining layer shall use at least the upstream reservoir water level and the dam site air temperature as modeling factors when establishing the SVM interpolation prediction model. The priority criterion for the same level is: For temperature time series to be interpolated that are divided into the same interpolation layer, the sum of similarity distances between the temperature time series to be interpolated and all complete temperature time series in the previous layer is calculated one by one. The smaller the sum of similarity distances, the higher the interpolation priority of the corresponding measurement point in the same layer.

2. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects as described in claim 1, characterized in that, The linear interpolation criterion satisfies either case A or case B; wherein... Case A: The missing value segment is a discontinuous missing value, and the number of missing value dates does not exceed the preset number of dates; Case B: The missing value segment is a continuous missing value segment, located in the rising or falling segment of a periodic cycle, and the relative change amplitude is less than the preset threshold.

3. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects according to claim 2, characterized in that, The formula for calculating the relative change amplitude is: ； In the formula, and The temperature measurements are taken at the beginning and end of the continuous missing value segment, respectively. and These are the annual maximum and minimum values ​​for the temperature time series, respectively.

4. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects as described in claim 1, characterized in that, In the process of dividing the layers to be interpolated, the similarity distance threshold increases as the layers are further back in the hierarchy.

5. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects according to claim 1, characterized in that, The neighboring temperature factor is selected from complete temperature time series that meet the similar distance threshold with the temperature time series to be interpolated.

6. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects as described in claim 1, characterized in that, The same-level priority criteria also include: For the remaining layers, the similarity distance between each temperature time series to be interpolated and all complete temperature time series is calculated. The smaller the sum of similarity distances, the higher the priority for interpolation in this layer. When the temperature time series interpolated first in this layer meets the similarity distance threshold with the subsequent temperature time series to be interpolated, the temperature time series interpolated first in this layer is used as the neighboring temperature factor of the subsequent temperature time series to be interpolated. The temperature time series interpolated first in this layer and the subsequent interpolated temperature time series without neighboring temperature factors only use the upstream reservoir water level and the dam site air temperature as modeling factors. Other temperature time series in this layer, except for the temperature time series interpolated first and the subsequent interpolated temperature time series without neighboring temperature factors, use the neighboring temperature factor, the upstream reservoir water level, and the dam site air temperature as modeling factors.

7. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects according to claim 1, characterized in that, The same-level priority criteria also include: In the same interpolation layer, if the temperature time series that has been interpolated previously meets the similarity distance threshold with the temperature time series that is to be interpolated later, it is used as the neighboring temperature factor of the temperature time series that is to be interpolated later.

8. The method for interpolating missing values ​​in arch dam temperature field monitoring data based on causality and proximity effects as described in claim 6 or 7, characterized in that, If the total number of neighboring temperature factors exceeds 5, select the top 5 with the smallest similarity distance.

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