Causal prediction method for temperature field of high arch dam considering hysteresis effect mechanism

Abstract

The present application relates to a kind of high arch dam temperature field causal prediction method considering hysteresis influence mechanism, make full use of dam mass temperature monitoring data, based on cosine similarity theory and Shapley method, the causal action law of dam site air temperature and reservoir water level to arch dam temperature field evolution is mined, quantifies lag time, according to this, arch dam temperature field is zoned, and modeling factor is optimally selected in zone, finally, the causal type prediction model of arch dam temperature field is established in combination with NARX neural network, temperature field is predicted, the present application considers hysteresis influence mechanism from two angles of modeling factor and modeling method, to realize accurate prediction to high arch dam measured temperature field.

Description

Technical Field

[0001] This invention relates to the field of dam temperature prediction, and more specifically to a causal prediction method for the temperature field of high arch dams that considers the mechanism of hysteresis. Background Technology

[0002] Structural health monitoring plays a crucial role in ensuring the safe operation of arch dams. A key technology required is the establishment of data-driven mathematical monitoring models to provide causal explanations and predictive diagnoses of the dam's operational behavior. Among all monitored effects on arch dams, dam displacement, especially the displacement of the arch crown beam, comprehensively reflects the overall deformation behavior of the dam and has therefore received widespread attention. For concrete dam displacement, the commonly used causal data monitoring model is the HST (Hydraulic, Seasonal and Time) model, which includes water pressure, temperature, and time-dependent components. It uses periodic harmonic functions to characterize the temperature deformation effect of the concrete dam, essentially providing an idealized description of the air temperature at the dam site, which largely conforms to the actual conditions of most arch dams. However, with the increase in dam height and the implementation of insulation measures in frigid regions, the lag effect of reservoir depth and reservoir operation on the temperature field of concrete dams will become more complex. The differences in the lag and attenuation phenomena of the dam body with changes in ambient temperature in different parts will also become more prominent, even deviating significantly from the commonly used harmonic factor type. Consequently, the periodic harmonic factor type temperature component in the HST model cannot accurately reflect the temperature deformation effect of ultra-high arch dams.

[0003] From a mechanical perspective, using measured dam body temperature to construct temperature components is the most reasonable way to simulate the temperature deformation effect of arch dams. This not only effectively overcomes the defects of harmonic factors in the HST model but is also an effective method to improve the interpretability and prediction accuracy of concrete dam deformation monitoring models. However, when using a mathematical model established with measured dam body temperature as an input factor for predicting future displacement of arch dams, an unavoidable problem arises: dam body temperature and displacement are both unknowns, thus requiring the prediction of the dam body's temperature field first. Furthermore, factors such as concrete cracking and seepage, and aging of the insulation layer can lead to anomalies in the dam body's temperature field. If abnormal temperature monitoring data is directly used to predict arch dam displacement, the abnormal signs of dam body displacement may be concealed. Therefore, anomaly diagnosis of the dam body's temperature field based on the prediction results is also necessary. For this reason, it is necessary to predict the dam body's temperature field based on initial influencing factors such as dam site air temperature and reservoir water level. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a causal prediction method for the temperature field of high arch dams that considers the lag effect mechanism. The lag effect mechanism is considered from the perspectives of modeling factors and modeling methods, so as to accurately predict the measured temperature field of high arch dams.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is: a causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism, the method comprising:

[0006] Using an annual cycle as the upper limit, the sliding matching method is employed to calculate the maximum cosine similarity between the measured temperature time series at each measuring point on the dam body and the temperature and water level time series at the dam site and upstream reservoir, respectively. During the sliding process, the position of the maximum cosine similarity value of temperature is the optimal lag time for temperature, and the position of the maximum cosine similarity value of reservoir water level is the optimal lag time for reservoir water level.

[0007] Based on the maximum cosine similarity of air temperature and reservoir water level at each measuring point, all effective temperature measuring points on the dam body are divided into air temperature-determining areas, air temperature and reservoir water level jointly affected areas, and trend change areas.

[0008] For each measuring point within the temperature-determining zone, modeling factors are selected within the dam site temperature time series based on the optimal temperature lag time. For each measuring point within the zone jointly influenced by temperature and reservoir water level, modeling factors are selected within the dam site temperature and upstream reservoir water level time series based on the optimal temperature lag time and the optimal reservoir water level lag time, respectively.

[0009] For each measuring point in the temperature-determining zone and the zone jointly affected by temperature and reservoir water level, a high arch dam temperature prediction model based on NARX neural network is established based on its respective modeling factors to predict the temperature; for each measuring point in the trend-changing zone, multiple linear regression is used to model and predict the temperature with τ and lnτ as modeling factors, where τ is the cumulative number of days since the initial monitoring day.

[0010] By combining the predicted values ​​from all measuring points, the predicted temperature field of a high arch dam, characterized by typical measuring points, can be obtained.

[0011] Furthermore, based on the maximum cosine similarity of air temperature and reservoir water level at each measuring point, all effective temperature measuring points on the dam body are divided into an air temperature-determining zone, an area jointly influenced by air temperature and reservoir water level, and a trend-changing zone, including:

[0012] Draft similarity thresholds for air temperature and reservoir water level;

[0013] Based on whether the maximum cosine similarity of air temperature is greater than the air temperature similarity threshold and whether the maximum cosine similarity of reservoir water level is greater than the reservoir water level similarity threshold, all effective temperature measuring points on the dam body are divided into air temperature-determining areas, air temperature and reservoir water level jointly affected areas, and trend change areas.

[0014] Furthermore, the proposed temperature similarity threshold and reservoir water level similarity threshold include:

[0015] The maximum cosine similarity of air temperature and maximum cosine similarity of reservoir water level at all effective temperature measuring points on the dam body are sorted in order of magnitude.

[0016] Based on the abrupt changes in the process lines of the maximum cosine similarity values ​​of air temperature and reservoir water level after sorting, similarity thresholds for air temperature and reservoir water level are proposed respectively.

[0017] Furthermore, based on whether the maximum cosine similarity of air temperature and the maximum cosine similarity of reservoir water level are greater than the similarity threshold of reservoir water level, all effective temperature measuring points on the dam body are divided into an air temperature-determining zone, an air temperature and reservoir water level co-influenced zone, and a trend-changing zone, including:

[0018] Determine whether the maximum cosine similarity value of temperature between a temperature measuring point on the dam body and the temperature time series at the dam site is greater than the temperature similarity threshold. If yes, the measuring point is classified into the temperature-determining zone. If no, determine whether the maximum cosine similarity value of reservoir water level between the measuring point and the upstream reservoir water level time series is greater than the reservoir water level similarity threshold. If yes, the measuring point is classified into the zone jointly influenced by temperature and reservoir water level. If no, the measuring point is classified into the trend-changing zone.

[0019] Furthermore, for the temperature-determining region, modeling factors are selected within the dam site temperature time series based on the optimal lag time of the measuring points, including:

[0020] Based on the abrupt changes in the optimal lag time of the temperature at the measuring points within the temperature-determining zone, the temperature-determining zone is divided into several temperature-determining sub-zones.

[0021] The average of the best lag time of temperature at all measuring points in each temperature determination zone is taken and rounded down to obtain the reference lag time of temperature for that temperature determination zone.

[0022] For each measuring point within the temperature-determining zone, the average value of the temperature time series at the dam site is taken in segments to both sides within the temperature lag influence time range of the zone, with the temperature lag time of the zone as the center, and used as the modeling factor for the measuring point.

[0023] Furthermore, for the area jointly affected by air temperature and reservoir water level, modeling factors are selected for the two time series of air temperature at the dam site and upstream reservoir water level based on the optimal lag time of the measuring points for air temperature and the optimal lag time for reservoir water level, respectively. These factors include:

[0024] Based on the abrupt changes in the optimal lag time of reservoir water level at the measuring points included in the area jointly affected by temperature and reservoir water level, the area jointly affected by temperature and reservoir water level is divided into several jointly affected zones.

[0025] The optimal lag time of temperature and the optimal lag time of reservoir water level at all measuring points in each common influence zone are averaged and rounded down to be used as the benchmark lag time of temperature and the benchmark lag time of reservoir water level for that common influence zone.

[0026] For each measuring point within the common influence zone, the average value of the temperature time series at the dam site within the temperature lag influence time range of the zone, centered on the temperature benchmark lag time of the zone, and the average value of the upstream reservoir water level time series within the reservoir water level lag influence time range of the zone, centered on the reservoir water level benchmark lag time of the zone, are taken in segments to both sides, and used as the modeling factor for the measuring point.

[0027] Furthermore, the time range of the temperature lag effect covers the optimal temperature lag time of all measuring points within the corresponding temperature-determining zone or the common-affecting zone, as well as the main interval of the normal distribution of the temperature lag effect determined by the Shapley method.

[0028] The time range of the reservoir water level lag effect covers the optimal lag time of the reservoir water level at all measuring points within the corresponding common influence zone, as well as the main interval of the normal distribution of the reservoir water level lag effect determined by the Shapley method.

[0029] Furthermore, the total length of the time period for averaging the values ​​segmented forward from the temperature reference lag time shall not exceed the temperature reference lag time;

[0030] The total length of the time period for taking the average value of segments forward from the reservoir water level reference lag time shall not exceed the reservoir water level reference lag time.

[0031] Furthermore, the high arch dam temperature prediction model based on the NARX neural network has an input layer, hidden layers, and an output layer, and introduces input delay and historical output to achieve memory function. Its mathematical description is as follows:

[0032] y(t)=f(y(t-1),y(t-2),...,y(tn y ),x(t),x(t-1),x(t-2),...,x(tn x ))

[0033] In the formula, f is a nonlinear function; y(t) is the output of the neural network at time t; x(t) is the external input at time t; y(tn) is the output of the neural network at time t. y ) represents the delay n y Historical output after time; x(tn) x ) represents the delay n x External delay input amount after time.

[0034] By adopting the above technical solution, the present invention has the following beneficial effects:

[0035] (1) This invention makes full use of massive temperature monitoring data of the dam body, explores the causal relationship between air temperature at the dam site and reservoir water level on the evolution of the temperature field of the arch dam, quantifies the lag effect time, and proposes a zoning method for the temperature field of the arch dam according to the main influencing factors and the optimal lag time, realizing the quantification of the zoning basis, and the zoning results are consistent with the lag effect mechanism of the temperature field of the arch dam.

[0036] (2) This invention uses the Shapley method to determine the time range of the lag effect, and combines the optimal lag time determined by cosine similarity to solve the problem of how to quantitatively analyze the temperature lag effect of various parts of the dam body, and provides a quantitative basis for the selection of early modeling factors.

[0037] (3) This invention considers the lag of the causal effect of the temperature field of the arch dam from the perspectives of modeling factors and modeling methods, which significantly improves the prediction accuracy of the temperature field of the arch dam. Attached Figure Description

[0038] Figure 1 This is a flowchart of the causal prediction process for the measured temperature field of high arch dams according to the present invention.

[0039] Figure 2 A graph showing the time-varying temperature at different depths;

[0040] Figure 3 The time-varying temperature at a depth of 30m from the surface under different thermal conductivity conditions is shown in the figure.

[0041] Figure 4 This is a schematic diagram of the NARX neural network model.

[0042] Figure 5 Time series plot of measured temperature at all measuring points;

[0043] Figure 6 This is a time series plot of the measured temperature at some measuring points;

[0044] Figure 7 A graph showing the variation of the cosine similarity between temperature measurement points and air temperature with the number of lag days;

[0045] Figure 8 A diagram showing the lag effect of air temperature and reservoir water level on the temperature measuring points of the dam body;

[0046] Figure 9 The graph shows the variation of the maximum cosine similarity values ​​of air temperature and reservoir water level at each temperature measuring point from largest to smallest.

[0047] Figure 10 A chart showing the sorting pattern for optimal lag time;

[0048] Figure 11 The layout and zoning diagram of all measuring points for section 13 of the arch crown beam dam;

[0049] Figure 12 The measured temperature time series plots for each zone are shown.

[0050] Figure 13 Line graph showing the optimal lag time for each measuring point in the temperature-determining zone;

[0051] Figure 14 A line graph showing the optimal lag time for relative air temperature and reservoir water level at various measuring points in the common influence area;

[0052] Figure 15 Time series plots of measured and predicted temperatures at measuring points in the temperature-determining region;

[0053] Figure 16 Time series plots of measured and predicted temperatures at various measuring points in the common influence area;

[0054] Figure 17 Time series plots of measured and predicted temperatures at measuring points T13-13 in the trend change zone;

[0055] Figure 18 Box plot for evaluating model prediction performance; where,

[0056] Figure 8 In the diagram, (a) shows the lag effect of air temperature on the temperature measuring point of the dam body, and (b) shows the lag effect of the upstream reservoir water level on the temperature measuring point of the dam body.

[0057] Figure 9 In the figure, (a) shows the variation pattern of the maximum cosine similarity value of the air temperature at each temperature measuring point from large to small, and (b) shows the variation pattern of the maximum cosine similarity value of the reservoir water level at each temperature measuring point from large to small.

[0058] Figure 10 In the diagram, (a) shows the ranking pattern of the optimal lag time of temperature in the temperature-determining zone, and (b) shows the ranking pattern of the optimal lag time of reservoir water level in the common influence zone.

[0059] Figure 12 In the diagram, (a) is the time series plot of the measured temperature in Zone 1, (b) is the time series plot of the measured temperature in Zone 2, (c) is the time series plot of the measured temperature in Zone 3, (d) is the time series plot of the measured temperature in Zone 4, (e) is the time series plot of the measured temperature in Zone 5, (f) is the time series plot of the measured temperature in Zone 6, and (g) is the time series plot of the measured temperature in Zone 7.

[0060] Figure 13In the figure, (a) is a line graph of the best lag time of temperature for each measuring point in Zone 1; (b) is a line graph of the best lag time of temperature for each measuring point in Zone 2; (c) is a line graph of the best lag time of temperature for each measuring point in Zone 3; and (d) is a line graph of the best lag time of temperature for each measuring point in Zone 4.

[0061] Figure 14 In the figure, (a) is a line graph of the optimal lag time of air temperature and reservoir water level at each measuring point in Zone 5, and (b) is a line graph of the optimal lag time of air temperature and reservoir water level at each measuring point in Zone 6.

[0062] Figure 15 In the figure, (a) is the time series plot of measured and predicted temperature at point T13-61 in Zone 1, (b) is the time series plot of measured and predicted temperature at point T13-60 in Zone 2, (c) is the time series plot of measured and predicted temperature at point T13-133 in Zone 3, and (d) is the time series plot of measured and predicted temperature at point T13-93 in Zone 4.

[0063] Figure 16 In the figure, (a) is the time series plot of measured and predicted temperature at point T13-45 in Zone 5, and (b) is the time series plot of measured and predicted temperature at point T13-52 in Zone 6.

[0064] Figure 18 In the figure, (a) is the RMSE box plot of the model, and (b) is the MAE box plot of the model. Detailed Implementation

[0065] 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.

[0066] Ideally, the influence of external temperature changes on the temperature field of the arch dam follows Fourier's law of heat conduction and can be simplified to a superposition of transient heat conduction problems on an infinitely large half-plane. Assume the initial uniform temperature of the homogeneous semi-infinite solid is T0, and at a certain moment, a temperature T is applied to the boundary at x=0. w The thermal disturbance, and its internal heat conduction process, can be mathematically described as follows:

[0067]

[0068] t=0, T=T0

[0069] x = 0, T = T w

[0070] T = T0

[0071] In the formula, T is the dam body temperature, t is time, α is thermal conductivity, and x is the depth from the temperature disturbance boundary surface.

[0072] To investigate the internal heat conduction process, it is assumed that the boundary temperature cycles annually between 0 and 30°C, and the thermal conductivity α of the medium is 0.0032 m. 2 / h, the time-varying law of temperature at measuring points at different depths is calculated as follows: Figure 2 As shown in the figure, the influence of the periodically changing external temperature on the temperature of the measuring point inside the semi-infinite body remains periodic, with a consistent fluctuation period. However, as the depth from the surface increases, the lag phase difference increases, and the amplitude of the temperature change decreases. Furthermore, thermal conductivity has a significant impact on the internal heat conduction process and temperature. Taking a depth of 30m from the surface (x=30) as an example, the time-varying temperature at this measuring point under different thermal conductivity is shown below. Figure 3 As shown, the peak temperatures for the four thermal conductivity values ​​are 15.3, 15.5, 15.8, and 16.0℃, respectively, and the times of occurrence are 153, 150, 147, and 144 days, respectively. This means that the lower the thermal conductivity, the lower the temperature at the same time and the longer the lag time.

[0073] from Figure 2 and Figure 3 It is clear that the degree to which external temperature changes affect the internal temperature of an arch dam varies with depth. The greater the depth from the surface, the longer the lag time and the smaller the temperature change amplitude, while also being affected by thermal conductivity. However, when applying the Fourier heat conduction equation to an arch dam in actual operation, the dam body temperature boundary conditions are complex and variable. Concrete exhibits a certain degree of dispersion, and during long-term service, material aging and changes in moisture content lead to variations in the thermal conductivity of the concrete. Therefore, the lag effect mechanism of the dam body temperature field becomes more complex. A data-driven causal prediction model is more ideal, but the uncertainty and volatility of the lag time must be carefully addressed.

[0074] Temperature changes in arch dams lag behind changes in ambient temperature. Therefore, accurately measuring this lag and incorporating it into the selection of modeling factors is a challenge in constructing a temperature field prediction model for arch dams. Cosine similarity is a time series similarity measure that treats two time series as vectors from a multi-dimensional perspective and calculates the cosine of the angle between them.

[0075]

[0076] In the formula, X i and Y i Let be the values ​​of the two time series at time i, and n be the number of measurements in a single time series.

[0077] Based on data normalization, the cosine value between two time series under different lag time assumptions is calculated using the sliding matching method. The closer the value is to 1, the higher the similarity between them in high-dimensional space. That is, the greater the influence of the previous temperature at the current lag time on the temperature of the measuring point inside the dam. Therefore, the location of the maximum cosine value during the sliding process is the optimal lag time.

[0078] Heat conduction inside an arch dam is a long and slow process. Temperature changes at a measuring point are the cumulative effect of changes in the external environment over a preceding period. However, cosine similarity can only determine the optimal lag time between the measuring point's temperature and the ambient air temperature—that is, the preceding air temperature that contributes most to the current temperature change at the measuring point. It cannot define the influence time range centered on the optimal lag time, and the degree of influence of daily ambient temperature changes on the measuring point's temperature change within this range is also unknown. In machine learning, the Shapley method is often used to analyze the contribution of input factors. Specifically, this method can traverse all feature subsets of the entire set of input factors and determine the contribution rate of each input factor to the model output by weighted averaging of the marginal contributions of individuals under different input combinations. Based on this, with the optimal lag time as the center, this embodiment uses the preceding air temperature over different time periods as input, uses random forest regression to fit the measuring point temperature, and calculates the contribution rate of each preceding air temperature to the measuring point temperature accordingly.

[0079]

[0080] In the formula, Let |S| be the weighting factor, |S| be the number of variables contained in a certain feature subset S, S / i represent that S does not contain input factor i for calculating contribution, v(S) be the value corresponding to set S, and n be the number of variables in the whole set of input factors.

[0081] NARX is a neural network model with a feedback correlation layer, belonging to a special type of recurrent neural network (RNN). Its output depends simultaneously on the current external input and the model's historical output, thus possessing good memory capabilities. It can simultaneously capture temporal dependencies and nonlinear dynamic causal relationships. Therefore, based on previous temperature and reservoir water level modeling factors, it can further refine the characterization of the lag effect mechanism of the temperature field in high arch dams by utilizing the model's input delay and historical output. The topology of the NARX neural network model is as follows: Figure 4 As shown.

[0082] Similar to other neural network models, the NARX network structure consists of an input layer, hidden layers, and an output layer. Building upon this, the network achieves its memory function by introducing input delay and historical outputs, as described mathematically below:

[0083] y(t)=f(y(t-1),y(t-2),...,y(tny ),x(t),x(t-1),x(t-2),...,x(tn x ))

[0084] In the formula, f is a nonlinear function; y(t) is the output of the neural network at time t; x(t) is the external input at time t; y(tn) is the output of the neural network at time t. y ) represents the delay n y Historical output after time; x(tn) x ) represents the delay n x External delay input amount after time.

[0085] Based on the above description, in one embodiment, such as Figure 1 As shown, a causal prediction method for the temperature field of a high arch dam considering the hysteresis mechanism includes:

[0086] S1, with an annual cycle as the upper limit, uses the sliding matching method to calculate the maximum cosine similarity of the measured temperature time series at each measuring point on the dam body with the temperature at the dam site and the water level at the upstream reservoir, respectively; where, during the sliding process, the position of the maximum cosine similarity value of the temperature is the optimal lag time of the temperature, and the position of the maximum cosine similarity value of the reservoir water level is the optimal lag time of the reservoir water level.

[0087] S2, based on the maximum cosine similarity of air temperature and reservoir water level at each measuring point, divides all effective temperature measuring points on the dam body into three zones: the air temperature-determining zone, the zone jointly influenced by air temperature and reservoir water level, and the trend-changing zone; specifically:

[0088] S21. Sort the maximum cosine similarity of air temperature and maximum cosine similarity of reservoir water level at all effective temperature measuring points on the dam body in order of magnitude.

[0089] S22. Based on the abrupt changes in the process lines of the maximum cosine similarity values ​​of air temperature and reservoir water level after sorting, propose the air temperature similarity threshold and the reservoir water level similarity threshold respectively.

[0090] S23, determine whether the maximum cosine similarity value of temperature between a certain temperature measuring point on the dam body and the temperature time series at the dam site is greater than the temperature similarity threshold; if yes, the measuring point is classified into the temperature-determining zone; if no, determine whether the maximum cosine similarity value of reservoir water level between the measuring point and the upstream reservoir water level time series is greater than the reservoir water level similarity threshold; if yes, the measuring point is classified into the zone jointly influenced by temperature and reservoir water level; if no, the measuring point is classified into the trend-changing zone; perform this step for all valid temperature measuring points on the dam body;

[0091] S3.

[0092] S31, For each measuring point within the temperature-determining zone, modeling factors are selected within the dam site temperature time series based on the optimal temperature lag time; specifically:

[0093] Based on the abrupt changes in the optimal lag time of the temperature at the measuring points within the temperature-determining zone, the temperature-determining zone is divided into several temperature-determining zones. The average optimal lag time of all measuring points in each temperature-determining zone is taken and rounded down to obtain the baseline lag time of the temperature for that zone. For each measuring point within a temperature-determining zone, the average value of the temperature time series at the dam site is taken in segments to both sides within the temperature lag time range of that zone, centered on the baseline lag time of that zone, and used as the modeling factor for that measuring point.

[0094] S32, for each measuring point within the area jointly affected by air temperature and reservoir water level, modeling factors are selected for the two time series of air temperature at the dam site and reservoir water level, respectively, based on the optimal lag time of air temperature and the optimal lag time of reservoir water level; specifically:

[0095] Based on the abrupt changes in the optimal lag time of reservoir water level at the measuring points within the area jointly affected by temperature and reservoir water level, the area jointly affected by temperature and reservoir water level is divided into several common influence zones. The optimal lag time of temperature and optimal lag time of reservoir water level at all measuring points in each common influence zone are averaged and rounded down to obtain the baseline lag time of temperature and the baseline lag time of reservoir water level for that common influence zone. For each measuring point within a common influence zone, the average value of the temperature time series at the dam site within the temperature lag time range of that zone and the average value of the upstream reservoir water level time series within the reservoir water level lag time range of that zone are taken in segments to both sides, centered on the baseline lag time of temperature in that zone, and used as the modeling factor for that measuring point.

[0096] S4. For each measuring point in the temperature-determining zone and the zone jointly affected by temperature and reservoir water level, a high arch dam temperature prediction model based on NARX neural network is established based on its respective modeling factors to predict the temperature. For each measuring point in the trend-changing zone, multiple linear regression is used to model and predict the temperature with τ and lnτ as modeling factors, where τ is the cumulative number of days since the initial monitoring day.

[0097] S5. By combining the predicted values ​​of all measuring points, the predicted temperature field of the high arch dam can be obtained, characterized by typical measuring points.

[0098] It should be noted that the time range of the temperature lag effect covers the optimal temperature lag time of all measuring points within the corresponding temperature-determining zone or common influence zone, as well as the main interval of the normal distribution of the temperature lag effect determined by the Shapley method. Similarly, the time range of the reservoir water level lag effect covers the optimal reservoir water level lag time of all measuring points within the corresponding common influence zone, as well as the main interval of the normal distribution of the reservoir water level lag effect determined by the Shapley method.

[0099] In this embodiment, the segmented time intervals can be: 1, 2-3, 4-7, 8-14, 15-30, 31-60, 61-120, and 121-182. It is important to note that the total length of the time interval averaging forward from the temperature reference lag time does not exceed the temperature reference lag time, and the total length of the time interval averaging forward from the reservoir water level reference lag time does not exceed the reservoir water level reference lag time. In other words, the modeling factors can only include the temperature on the day of temperature monitoring and the upstream reservoir water level. Furthermore, some measuring points on the dam surface are directly affected by solar radiation, and the optimal lag time and lag effect time range are both very short; in this case, segmented averaging is not required.

[0100] The technical solutions involved in the above embodiments will be described in detail below with reference to specific examples.

[0101] A hydroelectric power station is located at the border of Yanyuan County and Muli County in Liangshan Prefecture, Sichuan Province. Its concrete double-curvature arch dam has a maximum height of 305m, making it the highest arch dam currently built in the world. The dam crest elevation is 1885m, the normal reservoir water level is 1880m, and the dead water level is 1800m. For arch dams, the measured temperature of the arch crown beam section is typically used to characterize the dam's temperature field. This study focuses on dam section No. 13. Excluding a few monitoring points with poor data continuity, a total of 134 effective temperature monitoring points were included. Five thermometers were buried at each monitoring elevation: two located 5cm inside the upstream and downstream faces of the dam body, and the other three evenly distributed between them. The selected monitoring data period was from June 8, 2014 to December 31, 2018, with data recorded daily. Data from December 31, 2017 to December 31, 2018 was used for model prediction performance evaluation, while the remaining data was used for model training.

[0102] Figure 5 The monitoring data flow charts for all temperature measuring points in the arch crown beam dam section are displayed, with some measuring point flow charts shown below. Figure 6 As shown. From Figure 5 and Figure 6 It can be found that the measured temperature time series of multiple measuring points have similar regularities, indicating that the main influencing factors are similar. Therefore, these measuring points can be classified into one category, and the same modeling factor can be used for measuring points of the same category when establishing the prediction model.

[0103] The various measuring points inside the dam face different service environments, so the factors that need to be considered when predicting their temperature are also different. This study considers two main influencing factors: the air temperature at the dam site and the water level of the upstream reservoir. Based on two quantitative indicators, the maximum cosine similarity and the optimal lag time, all temperature measuring points in the dam are first divided into zones.

[0104] Air temperature and upstream reservoir water level exhibit annual periodicity, therefore the maximum lag time is calculated to be 365 days. Calculation results under different lag time assumptions show that the cosine similarity between the temperature at the measuring point and the air temperature and reservoir water level exhibits similar variation patterns, and the similarity is relatively high for most measuring points. Taking measuring points PL13-60 and PL13-93 as examples, the calculation results are as follows... Figure 7 As shown, this indicates that the optimal lag times between the two measuring points and the relative temperature are 36 days and 233 days, respectively, and their cosine similarities with the temperature are 0.9779 and 0.9771, respectively.

[0105] Using a maximum lag time of 365 days as the upper limit, the Shapley method was used to investigate the influence of daily temperature changes and reservoir water level changes on the temperature at various measuring points on the dam body. Shapley values ​​calculated for some measuring points are shown below. Figure 8 As shown, other measuring points are similar. The directly calculated Shapley values ​​can be positive or negative. This embodiment focuses on the degree of influence, therefore the calculation results are processed as absolute values; the larger the value, the higher the degree of influence. From Figure 8 As can be seen, the Shapley values ​​at each measuring point all follow a normal distribution. This indicates that the lag effect of air temperature and reservoir water level on dam temperature conforms to a normal distribution, and therefore, their previous piecewise average values ​​can be used as modeling factors for predicting the dam temperature field. Taking air temperature as an example, the T13-61 measuring point, located on the downstream face of the dam, is directly affected by air temperature and exhibits almost no lag. Figure 8 (a) The Shapley peak value of the measuring point is relatively large and the range is small. The Shapley value of the measuring point T13-60, which is located at the same elevation as T13-61, also shows a normal distribution due to the increased depth from the downstream face of the dam. However, the peak value is delayed and significantly smaller, and the range of influence is larger. The measuring point T13-133, which is deeper from the downstream face, further expands this variation. In addition, based on the Shapley peak value, the optimal lag time relative to the air temperature of the three measuring points can be determined to be 1, 42 and 122 days, respectively. The results calculated by cosine similarity are 1, 36 and 117 days, respectively. The two are relatively close, thus verifying the rationality of the latter. However, it also shows that the optimal lag time has a certain degree of fluctuation and needs to be averaged by region.

[0106] Figure 9 The variation of cosine similarity values ​​at each temperature measurement point from large to small is shown. Based on the catastrophe criterion and... Figure 9(a) The temperature similarity threshold can be set to 0.9625, at which point 78 measuring points should be classified into the temperature-determining zone; similarly, according to... Figure 9 (b) The cosine similarity threshold between the temperature at the measuring point and the water level in the reservoir can be determined as 0.8954. There are 23 measuring points with a value less than this threshold. Therefore, the number of measuring points in the common influence area and the trend change area are 33 and 23, respectively.

[0107] For the temperature-determining region, the cosine similarity between all measuring points and the air temperature is extremely high, and the evolution of the measured temperature process curve is basically consistent with that of the air temperature. However, the lag phase difference shows significant differences, and the increasing pattern of the optimal lag time is as follows: Figure 10 As shown in (a), it exhibits a certain degree of clustering. This can be addressed according to... Figure 10 (a) The clustering and abrupt changes in the optimal lag time further subdivide the temperature-determining zone into four sub-zones, with optimal lag time intervals of 1–4 days, 5–50 days, 51–156 days, and 157–365 days, respectively, containing 21, 22, 30, and 5 measuring points. For the common influence zone, the decreasing trend of the optimal lag time of the measuring point temperature relative to the reservoir water level is as follows: Figure 10 As shown in (b), it can be subdivided into two sub-regions with optimal lag time intervals of 287–352d and 50–245d, respectively, containing 16 and 17 measurement points.

[0108] Based on cosine similarity and its threshold, all temperature measuring points in the dam body are divided into 7 zones (the temperature-determining zone has four sub-zones, the common-influence zone has two sub-zones, and there is one trend-change zone). Taking one measuring point in each zone as an example, the zoning process is shown in Table 1. The zoning results for other measuring points are as follows. Figure 11 As shown, the measured temperature process lines at each zone's measuring points are as follows: Figure 12As shown, the measured temperature process lines at the same measurement points in the same zone exhibit very similar evolution patterns, especially in terms of periodicity and lag phase difference. Overall, the measurement points in the air temperature-determining zone are mainly distributed on the downstream face of the dam and the dam area above the 1880m dead water level. Further subdivision reveals that in Zone 1, all measurement points are located on the dam crest surface and the downstream face of the dam above the stilling basin water level, directly affected by solar radiation. In Zone 2, measurement points are mainly located on the upstream side of the dam near the 1800m dead water level and the downstream face of the dam below the stilling basin water level; due to the influence of surface reservoir water, temperature changes lag behind air temperature. In Zone 3, measurement points are mainly distributed in the internal area of ​​the dam above the 1800m dead water level and the downstream dam area between 1740m and 1800m elevations. Zone 4 has fewer measurement points and their distribution is not concentrated. In the common influence zone, Zone 5 is mainly concentrated in the middle area of ​​the dam interior below the dead water level; Zone 6 is mainly distributed on the upstream face of the dam within 140m below the dead water level. Zone 7, characterized by a trend of change, is primarily located within the dam heel and the lower half of the dam body. This region has the greatest reservoir depth and dam thickness, thus external temperature and water level changes have virtually no impact on it. Due to slow hydration and heat dissipation in the later stages, it exhibits a trend of change overall. The above analysis verifies the rationality of the zoning method presented in this invention, and it can be used for zoning prediction of the dam body temperature field.

[0109] Table 1 Typical measurement point zoning process

[0110]

[0111] For temperature-determining regions, the optimal lag time for relative temperature at each measuring point is as follows: Figure 13 As shown in the figure, although the optimal lag time of all measuring points in each zone is slightly different, there is still a certain degree of clustering within the same zone. Therefore, the average value of each zone is rounded down as the baseline lag time, which is 1, 35, 120 and 185 days for the four zones respectively.

[0112] Figure 14 The optimal lag time of measured temperature relative to air temperature and reservoir water level at each measuring point in the common influence zone is given. Based on this, the baseline lag days for air temperature and reservoir water level in Zone 5 can be taken as 85 and 330 days, and in Zone 6 as 200 and 120 days.

[0113] In order to cover the temperature lag of all measuring points within the same zone of the dam to the greatest extent, the input factors of the model constructed for the temperature-determining zone and the common influence zone are shown in Table 2, based on the baseline lag time and the normally distributed lag influence range determined by the Shapley method.

[0114] Table 2. Model input factors for temperature-determining and co-influenced regions.

[0115]

[0116]

[0117] Note: T and H represent the air temperature at the dam site and the water level of the upstream reservoir, respectively; the subscript number indicates the number of days that the measured value is earlier than the current monitoring value of the dam body temperature, for example, T1 is the air temperature of the previous day.

[0118] In the construction of the NARX model, the main parameters that need to be optimized are the number of hidden layers, the number of hidden layer units, and the number of lag days. Generally speaking, a single hidden layer can meet the needs of most engineering projects and has the advantages of low overfitting and fast training speed. For the number of hidden layer units and the number of lag days, this invention adopts the grid search method, taking the minimum cross-validation RMSE as the criterion. Taking T13-60 as an example, the number of hidden layer units and the number of lag days are set to 20 and 7, respectively. To compare the advantages of the NARX model in further considering the lag effect, SVM and MLR models were simultaneously established for each measuring point in the temperature-determining region and the common influence region.

[0119] Overall results show that the fitted and predicted values ​​of the NARX model are closer to the monitored values. A process line is shown by randomly selecting one measurement point from each partition as an example, and other measurement points are compared and analyzed based on the quantitative evaluation index of model performance.

[0120] In the temperature determinant region, Zones 1, 2, 3, and 4 are exemplified by T13-61, T13-60, T13-133, and T13-93, respectively. Their measured and predicted temperature time series are as follows: Figure 15 As shown. Overall, in both the training and prediction phases, the NARX model significantly outperforms the MLR and SVM models, especially in the prediction phase, which characterizes model performance. The NARX model exhibits less volatility and more accurate predictions. The SVM model shows a better fit, but its predictions are more volatile, which is because the SVM model is more sensitive to the volatility of the modeling data. In addition, the predictions of both the SVM and MLR models deviate significantly from the monitored values.

[0121] In the common influence region, Zone 5 and Zone 6, taking PL13-45 and PL13-52 as examples respectively, have the following fitting and prediction results: Figure 16 As shown. Overall, the fitted and predicted values ​​of the NARX model are still closer to the monitored values, especially for temperature measurement points with certain trend-like changes. From Figure 16(a) It can be seen that in addition to the annual periodic variation, the measured temperature time series of PL13-45 also has a gradually increasing time-dependent trend. However, neither the MLR model nor the SVM model has discovered this trend throughout the entire process. The reason for this is that the selected modeling factors are only the previous air temperature and reservoir water level, neither of which contains trend factors. The reason why the NARX model can explain this phenomenon is that, in addition to the separately constructed modeling factors, the NARX model also has the function of a time series analysis model, which can automatically use the previous measured temperature as input data when the model predicts the current temperature. For this measuring point, the optimized lag time is 6 days, which means that the input data of the NARX model for the PL13-45 measuring point includes the measured temperature of its previous 6 days.

[0122] The trend change zone 7 was fitted using only a linear function plus a logarithmic function, where the measured and predicted temperature time series of the T13-13 measuring points are as follows: Figure 17 As shown, it can be seen that, whether in the fitted segment or the predicted segment, the actual temperature change trend basically conforms to the preset function form.

[0123] The statistical box plot of the predictive performance evaluation index of all measuring points in each sub-region of the temperature-determining zone and the common influence zone is shown below. Figure 18 As shown. Overall, the NARX model exhibits the best predictive performance across all partitions. Its RMSE and MAE, in terms of both mean and box length, are significantly superior to the MLR and SVM models. The SVM model's predictive performance is slightly better than the MLR model. This is because the NARX model can simultaneously consider the complex nonlinearity and lag between the influencing factors and the output, while SVM can only consider the former, and MLR cannot consider either. The comparison results of the above three models also indicate that the relationship between air temperature and reservoir water level and dam temperature is mainly linear, which is consistent with the heat conduction mechanism of arch dams. However, the lag is very complex. Therefore, strengthening the characterization ability of the lag influence mechanism of the arch dam temperature field is the best way to improve the accuracy of temperature prediction. For Zones 3, 4, and 5, the measured temperature time series show strong regularity with few abrupt changes and drastic fluctuations, resulting in excellent prediction performance. For Zones 1, 2, and 6, the measuring points are mainly located on the surface of the arch dam, and the short-distance heat conduction process has a smaller effect on reducing the impact of temperature fluctuations. Therefore, the monitoring data is highly volatile, and the dispersion and mean of the prediction evaluation indicators are relatively large, indicating that their prediction accuracy is slightly worse than other zones.

[0124] Both are machine learning models, Figure 18The average RMSE obtained by the NARX model for the six zones were 0.4913, 0.1171, 0.0180, 0.0024, 0.0141, and 0.3120, respectively, while those of the SVM model were 1.4299, 1.3576, 0.3073, 0.0289, 0.0946, and 0.5712, respectively. The SVM model is widely used in dam displacement prediction. Therefore, compared with the commonly used SVM model, the NARX model can improve the temperature prediction accuracy of the six zones by 65.64%, 91.38%, 94.16%, 91.82%, 85.14%, and 45.25%, respectively, and by 75.75% for all temperature measurement points on the dam body.

[0125] In summary, the case study of an arch dam demonstrates that the prediction method presented in this invention is simple to operate, highly feasible, and achieves quantitative zoning. The resulting temperature field zoning of the arch dam conforms to the actual lag effect mechanism. The causal mechanism of the temperature field of the arch dam exhibits complex nonlinearity and lag. Compared with the widely used SVM model, the NARX model improves the prediction accuracy of the six temperature field zonings by 45% to 95%, and the average improvement for the 134 temperature measuring points on the dam body is 76%.

[0126] 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 causal prediction method for the temperature field of a high arch dam considering the hysteresis mechanism, characterized in that, The methods include: Using an annual cycle as the upper limit, the sliding matching method is employed to calculate the maximum cosine similarity between the measured temperature time series at each measuring point on the dam body and the temperature and water level time series at the dam site and upstream reservoir, respectively. During the sliding process, the position of the maximum cosine similarity value of temperature is the optimal lag time for temperature, and the position of the maximum cosine similarity value of reservoir water level is the optimal lag time for reservoir water level. Based on the maximum cosine similarity of air temperature and reservoir water level at each measuring point, all effective temperature measuring points on the dam body are divided into air temperature-determining areas, air temperature and reservoir water level jointly affected areas, and trend change areas. For each measuring point within the temperature-determining zone, modeling factors are selected within the dam site temperature time series based on the optimal temperature lag time. For each measuring point within the zone jointly influenced by temperature and reservoir water level, modeling factors are selected within the dam site temperature and upstream reservoir water level time series based on the optimal temperature lag time and the optimal reservoir water level lag time, respectively. For each measuring point in the temperature-determining zone and the zone jointly influenced by temperature and reservoir water level, a high arch dam temperature prediction model based on a NARX neural network is established based on its respective modeling factors to predict temperature; for each measuring point in the trend-changing zone, ... and As the modeling factor, multiple linear regression is used to model and predict temperature, where This represents the cumulative number of days since the initial monitoring date; By combining the predicted values ​​from all measuring points, the predicted temperature field of a high arch dam, characterized by typical measuring points, can be obtained. For the temperature-determining region, modeling factors are selected within the temperature time series at the dam site based on the optimal lag time of the measuring points, including: Based on the abrupt changes in the optimal lag time of the temperature at the measuring points within the temperature-determining zone, the temperature-determining zone is divided into several temperature-determining sub-zones. The average of the best lag time of temperature at all measuring points in each temperature determination zone is taken and rounded down to obtain the reference lag time of temperature for that temperature determination zone. For each measuring point within the temperature-determining zone, taking the temperature baseline lag time of that zone as the center, the average value of the temperature time series at the dam site is taken in segments to both sides within the temperature lag influence time range of that zone, and used as the modeling factor for that measuring point; For the area jointly affected by air temperature and reservoir water level, modeling factors are selected for the two time series of air temperature at the dam site and upstream reservoir water level, based on the optimal lag time of air temperature and the optimal lag time of reservoir water level at the measuring points. These factors include: Based on the abrupt changes in the optimal lag time of reservoir water level at the measuring points included in the area jointly affected by temperature and reservoir water level, the area jointly affected by temperature and reservoir water level is divided into several jointly affected zones. The optimal lag time of temperature and the optimal lag time of reservoir water level at all measuring points in each common influence zone are averaged and rounded down to be used as the benchmark lag time of temperature and the benchmark lag time of reservoir water level for that common influence zone. For each measuring point within the common influence zone, the average value of the temperature time series at the dam site within the temperature lag influence time range of the zone, centered on the temperature reference lag time of the zone, and the average value of the upstream reservoir water level time series within the reservoir water level lag influence time range of the zone, centered on the reservoir water level reference lag time of the zone, are taken in segments to both sides, and used as the modeling factor for the measuring point. The time range of temperature lag effect covers the optimal temperature lag time of all measuring points in the corresponding temperature-determining zone or common-affecting zone, as well as the main interval of the normal distribution of temperature lag effect determined by the Shapley method. The time range of the reservoir water level lag effect covers the optimal lag time of the reservoir water level at all measuring points within the corresponding common influence zone, as well as the main interval of the normal distribution of the reservoir water level lag effect determined by the Shapley method.

2. The causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism according to claim 1, characterized in that, Based on the maximum cosine similarity of air temperature and reservoir water level at each measuring point, all effective temperature measuring points on the dam body are divided into three zones: the air temperature-determining zone, the zone jointly influenced by air temperature and reservoir water level, and the trend-changing zone. Draft similarity thresholds for air temperature and reservoir water level; Based on whether the maximum cosine similarity of air temperature is greater than the air temperature similarity threshold and whether the maximum cosine similarity of reservoir water level is greater than the reservoir water level similarity threshold, all effective temperature measuring points on the dam body are divided into air temperature-determining areas, air temperature and reservoir water level jointly affected areas, and trend change areas.

3. The causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism according to claim 2, characterized in that, The proposed temperature similarity threshold and reservoir water level similarity threshold include: The maximum cosine similarity of air temperature and maximum cosine similarity of reservoir water level at all effective temperature measuring points on the dam body are sorted in order of magnitude. Based on the abrupt changes in the process lines of the maximum cosine similarity values ​​of air temperature and reservoir water level after sorting, similarity thresholds for air temperature and reservoir water level are proposed respectively.

4. The causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism according to claim 2, characterized in that, Based on whether the maximum cosine similarity of air temperature and reservoir water level exceeds the air temperature similarity threshold and the maximum cosine similarity of reservoir water level exceeds the reservoir water level similarity threshold, all effective temperature measuring points on the dam body are divided into air temperature-determining zones, zones jointly influenced by air temperature and reservoir water level, and trend-changing zones, including: Determine whether the maximum cosine similarity value of temperature between a temperature measuring point on the dam body and the temperature time series at the dam site is greater than the temperature similarity threshold. If yes, the measuring point is classified into the temperature-determining zone. If no, determine whether the maximum cosine similarity value of reservoir water level between the measuring point and the upstream reservoir water level time series is greater than the reservoir water level similarity threshold. If yes, the measuring point is classified into the zone jointly influenced by temperature and reservoir water level. If no, the measuring point is classified into the trend-changing zone.

5. The causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism according to claim 1, characterized in that, The total length of the time period for averaging the values ​​segmented forward from the temperature reference lag time shall not exceed the temperature reference lag time. The total length of the time period for taking the average value of segments forward from the reservoir water level reference lag time shall not exceed the reservoir water level reference lag time.

6. The causal prediction method for the temperature field of high arch dams considering the hysteresis mechanism according to claim 1, characterized in that, The high arch dam temperature prediction model based on NARX neural network has an input layer, hidden layers, and an output layer, and introduces input delay and historical output to realize the memory function. Its mathematical description is as follows: ； In the formula, It is a nonlinear function; for The output of the neural network at any given time; for External input at any given time; For delay Historical output over time; For delay External delay input amount after time.

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