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Numerical simulation analysis of ecological monitoring of small reservoir dam based on maximum entropy algorithm

  • Qing Wang EMAIL logo , Zhiwei Zhou , Shaolong Tang , Siyuan Wan and Weiran Yu
Published/Copyright: August 14, 2023
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Abstract

Displacement monitoring method of reservoir dam is a key research topic at present. In order to better display the overall efficiency of horizontal displacement and vertical displacement monitoring, a numerical simulation analysis method of ecological monitoring of small reservoir dam based on the maximum entropy algorithm is proposed. The virtual value is calculated by the maximum entropy algorithm, and the probability distribution function of random variables is obtained. The comprehensive prediction model of ecological monitoring results is constructed by the probability distribution function, and the daily monitoring values of ecological history of small reservoir dams are obtained. The maximum entropy probability density function is used to calculate the initial moment of small reservoir displacement samples, calculate the abnormal probability of the dam, get the maximum entropy probability density, realize the unbiased distribution of simulation values, and complete the dam deformation monitoring of small reservoirs. The simulation experiment is verified by numerical simulation. The results show that this method can effectively monitor the horizontal and vertical displacement of the dam; monitor the water-level hydrograph of pressure pipes at each measuring point; and obtain the changes of ecological runoff, temperature difference, and sediment discharge around the dam of small reservoirs in real time, which provides data guarantee for improving the ecological added value of small reservoirs.

1 Introduction

The ecological monitoring of small reservoir dams is to observe and collect the data of life support capacity in all or part of the earth, and analyze it to understand the present situation and changes of the ecological environment of small reservoir dams. Speeding up the construction of flood control hub projects, harnessing small and medium-sized rivers, and strengthening dangerous reservoirs are conducive to strengthening the protection and comprehensive management of key rivers and lakes, restoring the water ecosystem with clean water and green shores, and promoting the protection and construction of beautiful rivers and lakes [1,2]. Small reservoirs have played a great role in flood control, drought resistance, water supply, and irrigation. Under the new situation, the traditional development model of small reservoirs can no longer meet the practical needs of China’s reform and development. In order to continuously improve the quality of wading ecological environment and promote high-quality development, ecological monitoring of small reservoir dams is of great significance. A typical reservoir landslide observation data is selected as the benchmark data set, and a geological disaster model is constructed by machine learning to predict the displacement of Shuping landslide [3]. The maximum entropy algorithm is a kind of reasoning viewpoint. When inferring the system state, the entropy value is maximized to complete the prediction when only some information constraints are mastered. The maximum entropy algorithm obtains the information entropy that satisfies all constraints, and the accuracy is high. The maximum entropy algorithm can flexibly set constraints, and the fitness of the model to unknown data and the fitting degree to known data can be adjusted by the number of constraints [4].

Relevant researchers have studied ecological monitoring under different conditions. Ma et al. [5] selected input variables based on mutual information, optimized support vector regression to predict the displacement of seepage-driven landslide, and improved the accuracy of seepage-driven landslide prediction by combining mutual information and dual-input symmetry correlation criteria. However, the monitoring rate of this method needs to be verified. Shirokova et al. [6] proposed a method of urban ecological monitoring based on microwave communication channel. The initial phase of low-frequency signal was obtained by homodyne conversion, and the meteorological component was subtracted from the reading of the measuring instrument, and the monitoring data set was updated to complete the global urban ecological monitoring. However, this method takes a long time to calculate the ecological monitoring data set. Klimetzek et al. [7] monitored the distribution of animal species under habitat conditions, observed the changes of forest canopy coverage, and completed the distribution study based on normalized difference vegetation index images. However, the monitoring time of this method needs to be verified. Jiedeerbieke et al. [8], put forward a visual monitoring method for dam safety based on building information management and browser/server architecture. By processing, analyzing and evaluating the data, the safety status of the dam can be judged. However, the displacement and deformation of the reservoir dam cannot be clearly monitored during the monitoring process, and the monitoring of the ecology around the dam cannot be realized. Ma et al. [9] put forward a hybrid method integrating k-fold cross-validation, meta-heuristic support vector regression, and nonparametric Friedman test to study Shuping landslide and Baishuihe landslide, and introduced particle swarm optimization to adjust displacement prediction parameters to improve the accuracy and reliability of prediction based on the maximum-likelihood method. However, the application of this method in flood control, drought resistance, water supply, and irrigation needs to be verified. Casserly et al. [10] monitored the bed load transport quantity of rivers in southeast Ireland in real time according to the water framework instruction, used pit sediment catcher to continuously record the water level and downstream sediments, and used radio frequency identification to obtain the critical discharge value of particle entrainment, which provided guarantee for the dam to interrupt sediment transport for a long time. However, the computational power of this method is low. Brantschen et al. [11] studied river ecosystem, constructed a standardized framework for sampling surface water quality evaluation, collected biodiversity and biological state of river system, and completed biological monitoring. However, this method needs to be improved in adjusting the monitoring function.

Therefore, this article studies the ecological monitoring of small reservoirs based on the maximum entropy algorithm, through the maximum entropy algorithm to achieve unbiased distribution of monitoring results, to achieve small reservoir monitoring. Theoretical contribution of comprehensive prediction model of ecological monitoring results based on the maximum entropy algorithm:

  1. The virtual value is calculated by the maximum entropy algorithm, and the daily monitoring value of the ecological history of small reservoir dams is obtained according to the results, so as to realize the adjustment of the displacement value of small reservoirs and meet the higher-level wading demand.

  2. The maximum entropy probability density function is used to calculate the initial moment of displacement samples of small reservoirs, and the maximum entropy probability density is obtained to complete dam deformation monitoring of small reservoirs and improve the excavation effect of the ecological added value of small reservoirs.

2 Numerical simulation of ecological monitoring for small reservoirs and dams

2.1 The principle of maximum entropy

The concept of entropy was first devised by the scholar Shannon, who presented entropy as a measure of the amount of information available for random events [12]. The value of random variable is less than a certain numerical probability in the sample space, and the dispersion degree of a group of data measures that the number of samples will affect the probability distribution function under negative binomial distribution. Set the number of simulated samples to 1,000, and the information entropy of discrete random variables can be calculated by formula (1):

(1) T ( X ) = i = 1 n p i ln p i .

In formula (1), the entropy of random variable X is described by T ( X ) . The probability of random variable T ( X ) = x i is described by p i . According to formula 1, there are two aspects of the main calculation: one is the use of this formula that can be used to directly calculate the probability of information known entropy. The second is that the functional of distribution probability p i can be regarded as T ( X ) . If p i changes, so does T ( X ) , so T ( X ) can be used to calculate the probability distribution function. Based on the statistical inference rule of probability distribution, the probability distribution with the maximum entropy should be selected when only part of the information is used in reasoning process [13,14,15]. The meaning of maximum entropy is that the least man-made information is added in the data, which makes the deviation of calculation result lowest. Therefore, the maximum entropy can make the simulation result closer to reality in all probability distributions under corresponding conditions.

2.2 Comprehensive prediction model of ecological monitoring results based on maximum entropy algorithm

Numerical simulation of ecological monitoring of small reservoirs is a process of comprehensive information processing. Simulation of ecological monitoring data is a process of comprehensive prediction. Ecological monitoring values are regarded as discrete random sequences in time [16]. In this series, the monitoring values of a forecast date are predicted by a single model, and the probability distribution of the predicted time point monitoring effect is regarded as effective information. Then, the information is provided to the comprehensive prediction model. Set the actual monitoring value of the historical day as the core point of the forecast. The deviations of the historical reference days were summarized, and the center moments of each order were obtained [17,18,19]. The prediction algorithm is used to predict the ecological monitoring characteristics of small reservoirs in historical days, and the maximum entropy algorithm is used to infer the ecological monitoring characteristics.

The specific calculation steps are as follows:

  1. Predict the daily monitoring value of ecological history of small reservoir dams in a virtual form.

    Fictitious projections of a large number of historical days enable statistical information on actual monitoring results to be obtained [20,21,22]. Then, ecological characteristic values were obtained according to actual monitoring. Suppose there are N historical reference days and x i ( i = 1 , 2 , 3 , , N ) is the monitoring value of the i reference day. The monitoring values of each reference day are predicted by K prediction models, and the prediction result is x ˆ i k ( k = 1 , 2 , , N ) . Then, the numerical eigen values of the effect quantity of the results are calculated. If the second central moment of the predicted effect is e t k , x ˆ t k ( k = 1 , 2 , , N ) . e t k can be calculated using formula (2):

    (2) e t k = 1 N i = 1 N x i x ˆ i k x ˆ i k 2 , k = 1 , 2 , , K .

  2. Pick a single-model algorithm

    According to the matching of historical reference sample and single model, the prediction effect of different algorithms is analyzed and the virtual prediction error is judged.

    1. Calculating the average sum of squares of the errors of the comprehensive prediction model of ecological monitoring results, as shown in formula (3):

      (3) ε k = 1 N i = 1 N [ ( x ˆ i k x i ) / x i ] 2 , k = 1 , 2 , , K .

    2. Filter the prediction algorithms and set the threshold δ , such as δ = 0.01 . For the k model algorithm, if ε k > δ , the algorithm is eliminated.

    3. Through the aforementioned form of filtering, if the elimination of more algorithms can increase the value of the threshold δ and pick again. Each algorithm is sorted according to ε k ’s size, and the lowest ε k algorithm is selected as the algorithm used in this model.

  3. Forecast the monitoring effect of the forecast day.

    In order to analyze the monitoring effect of the next U day, K model algorithm is used to predict the monitoring effect of ( t = 1 , 2 , , U ) on t day in turn. The prediction result is expressed by x ˆ i k ( k = 1 , 2 , , K ) .

  4. A comprehensive prediction model based on the maximum entropy algorithm is constructed and solved.

    The predicted effect is represented by a discrete random variable X . According to the maximum entropy theory, the distribution of random variable X is deduced. The model objective function is constructed as shown in formula (4):

    (4) max T ( X ) = i = 1 N p i ln p i .

    If it is calculated according to the second-order moment, then:

    (5) g k ( x ) = [ ( x x ˆ t k ) / x ˆ t k ] 2 .

    At the same time, the constraints of the objective function are designed, as shown in formula (6):

    (6) i = 1 N p i = 1 , p i 0 i = 1 N x i x ˆ t k x ˆ t k 2 p i = e t k , k = 1 , 2 , , K .

    The probability distribution of maximum entropy is described by the Lagrangian λ k ( i = 0 , 1 , . . . , K ) , and then the λ k ( i = 0 , 1 , . . . , K ) . The probability density function for the i th-order measurement of the predicted effect is derived, as shown in formula (7):

    (7) p ( X = x i ) = exp λ 0 + k = 1 K λ k x x ˆ t k x ˆ t k 2 .

    The predicted value of the t -th effect size calculated by this formula is the mathematical expectation value E ( X ) that can describe X .

  5. Repeat steps (1) to (5) until the forecast for each monitoring day is completed, that is, the calculation of the forecast sequence value of the monitoring effect can be completed.

2.3 Maximum entropy algorithm for dam deformation monitoring

The dam deformation monitoring of small reservoirs is the basis of ecological monitoring. According to the data results of surface deformation, internal shape change, crack formation, water seepage and bank slope displacement, and the vertical displacement and horizontal displacement of the dam are obtained in time, and then, the dam safety state is analyzed, which provides a strong guarantee for the safety monitoring of small reservoirs. Calculating the reservoir displacement value can help to monitor the dam deformation, determine the safe limit displacement value of the reservoir, and ensure the safe operation of the dam. By calculating the reservoir displacement value, the dam deformation is determined, the dam deformation trend is predicted, and whether the dam moves horizontally or vertically is judged. According to the displacement variation, the reservoir displacement trend is determined to ensure the dam to play a safe and stable role. Because the moment of origin of the measured point at the top of the dam is large, the displacement monitoring sequence is adjusted. The measured displacement values are adjusted to ( x δ ) / σ samples, and the maximum entropy probability density function and sample eigenvalues are obtained. When calculating, first calculate the origin moment u i ( i = 1 , 2 , 3 , 4 ) of the sample [23,24]. Then, the aforementioned probability density calculation process is used to obtain the maximum entropy probability density.

If the monitoring index of dam deformation or the extreme value is x m , the probability of dam abnormality can be calculated by using formula (8):

(8) P a = x m + f ( x ) d x , x > x m .

In formula (8), the probability of abnormality shall be described by P a . Under normal circumstances, the probability of abnormal dam displacement measurement is not large; if there is abnormality, the probability is usually 1 or 5%.

The specific method flow is shown in Figure 1.

Figure 1 
                  Flow chart of ecological monitoring of small reservoir dams based on the maximum entropy method.
Figure 1

Flow chart of ecological monitoring of small reservoir dams based on the maximum entropy method.

2.4 Project overview

A small reservoir is located in a village in the northwestern region, with the main river channel length of 14.2 km, control basin area of 42.2 km2, and river longitudinal slope of 18.1%. The dam is located around the reservoir and is about 3.8 km long. Small reservoirs meet the water supply demand by means of fixed water supply. The dam height of the reservoir is 70 m, the elevation of the dam bottom is −11.25 m, the water surface area is 300,000,000 m2, the storage capacity is 200,000,000 m3, the reservoir water level is 60 m, the inflow is 65.6 m3/s, and the storage capacity is 89.1 m3/s (Figure 2).

Figure 2 
                  Actual diagram of small reservoir dam.
Figure 2

Actual diagram of small reservoir dam.

When monitoring the deformation of the dam surface, there are three cross sections; the pile numbers are 0 + 030, 0 + 055, and 0 + 080; each section has 4 punctuation points and 12 monitoring points. The monitoring facilities operate normally, and the quantity and arrangement meet the requirements of the code. The specific arrangement is shown in Table 1.

Table 1

Layout of dam surface deformation monitoring facilities

Serial number Measuring point number Measuring point position Section Wheelbase Initial elevation (m) Installation date Working status
1 W1 X: 66.24, Y: 4.17 0 + 030 −6 150.1125 2019/6/11 Normal
2 W4 X: 20.47, Y: 9.36 0 + 030 4.5 149.8003 2019/6/4 Normal
3 W7 X: 57.17, Y: 6.94 0 + 030 25.3 143.1325 2019/6/11 Normal
4 W10 X: 17.34, Y: 1.89 0 + 030 60.5 130.7587 2019/6/11 Normal
5 W2 X: 17.48, Y: 7.39 0 + 055 −6 150.1266 2019/6/11 Normal
6 W5 X: 4.77, Y: 7.92 0 + 055 4.5 149.8165 2019/6/12 Normal
7 W8 X: 14.66, Y: 9.18 0 + 055 25.3 143.0533 2019/6/11 Normal
8 W11 X: 8.04, Y: 6.74 0 + 055 60.5 130.9319 2019/6/11 Normal
9 W3 X: 9.36, Y: 3.69 0 + 080 −6 150.0852 2020/12/17 Normal
10 W6 X: −18.74, Y: 4.18 0 + 080 4.5 149.8243 2020/6/15 Normal
11 W9 X: 14.61, Y: 2.91 0 + 080 25.3 143.0839 2019/6/11 Normal
12 W12 X: −27.42, Y: 7.45 0 + 080 60.5 131.4008 2019/6/11 Normal

In the monitoring, the dam buried a total of 12 piezometric tubes, arranged into three cross-sections. The pile numbers are 0 + 030, 0 + 055, and 0 + 080; each section has four punctuation points, and the number and layout of manometric tubes meet the code requirements.

The verification table of the piezometric pipe of the dam body is shown in Table 2.

Table 2

Verification form of piezometric pipe of dam body

Serial number Measuring point number Measuring point position Section Wheelbase Nozzle elevation Installation date Working status
1 UP11 X: 24.07, Y: 4.21 0 + 030 −4.5 118.79 2019/9/24 Normal
2 UP12 X: 2.04, Y: 5.43 0 + 030 4.5 118.93 2019/9/24 Normal
3 UP13 X: 21.88, Y: 6.07 0 + 030 25.3 119.13 2019/9/24 Normal
4 UP14 X: 6.31, Y: 3.14 0 + 030 40.5 119.04 2019/9/24 Normal
5 UP21 X: −5.37, Y: 4.17 0 + 055 −4.5 113.01 2019/9/24 Normal
6 UP22 X: −12.97, Y: 1.98 0 + 055 −4.5 112.63 2019/9/24 Normal
7 UP23 X: −11.18, Y: 6.03 0 + 055 25.3 117.33 2019/9/24 Normal
8 UP24 X: −17.01, Y: 1.74 0 + 055 40.5 117.5 2019/9/24 Normal
9 UP31 X: 37.18, Y: 9.74 0 + 080 −4.5 126.15 2019/9/24 Normal
10 UP32 X: 11.47, Y: 2.69 0 + 080 4.5 124.1 2019/9/24 Normal
11 UP33 X: 20.17, Y: 2.68 0 + 080 25.3 125.95 2019/9/24 Normal
12 UP34 X: 10.92, Y: 7.39 0 + 080 40.5 129.44 2019/9/24 Normal

3 Experiment analysis

3.1 Deformation analysis

3.1.1 Statistical analysis

The numerical simulation method is used to simulate and analyze the horizontal and vertical displacement of the dam in the next year. The horizontal displacement mainly refers to the upstream and downstream direction displacement. There is a certain horizontal deformation in the left and right banks, and the horizontal displacement at the top of the dam is the operational behavior of the most earth gravity dam, and the horizontal displacement of 0 + 055 can play a better practical effect. Alternative schemes such as 0 + 030 and 0 + 080 can also be adopted, but the horizontal displacement of 0 + 055 can be combined with the actual deformation reflected by the two adjacent monitoring periods, which can better play the overall efficiency of horizontal displacement and vertical displacement monitoring and obtain the calculation results in a short time. Therefore, the horizontal displacement scheme of 0 + 055 main dam is selected in the text. In this article, the horizontal displacement and vertical displacement of the 0 + 055 main dam is simulated and analyzed (Table 3).

Table 3

Simulation result/mm

Feature statistics Reservoir water level (m) Main dam 0 + 055 section
W2 W5 W8 W11
Horizontal displacement Vertical displacement Horizontal displacement Vertical displacement Horizontal displacement Vertical displacement Horizontal displacement Vertical displacement
Maximum value 143.42 0 0.4 0 0.3 0.1 0.1 0.0 0.8
Minimum value 135.83 −3.3 0.0 −3.1 0.0 0.0 0.0 0.0 0.0
Average value 140.27 −1.7 0.2 −1.5 0.2 0.1 0.1 0.0 0.4
Year-to-year variation 7.59 3.3 0.4 3.1 0.3 0.1 0.1 0.0 0.8

The downstream displacement is positive, and the downstream displacement is negative. According to the results of numerical simulation in this study, the data of W2, W5, W8, and W11 in the 0 + 055 section of the main dam are not very large. Among them, the maximum displacement is 3.3 mm, the maximum annual amplitude is 3.3 mm, and there is no larger displacement. The monitoring data simulated by W8 and W11 did not change amplitude. The vertical displacement of W2, W5, W8, and W11 is observed. The vertical displacement of W11 is the largest, and the annual variation is 0.8 mm. The vertical displacement of W8 position is relatively small, only 0.1 mm. After the simulation, the effect is very clear, which can simulate the next year’s monitoring results.

3.1.2 Process analysis

This article simulates the water-level change under different dates and the horizontal displacement of the main dam 0 + 055. The analysis results are shown in Figure 3.

Figure 3 
                     Changes in water level and horizontal displacement.
Figure 3

Changes in water level and horizontal displacement.

According to Figure 3, we can know the horizontal displacement and water-level change of different measuring points. From the change trend of each measurement point, the horizontal displacement extends upstream when the reservoir water level drops, and the change amplitude of horizontal displacement is low. The horizontal displacement is clearer after the simulation.

Use this study to simulate the water-level changes on different dates and the vertical displacement of the four measuring points of the main dam at 0 + 055. The analysis results are shown in Figure 4.

Figure 4 
                     Changes in water level and vertical displacement.
Figure 4

Changes in water level and vertical displacement.

According to the simulation in Figure 4, according to the changing trend of 0 + 055 section, the vertical displacement is sinking. During the whole period, the simulation of monitoring results is more accurate and reliable.

3.1.3 Analysis of tensile strength of dam concrete

Using the method in this study, the concrete tensile strength of 12 monitoring points of the dam is simulated. The analysis results are shown in Table 4.

Table 4

Monitoring and simulation of concrete tensile strength

Serial number Measuring point number Maximum tensile stress/MPa Age corresponding to maximum tensile stress/days Corresponding stretch deformation
1 W1 1.52 110.1 35.63 × 10−6
2 W4 1.14 109.7 26.72 × 10−6
3 W7 1.76 172.1 27.51 × 10−6
4 W10 1.87 185.3 45.21 × 10−6
5 W2 1.45 203.5 33.89 × 10−6
6 W5 2.26 87.9 53.46 × 10−6
7 W8 1.42 95.6 33.72 × 10−6
8 W11 1.73 122.8 41.01 × 10−6
9 W3 1.32 108.7 26.52 × 10−6
10 W6 1.14 141.2 27.02 × 10−6
11 W9 1.25 125.8 28.45 × 10−6
12 W12 1.15 141.1 27.67 × 10−6

According to Table 4, the deformation monitoring of concrete can be realized effectively in the numerical simulation analysis of tensile strength of dam concrete at different measuring points. And the maximum tensile stress and the corresponding age can be analyzed by the monitoring results at each measuring point.

3.2 Process line analysis

The method of this study is used to simulate the water-level hydrograph of each piezometer at the 0 + 030 section, and the analysis results are shown in Figure 5.

Figure 5 
                  Analysis of hydrograph of piezometric pipe at 0 + 030 section.
Figure 5

Analysis of hydrograph of piezometric pipe at 0 + 030 section.

From Figure 5, it can be seen that the water-level data of each piezometric tube in this section have good continuity. From the trend of change, the reservoir water level changes periodically, which is mainly affected by rainfall, and there is no unreasonable increase or decrease. Except for UP12, other manometric tubes decrease from upstream to downstream, which accords with the general rule. The percolation pressure of the piezometric tube on the upstream slope top is higher, and then, the variation amplitude of the water level decreases gradually until it becomes stable.

3.3 Simulation analysis of ecological monitoring of small reservoirs and dams

In this study, the ecological runoff of a small reservoir dam under different months after construction is simulated and monitored and compared with the runoff before construction.

According to the simulation results in Figure 6, the reservoir runoff is different in different months. The runoff in July, August, and September is relatively high, which is similar to the results before the dam is built. At the same time, the runoff is well controlled after dam construction and is obviously lower than before dam construction. Therefore, the real-time change of the runoff can be obtained by the monitoring simulation.

Figure 6 
                  Runoff analysis.
Figure 6

Runoff analysis.

This method is used to simulate and analyze the temperature difference between storage period and detention period in different months. The result is shown in Figure 7.

Figure 7 
                  Temperature difference before and after water storage.
Figure 7

Temperature difference before and after water storage.

According to Figure 7, it can be seen that the temperature difference before and after water storage is very clear after the simulation monitoring in this study. Among them, the temperature deviation before and after water storage in summer and autumn is large. The temperature deviation before and after water storage from May to June can reach about 4°C, and that before and after water storage from September to October can reach about 3.7°C. The temperature deviation in other months is relatively small, about 2°C.

This method is used to monitor the sediment discharge in flood and non-flood seasons in different months. The results are shown in Figure 8.

Figure 8 
                  Monitoring of sand output in flood season and non-flood season.
Figure 8

Monitoring of sand output in flood season and non-flood season.

According to the monitoring simulation results in Figure 8, it can be seen that the amount of sediment discharged from the dam during flood season is obviously higher than that during non-flood season. The maximum sediment discharge in flood season is 26 × 108t, while the maximum discharge in non-flood season is about 19 × 108t. The simulation results in this study can clearly distinguish the state of flood season and non-flood season.

3.4 Comparative analysis of simulation results and actual measurement results of ecological monitoring of small reservoir dams

Adjacent points of settlement experiment are set at the top of the dam, and the distance between adjacent points is 10 m, which are evenly distributed on the dam axis. Use precision level (S1 or S05 level) to obtain the actual measurement results, and use this method to calculate and obtain the simulation results. The rationality of the simulation method is verified by comparing the numerical results. The results are shown in Figure 9.

Figure 9 
                  Comparison between simulation results and actual results.
Figure 9

Comparison between simulation results and actual results.

According to the experimental results in Figure 9, the simulation results obtained by this method are consistent with the actual measurement results, which shows that the simulation method is reasonable. In the later ecological example project of small reservoir dam, this method can be used to complete intelligent monitoring of landslide, collapse, debris flow, goaf collapse, land subsidence and other data.

4 Conclusion

In this study, the maximum entropy algorithm based on the ecological monitoring of small reservoirs is numerical simulation. The virtual value is calculated by the maximum entropy algorithm, and the daily monitoring results of ecological history of small reservoir dams are obtained, so as to realize comprehensive ecological monitoring of small reservoirs. The maximum entropy probability density function is used to calculate the initial moment of small reservoir displacement samples, and the maximum entropy probability density is obtained, which verifies the observation facilities of dam surface deformation comprehensively. Seepage observation can be realized according to the frequency requirements of the specification, and the working stability of piezometers can be improved, so that the safety of dam seepage observation facilities can be improved, the seepage situation can be observed in time, and the management of small reservoirs can be changed from extensive management to intelligent management.

However, due to the limited research time and conditions, the calculation delay was not considered in the research process. Therefore, in the future work, based on the research in this study, the time delay matrix will be added in the process of adopting the maximum entropy model to further optimize the model; establish and improve the intelligent sensing system of settlement, displacement, deformation, leakage and cracks of small reservoirs; and improve the ecological monitoring effect of small reservoirs.

Acknowledgments

The study was supported by Water Conservancy Science and Technology Project of Jiangxi Province Water Resource Department “Study on LOF threshold of dam warning under variable spatiotemporal data (Grant No. 202223YBKT14)”.

  1. Funding information: The study was supported by Water Conservancy Science and Technology Project of Jiangxi Province Water Resource Department “Study on LOF threshold of dam warning under variable spatiotemporal data (Grant No. 202223YBKT14).”

  2. Conflict of interest: Authors state no conflict of interest.

  3. Data availability statement: The data that support the findings of this study are available from the corresponding author upon a reasonable request.

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Received: 2022-12-15
Revised: 2023-03-28
Accepted: 2023-05-24
Published Online: 2023-08-14

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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