Wind disaster accident prediction method of lightning rod tower based on nuclear density estimation
The wind-induced response statistical model of the lightning rod tower is constructed through the nuclear density estimation method, which predicts the fault of the lightning rod tower, solves the problem of the fault and damage of the lightning rod tower in wind disasters, and effectively predicts and prevents the wind-induced response of the lightning rod tower, enhancing the system safety and reliability.
Patent Information
- Application Number
- CN202411902351.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-23
- Publication Date
- 2025-05-06
AI Technical Summary
Lightning rod towers may be affected by wind-induced vibrations and stresses in complex and changeable natural environments, resulting in failures and damages. It is difficult for the existing technology to effectively predict and prevent these wind disasters.
The core density estimation method is used to construct the mechanical response statistical model of the lightning rod tower under wind load, and the probability density function of the wind-induced response data of the lightning rod structure under different wind speed conditions is constructed through the nuclear density estimation method, and the probability density function of the key mechanical characterization is predicted, and the lightning rod tower failure is predicted.
By constructing and analyzing the probability density function of the wind-induced response data of the lightning rod tower, the potential wind speed range that may cause the lightning rod tower failure can be identified, system safety can be enhanced, system reliability can be improved, maintenance strategies can be optimized, and operational risks can be reduced.
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Abstract
Description
Technical Field
[0001] The invention relates to the technical field of electric power equipment disaster prevention, and in particular to a method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation. Background Art
[0002] Lightning rod towers are an important part of the power system, and their normal operation is crucial to power supply. However, in complex and changeable natural environments, such as strong winds, ice and snow and other severe meteorological conditions, lightning rod towers may be affected by wind-induced vibrations and stress, and even cause failures and damage. Summary of the invention
[0003] In view of this, it is necessary to provide a wind disaster accident prediction method for lightning rod towers based on kernel density estimation to reduce wind disaster accidents of lightning rod towers.
[0004] A method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation comprises the following steps:
[0005] Step S1: constructing a statistical model of mechanical response of a lightning rod tower under wind load using a kernel density estimation method;
[0006] Let X 1 , X 2 , X 3 , …, X N For a sample of a univariate continuous population, the estimated value of the probability density function at any point is:
[0007]
[0008] Among them, K is the kernel function, h is the window width, n is the total number of samples, and i is the sample number;
[0009] Step S2, constructing the probability density function of the wind-induced response data of the lightning rod structure under different wind speed conditions using the kernel density estimation method;
[0010] Step S3, constructing a probability density function of key mechanical characterization quantities, wherein the key mechanical characterization quantities include tensile stress, compressive stress, and displacement of the top of the lightning rod;
[0011] Step S4, predicting lightning rod tower failures through probability density functions of key mechanical characterization quantities.
[0012] Preferably, in step S1, the kernel function is selected from one of a Gaussian kernel function, a Uniform kernel function, and a Triangle kernel function.
[0013] Preferably, in step S1, when the kernel function is a Gaussian kernel function,
[0014]
[0015] Preferably, in step S1, the optimal window width of the data is determined according to the rule of thumb:
[0016]
[0017] Preferably, the prediction of lightning rod tower failure includes wind speed extremes, wind-induced vibrations and stresses, and failure probability.
[0018] Preferably, the estimated values h of the window width of the maximum tensile stress of the lightning rod are 0.9166 and 2.1473 respectively.
[0019] Preferably, the estimated values h of the window width of the maximum compressive stress are 0.9157 and 3.579 respectively.
[0020] Preferably, the method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation further includes the following steps:
[0021] Step S5, comparing the cumulative distribution function of the kernel density estimation with the empirical distribution function of the sample to verify the correctness of the kernel density estimation.
[0022] The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation of the present invention has the following beneficial effects:
[0023] Enhance system security
[0024] Constructing the probability density of lightning rod tower wind-induced response data can help us better understand the response of the lightning rod tower system under different wind speeds and meteorological conditions. Through the analysis of probability density, the potential wind speed range that may cause fatigue and damage to lightning rods can be identified, so that targeted measures can be taken to enhance the safety of the system.
[0025] Improve system reliability
[0026] Constructing and analyzing the probability density of lightning rod tower wind-induced response data helps predict the performance of the system under different wind speed conditions. This can help power operators better plan and manage lightning rod towers, improve structural stability and reliability, and reduce the risk of power outages and damage.
[0027] Optimizing maintenance strategies
[0028] By analyzing the probability density of wind-induced response data of lightning rod towers, it is possible to determine which parts are susceptible to wind loads and under which wind speed conditions the probability of failure is higher. This helps to develop more effective maintenance strategies, reduce unnecessary repair costs, and extend the service life of equipment.
[0029] Reduce operational risks
[0030] The analysis of the probability density of wind-induced response data of lightning rod towers can also help reduce the risk of system operation. Understanding the response characteristics of the system under different wind speeds can help operators better respond to extreme weather events and reduce losses caused by natural disasters. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Figure 1 The frequency histogram of the kernel density estimate of the maximum tensile stress of the lightning rod when the wind speed is 10m / s.
[0032] Figure 2 This is a comparison chart of the kernel density estimation test of the maximum tensile stress of the lightning rod with a wind speed of 10m / s.
[0033] Figure 3 The frequency histogram of the kernel density estimate of the maximum tensile stress of the lightning rod when the wind speed is 15m / s.
[0034] Figure 4 This is a comparison chart of the kernel density estimation test of the maximum tensile stress of the lightning rod when the wind speed is 15m / s.
[0035] Figure 5 This is a comparison chart of the kernel density estimation of the maximum tensile stress of the lightning rod tower under different grouping conditions.
[0036] Figure 6 Schematic diagram of the prediction of the maximum tensile stress of a lightning rod and a comparison chart between the predicted probability and the calculated probability.
[0037] Figure 7 Schematic diagram of the prediction of the maximum compressive stress of a lightning rod and a comparison chart between the predicted probability and the calculated probability.
[0038] Figure 8 Schematic diagram of the prediction of the maximum tensile stress of a lightning rod and a comparison chart between the predicted probability and the calculated probability. DETAILED DESCRIPTION
[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0040] Please see Figure 1 , a method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation includes the following steps:
[0041] Step S1: constructing a statistical model of mechanical response of a lightning rod tower under wind load using a kernel density estimation method;
[0042] Let X 1 , X 2 , X 3 , …, XN For a sample of a univariate continuous population, the estimated value of the probability density function at any point is:
[0043]
[0044] Among them, K is the kernel function, h is the window width, n is the total number of samples, and i is the sample number;
[0045] Kernel density estimation does not require any assumptions about the data, and directly uses known data to determine the probability density function of the sample. The key lies in choosing the appropriate kernel function K and window width h.
[0046] The choice of kernel function has little effect on kernel density estimation. Common kernel functions include Gaussian kernel function, Uniform kernel function, Triangle kernel function, etc. Among them, Gaussian kernel function has better corresponding smoothness, so Gaussian kernel function is selected.
[0047] When the kernel function is a Gaussian kernel function,
[0048]
[0049] The choice of window width h has a great influence on the kernel density estimation. The optimal window width of the data is determined according to the thumb rule:
[0050]
[0051] After determining the appropriate kernel function and optimal window width, the probability density function of the kernel density estimation can be determined.
[0052] Step S2, constructing the probability density function of the wind-induced response of the lightning rod structure under different wind speed conditions using the kernel density estimation method;
[0053] Taking the maximum tensile stress as an example, the kernel density estimation method is used to construct the probability density function of the wind-induced response of the lightning rod structure under different wind speed conditions, and then tests are carried out.
[0054] When the wind speed is 10m / s, the kernel density estimate of the maximum tensile stress at any point of the lightning rod is as follows: Figure 1 As shown in the figure, the blue frequency histogram represents the kernel density estimation value corresponding to the maximum tensile stress, and the red curve represents the kernel density estimation diagram obtained by the frequency histogram. After that, it is tested by the empirical distribution function, and the results are as follows Figure 2 As shown in the figure, the black curve is the empirical distribution function curve of the maximum tensile stress and the kernel density estimate, and the yellow * is the discrete coordinate of the kernel density estimate corresponding to the maximum tensile stress. Figure 2It can be seen that since no prior knowledge of the distribution of relevant data is required, the kernel density estimation has a good goodness of fit and can better reflect the probability density characteristics of the real mechanical parameters. Then, the window width estimate h of the maximum tensile stress of the lightning rod is calculated according to Formula 3 through the maximum tensile stress and the kernel density estimate, which is 0.9166.
[0055] When the wind speed is 15m / s, the kernel density estimate of the maximum tensile stress at any point of the lightning rod is as follows: Figure 3 As shown. After that, it is tested by the empirical distribution function, and the result is as follows Figure 4 Similarly, the goodness of fit of the kernel density estimation is good, and the estimated value of the window width of the maximum tensile stress of the lightning rod is calculated to be 2.1473.
[0056] When the wind speed is 10m / s, the data of the maximum tensile stress are divided into 30 groups and 60 groups to study the influence of data grouping on kernel density estimation. The results are as follows Figure 5 As shown, it can be found that the results of kernel density estimation are not affected by data grouping and can better reflect the characteristics of the data itself.
[0057] When the wind speed is 15m / s, the situation is the same and will not be repeated.
[0058] On the basis of calculating the wind-induced dynamic response of the lightning rod structure, the above method is used to obtain the kernel density estimation window width of other key mechanical characterization quantities, such as the kernel density estimation window width h of the mechanical characterization quantities of maximum compressive stress and top displacement. As shown in Table 1:
[0059] Table 1: Kernel density estimation window width of key mechanical characterization quantities
[0060]
[0061] Then, the dynamic response data and the corresponding window width h are substituted into Formula 1 to obtain the probability density function of each key mechanical characterization quantity, that is, step S3, to construct the probability density function of the key mechanical characterization quantity, wherein the key mechanical characterization quantity includes tensile stress, compressive stress, and displacement of the top of the lightning rod.
[0062] Step S4, predicting lightning rod tower failures through probability density functions of key mechanical characterization quantities.
[0063] By completing the construction of probability density functions of key mechanical characterization quantities, we can better grasp the statistical characteristics and probability distribution of the response values. At the same time, under the premise of stable wind speed, we can preliminarily complete the prediction and analysis of individual mechanical parameters.
[0064] Taking the maximum tensile stress of the lightning rod tower as an example, the maximum tensile stress unit of the lightning rod tower is obtained through wind-induced response calculation. The wind speed simulation time is extended and the wind-induced response calculation of the lightning rod is completed. The time series of the maximum tensile stress of the lightning rod is extracted and statistically analyzed. At the same time, according to the maximum tensile stress probability density function of the lightning rod constructed under study, the probability of the maximum tensile stress of the lightning rod tower reaching the limit load is calculated. Finally, the prediction results are compared and analyzed with the calculation results. The prediction schematic diagram and prediction result comparison of the maximum tensile stress unit of the lightning rod are shown in Figure 2. Figure 6 shown.
[0065] The prediction results and calculation results of the maximum tensile stress unit of the lightning rod are shown in Table 2.
[0066] Table 2: Comparison of predicted probability and calculated probability of maximum tensile stress in lightning rods
[0067] Parameters Unit Number 36% ultimate load 44% Ultimate Load 52% ultimate load 60% ultimate load Prediction probability 351 78.896 45.196 16.798 0.039 Calculating Probability 351 82.67 48.17 18 0.0467
[0068] (The maximum tensile stress limit load of the lightning rod is 235MPa)
[0069] It can be seen that the predicted results are basically consistent with the calculated results, with a small error. The predicted probability error is the largest at locations farther away from the ultimate load value, with a maximum difference of about 3% probability.
[0070] Similarly, taking the maximum compressive stress of the lightning rod tower as an example, the prediction diagram and prediction results of the maximum compressive stress unit of the lightning rod are compared. Figure 7 shown.
[0071] The prediction results and calculation results of the maximum compressive stress unit of the lightning rod are shown in Table 3.
[0072] Table 3: Comparison of predicted probability and calculated probability of maximum tensile stress in lightning rods
[0073] Parameters Unit Number 36% ultimate load 44% Ultimate Load 52% ultimate load 60% ultimate load Prediction probability 351 78.224 44.381 16.305 0.0353 Calculating Probability 351 80.000 45.334 15.667 0.03167
[0074] It can be seen that the predicted results are basically consistent with the calculated results, with a small error. The predicted probability error is the largest at locations farther away from the ultimate load value, with a maximum difference of about 2% probability.
[0075] Similarly, taking the displacement of the top of the lightning rod as an example, a preliminary prediction and verification analysis of the transmission tower head is carried out, and the predicted value of the probability density function of the transmission tower head is compared and verified with the calculated value of the actual wind-induced response, such as Figure 8 shown.
[0076] The prediction and calculation results of the displacement of the top of the lightning rod are shown in Table 4.
[0077] Table 4: Comparison of predicted probability and calculated probability of displacement at the top of lightning rod:
[0078] Parameters Unit Number 55% ultimate load 60% ultimate load 65% ultimate load 70% ultimate load Prediction probability 702 34.356 11.378 1.078 0.00154 Calculating Probability 702 36.500 12.667 2.334 0.00112
[0079] (The limit of the displacement of the top of the lightning rod is 2% of the height of the lightning rod, which is 0.6m)
[0080] In summary, under the premise of stable wind speed, through preliminary prediction and verification analysis of the key mechanical characterization quantities of lightning rods, it can be found that the calculated probability is basically consistent with the predicted probability, both within the allowable error range. This shows that the construction and prediction research of the probability density function of the wind-induced response of the key mechanical characterization quantities of lightning rods in this paper is reliable, which can provide help for the wind and disaster prevention of lightning rod towers.
[0081] In a preferred embodiment, the prediction of lightning rod tower failure includes wind speed extremes, wind-induced vibrations and stresses, and failure probability.
[0082] What is disclosed above is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of rights of the present invention. A person skilled in the art can understand that all or part of the processes of the above embodiments and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.
Claims
1. A method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation, characterized in that: The following steps are involved: Step S1: constructing a statistical model of mechanical response of a lightning rod tower under wind load using a kernel density estimation method; Let X1, X2, X3, ..., X N For a sample of a univariate continuous population, the estimated value of the probability density function at any point is: Among them, K is the kernel function and h is the window width; Step S2, constructing the probability density function of the wind-induced response data of the lightning rod structure under different wind speed conditions using the kernel density estimation method; Step S3, constructing a probability density function of key mechanical characterization quantities, wherein the key mechanical characterization quantities include tensile stress, compressive stress, and displacement of the top of the lightning rod; Step S4, predicting lightning rod tower failures through probability density functions of key mechanical characterization quantities.
2. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation as claimed in claim 1, characterized in that: In step S1, the kernel function is selected from one of the Gaussian kernel function, the Uniform kernel function, and the Triangle kernel function.
3. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation as claimed in claim 2, characterized in that: In step S1, when the kernel function is a Gaussian kernel function, 4. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation according to claim 1, characterized in that: In step S1, the optimal window width of the data is determined according to the rule of thumb:
5. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation as claimed in claim 1, characterized in that: The prediction of lightning rod tower failure includes wind speed extremes, wind-induced vibrations and stresses, and failure probability.
6. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation according to claim 1, characterized in that: The estimated values h of the window width of the maximum tensile stress of the lightning rod are 0.9166 and 2.1473 respectively.
7. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation as claimed in claim 1, characterized in that: The estimated values h of the window width of the maximum compressive stress are 0.9157 and 3.579 respectively.
8. The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation as claimed in claim 1, characterized in that: The method for predicting wind disaster accidents of lightning rod towers based on kernel density estimation also includes the following steps: Step S5, comparing the cumulative distribution function of the kernel density estimation with the empirical distribution function of the sample to verify the correctness of the kernel density estimation.