CN112990379A - Clustering-based method and equipment for rapidly analyzing wind load vulnerability of power transmission tower - Google Patents
Clustering-based method and equipment for rapidly analyzing wind load vulnerability of power transmission tower Download PDFInfo
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Abstract
The application belongs to the technical field of wind resistance of power transmission towers. The application provides a clustering-based method and equipment for rapidly analyzing wind load vulnerability of a power transmission tower, wherein the method comprises the following steps: the establishment includes
A power transmission tower sample library of base power transmission tower samples; obtaining key structure parameters of each power transmission tower sample, and performing dimensionality reduction processing by adopting a principal component analysis method to obtain principal component indexes; calculating and determining an optimal classification number k by combining a Sturges empirical formula and an elbow discrimination method; obtaining k clustering results by using a k-means clustering algorithm; and selecting a typical sample to obtain a typical sample library, establishing a finite element model, calculating the failure probability of the equipment under different wind intensities, and fitting to obtain a vulnerability curve of the power transmission tower. The dynamic classification of all power transmission towers is realized by selecting key structure parametersTherefore, the selected typical sample is more representative, and the accuracy and the universal applicability of the general vulnerability analysis curve result of the power transmission tower are ensured.
Description
Technical Field
The application belongs to the technical field of wind resistance of power transmission towers, and particularly relates to a clustering-based method for rapidly analyzing wind load vulnerability of a power transmission tower.
Background
In recent years, wind damage and ice damage cause huge damage to power transmission lines. A plurality of disaster records show that the earthquake vulnerability of the power system, especially the power transmission tower, is extremely high, once the damage is formed, serious consequences can be caused, if the damage is formed, part of line power transmission is interrupted, and if the damage is formed, the whole line of the regional power system is paralyzed, so that the normal social operation is seriously influenced, the disaster relief and post-disaster reconstruction work are more delayed, and the economic loss is difficult to estimate.
Engineering seismic resistance has progressed to today, countless scholars never stopped their efforts on even seemingly simple objects, as this is often the simple but common part of the problem that is critical. Similarly, many researchers have conducted extensive research on various types of transmission towers for the research on the vulnerability of transmission towers. With the increase of voltage class, the materials and structural forms of the transmission tower are continuously improved. The study of the power transmission tower by scholars is from the component part of the power tower to the main study object, from passive earthquake damage statistics, to comprehensive wind tunnel tests, and from one-way simplified calculation to multi-dimensional earthquake numerical simulation.
The above severe facts and theoretical research bases show that: the power grid earthquake disaster prevention and quick response technical research is developed, the safety of the power system in the earthquake and the quick evaluation capability after the earthquake are improved, and the guarantee of power supply is an irreparable task and challenge of the current power system.
There are three main methods for analyzing the vulnerability of the power transmission tower: a disaster data statistical analysis method, a test method and a calculation analysis method. The disaster statistical analysis method is a vulnerability analysis method based on historical disaster data, but is limited to timeliness, the power transmission tower is improved along with the time, and early disaster data are not suitable at present. In addition, disaster data is precious and lacking. The test method is limited by high cost of wind tunnel test of the power transmission tower. Therefore, computational analysis is favored.
The existing calculation analysis method for analyzing the vulnerability of the power transmission tower comprises two common schemes. The first method is that all power transmission tower samples are used for vulnerability analysis, so that the obtained vulnerability curve has high precision, but the method is time-consuming and low in efficiency; the second is to manually divide a fixed interval to perform static classification, and select a part of samples from the fixed interval for vulnerability analysis, so that although the number of the samples is reduced and the analysis efficiency is improved, the obtained vulnerability curve is not accurate enough.
Disclosure of Invention
In view of this, the application provides a method and a device for rapidly analyzing wind load vulnerability of a power transmission tower based on clustering, which are used for solving the problem that the existing computational analysis method cannot give consideration to both accuracy and universal applicability.
In order to solve the technical problem, a first aspect of the present application provides a method for quickly analyzing vulnerability of a wind load of a power transmission tower based on clustering, including the following steps:
s100: establishing a power transmission tower sample library, wherein the power transmission tower sample library comprises
Transmission tower samples, note
A sample is obtained;
s200: obtaining each transmission in a power transmission tower sample libraryOf electric tower samples
A key structural parameter, will
The key structure parameter is subjected to dimensionality reduction treatment by adopting a principal component analysis method to obtain
A principal component index;
s300: obtaining a preliminary classification number of the power transmission tower by using a Sturges empirical formula, and summing the preliminary classification number
Calculating and determining an optimal classification number k by using an elbow discrimination method for each principal component index;
s400: utilizing k-means clustering algorithm pair to optimize the classification number k
Classifying the samples to obtain k clustering results;
s500: selecting typical samples according to the k clustering results to obtain the number of the samples
A representative sample library of;
s600: establishing a finite element model of a typical sample library, and calculating the failure probability of the equipment under different wind strengths;
s700: and fitting the equipment failure probability by using a lognormal distribution function to obtain a vulnerability curve of the power transmission tower sample.
Further, in step S200,
the key structural parameters specifically include:
the cross arm, the cross arm and the main material are of the same cross section size.
Further, in step S200, the method will be described
The key structure parameter is subjected to dimensionality reduction treatment by adopting a principal component analysis method to obtain
The main component indexes specifically comprise:
will be provided with
The key structure parameters are combined according to the group linear combination relation to obtain
The indexes of the main components are shown in the specification,
all the main component indexes are linearly uncorrelated, and
。
further, in step S300, the Sturges empirical formula is specifically:
in the formula:
for the purpose of the preliminary classification number,
the number of transmission towers.
Further, step S300 specifically includes:
obtaining a preliminary classification number of the power transmission tower by using a Sturges empirical formula;
using the preliminary classification number as the reference classification number, sequentially increasing the number of the reference classification number according to the reference classification number
Calculating a cluster distortion degree corresponding to each reference classification number by each principal component index;
drawing a line graph by taking the reference classification number as a horizontal axis and the clustering distortion degree as a vertical axis;
and determining the classification number corresponding to the position with the maximum change of the slope of the broken line in the broken line graph as the optimal classification number.
Further, step S400 specifically includes:
s401: generating k uniformly distributed initial clustering center points according to the optimal classification number k;
s402: calculating the Euclidean distance from each sample to each initial clustering center point;
s403: dividing the samples into classes represented by initial clustering center points with the closest distances, and generating k classes;
s404: respectively calculating k classified new clustering central points, and judging whether the new clustering central points are converged;
s405: if yes, outputting a clustering result containing k classifications, otherwise, executing step S402.
Further, in step S500, the number of typical samples is:
selecting
In a sample
One sample was taken as a representative sample.
Further, step S500 specifically includes:
according to the distance from the sample to the cluster center to which the sample belongs
Uniformly spaced selection in the first cluster
The samples form a typical sample library with the number of the samples;
in the formula:
for a typical number of samples selected in each cluster,
is the number of samples of a typical sample library,
for the number of samples in the first cluster,
is the total number of samples.
Further, in step S600, calculating the failure probability of the equipment under different wind intensities further includes:
calculating the number of failure power transmission towers under preset wind strength, and calculating the failure probability of equipment under different wind strengths according to an equipment failure probability calculation formula;
the equipment failure probability calculation formula is as follows:
in the formula:
in order to be a probability of failure,
in order to be able to determine the number of failed transmission towers,
number of samples of a typical sample library.
The second aspect of the present application provides a cluster-based device for rapidly analyzing vulnerability to wind load of a power transmission tower, which is characterized in that the device includes a processor and a memory:
the memory is used for storing the computer program and sending the instructions of the computer program to the processor;
the processor executes a cluster-based method for rapidly analyzing wind load vulnerability of a transmission tower according to instructions of a computer program.
In conclusion, the method and the equipment for rapidly analyzing the wind load vulnerability of the power transmission tower based on clustering are provided, the key structure parameters of each power transmission tower sample are selected, the key structure parameters are reduced into principal component indexes, the clustering indexes suitable for power transmission tower classification in the aspect of structure wind resistance can be obtained, then the k-means clustering algorithm is used for clustering analysis, and finally the vulnerability curve of the power transmission tower is obtained. The method can realize vulnerability analysis by using fewer typical samples instead of all samples, greatly improves the vulnerability analysis efficiency, and can make the typical samples more representative by selecting key structure parameters as the basis for power transmission tower classification. The calculation cost is reduced, the accuracy and the universal applicability of the general vulnerability curve result of the power transmission tower are guaranteed, and accurate and quick vulnerability assessment can be realized on the power transmission tower.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive exercise.
Fig. 1 is a schematic flow chart of a clustering-based method for rapidly analyzing vulnerability of wind load of a power transmission tower according to the present application;
FIG. 2 is a schematic flow chart of the classification of the transmission towers by using a k-means clustering algorithm according to the present application;
FIG. 3 is a schematic flow chart of a transmission tower vulnerability analysis performed on a part of a representative sample selected by the application;
FIG. 4 is a diagram of an example calculation result of the elbow discrimination method for determining the optimal classification number according to the present application.
Detailed Description
In order to make the objects, features and advantages of the present application more obvious and understandable, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the embodiments described below are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The vulnerability curve of the power transmission tower is a curve with the abscissa as the strength of the wind field and the ordinate as the failure probability of the power transmission tower. Because the structural characteristics of the transmission towers are similar, wind resistance check is often needed to be carried out on a batch of similar transmission towers of a certain line, failure probability of the transmission towers under different strengths is predicted, a large number of transmission towers are classified and then researched, or a small number of typical transmission towers are used for replacing all the transmission towers for relevant research, so that differences and connection among problems can be found, and the research can be more efficient.
k-means clustering is a classic dynamic clustering method. Clustering transmission towers can be interpreted as dividing a set of transmission tower samples into different classes or clusters according to a certain criterion (e.g., distance criterion) to achieve the following: the data of the transmission towers in the same cluster are similar as much as possible, and the data of the transmission tower samples which are not in the same cluster are different as much as possible. The principal component analysis is a classical statistical analysis method for integrating a plurality of parameters into a small number of principal component indexes, and a small number of indexes can reflect original information of a plurality of indexes as much as possible. The principal component index is a special linear combination of a plurality of common power transmission tower structure parameters, and the principal components are not linearly related.
Based on this, referring to fig. 1, an embodiment of the present application provides a method for quickly analyzing vulnerability of a wind load of a power transmission tower based on clustering, including the following steps:
s100: establishing a power transmission tower sample library, wherein the power transmission tower sample library comprises
Base transmission tower, note
And (4) sampling.
It should be noted that, the transmission tower sample library is created, that is, the transmission tower sample library of the area to be studied is created, and includes all the transmission towers to be studied, and each transmission tower is regarded as a sample.
S200: for obtaining transmission towers
A key structural parameter, will
The key structure parameter is subjected to dimensionality reduction treatment by adopting a principal component analysis method to obtain
The index of each main component.
It should be noted that, in this step, the key structural parameters of each transmission tower are selected as needed for clustering. The optimized key structure parameters at least comprise parameters of breath height, root cut, cross arm, main material section size and the like, and are recorded as
。
The principal component analysis is a classical statistical analysis method for integrating a plurality of parameter indexes into a small number of principal component indexes, and a small number of indexes can reflect original information of a plurality of indexes as much as possible. Index of principal component
Is that the above-mentioned
A key structural parameter
The specific linear combination of (2) is shown as formula (1), and the indexes of the main components are not linearly related.
In the formula:
is as follows
The indexes of the main components are shown in the specification,
is as follows
And (5) grouping linear combination relations.
The principal component analysis aims at reducing dimension and generally selects
The principal component index is used as a classification index.
S300: obtaining the initial classification number of the power transmission tower by using a Sturges empirical formula, and obtaining the sum of the initial classification number and the initial classification number
And (4) calculating and determining the optimal classification number k by utilizing an elbow discrimination method for each principal component index.
It should be noted that the optimal clustering effect is achieved when the power transmission tower samples are classified into k types, and the k value is determined according to the following steps:
1) obtaining a preliminary classification number according to a Sturges empirical formula preliminary estimation
The Sturges empirical formula is shown in formula (2),
in the formula:
for the purpose of the preliminary classification number,
the number of transmission towers. 2) Elbow discrimination method for determining optimal classification number k
Firstly, the mahalanobis distance and the sum of squared errors criterion are used to determine the optimal classification number k by the elbow discrimination method.
The method uses distance to describe the similarity between samples, and the distance in the method adopts mahalanobis distance. That is, a device sample g is set to have l-dimensional coordinates g = (p)1，p2，…，pl) The l-dimensional coordinate of the sample g 'is g' = (p)1’，p2’，…，pl') wherein p is1，p2，…，plThe index of the main component is l, and is called as a clustering index. The mahalanobis distance between g and g' is given by equation (3):
in the formula:
is composed of
The mahalanobis distance between, and Σ is the covariance matrix of the ensemble samples.
The clustering performance is evaluated using a sum of squared errors criterion function, which represents the degree of distortion of the cluster. Given a sample set G, assume that the samples in G can be clustered into k classesI.e. G contains k classification subsets G1，G2，…，Gk(ii) a The number of samples in each classification is m1，m2，…，mkThe clustering center points of the respective classifications are e1，e2，…，ek(ii) a The sum of squared errors criterion function, i.e. the degree of distortion, is shown in equation (4).
Where D is the sum of squared errors, reflecting the degree of distortion of the cluster. The smaller the value, the better the clustering effect.
To determine the optimal classification number k of the reference samples, respectively
（
As a preliminary estimate of the Sturges empirical formula), cluster analysis is performed and D is calculated. The abscissa is a classification number, the ordinate is a clustering distortion degree corresponding to the classification number to draw a broken line graph, the initial k value is increased, the distortion degree is obviously reduced, the distortion improvement degree is weakened after k is larger than a certain value, the shape of the maximum part of the broken line slope change is similar to that of an elbow, and the corresponding value is the most appropriate k value. The results of an example calculation are shown in fig. 4.
S400: and classifying the optimal classification number k of the power transmission tower by using a k-means clustering algorithm to obtain k clustering results.
Please refer to fig. 2, the classification of the transmission towers by using the k-means clustering algorithm specifically includes:
s401: generating k uniformly distributed initial clustering center points according to the optimal classification number k;
s402: calculating the Euclidean distance from each sample to each initial clustering center point;
s403: dividing the samples into classes represented by initial clustering center points with the closest distances, and generating k classes;
s404: respectively calculating k classified new clustering central points, and judging whether the new clustering central points are converged;
s405: if yes, outputting a clustering result containing k classifications, otherwise, executing step S402.
S500: and selecting typical samples according to the k clustering results to obtain a typical sample library with the number of samples.
It should be noted that, referring to fig. 3, it is first necessary to determine the number of acceptable typical samples, that is, a small number of typical samples are selected to calculate the general vulnerability curve of the transmission tower instead of all the samples, and the number of typical samples is selected according to the need, and 1/5 typical samples of the total number of samples are empirically selected to have good representativeness.
The typical samples are determined based on clustering results, and are uniformly spaced from the i = 1-k samples according to the distances between the samples and the clustering centers of the samples
And (4) forming a typical sample library with the number of samples n.
Is determined by the number of samples classified
And total number of samples
Is determined by the following formula (5):
the above has enabled dynamic classification of transmission towers and selection of a small number of typical transmission towers in place of all such transmission towers. The subsequent steps for researching the wind resistance vulnerability analysis of the power transmission tower are as follows:
s600: and establishing a finite element model of the typical sample library, and calculating the failure probability of the equipment under different wind strengths.
It should be noted that, firstly, the finite element model of the typical transmission tower selected in the previous step is established, and before calculating the failure probability of the equipment under different wind strengths, the number of failed equipment under the preset wind strength needs to be calculated. The commonly used failure judgment criteria for failure equipment include: the interlayer displacement angle exceeds a limit value, the tower top displacement exceeds a limit value, and the strength of the main material at the tower root exceeds a limit value.
When different wind strengths are respectively calculated, the failure probability of the transmission tower is calculated according to the calculation formula of the equipment failure probability as shown in formula (6):
in the formula:
in order to be a probability of failure,
in order to be able to determine the number of failed transmission towers,
is the number of samples of a typical sample library.
S700: and fitting the equipment failure probability by using a lognormal distribution function to obtain a vulnerability curve of the power transmission tower.
It should be noted that, generally, a lognormal distribution function is adopted for fitting, a curve passes through most points, and the best fitting is achieved when the sum of distances from each point to the curve is the minimum. According to the theory and the example experience, the vulnerability curve calculated according to the typical transmission tower is similar to the result calculated according to all the transmission towers, but the vulnerability curve obviously saves a great deal of time due to the small quantity. The obtained vulnerability curve can be used as a similar representation of the vulnerability curves of all m transmission tower samples.
According to the method, the clustering index which is suitable for classification of the power transmission tower in the aspect of structural wind resistance is obtained by determining the structural parameters of the power transmission tower and performing principal component analysis on the structural parameters. Then, the transmission towers are classified by using a classical k-means clustering algorithm, and a small number of typical transmission tower samples are selected from the classification to replace all the samples for vulnerability analysis. The method can realize dynamic classification of the power transmission tower according to different structure types of the power transmission tower, and selects the typical sample on the basis of the dynamic classification of the power transmission tower, so that the representativeness of the sample is good when finally performing vulnerability analysis, the calculation cost is greatly reduced, and the accuracy is ensured.
The above is a detailed description of an embodiment of the clustering-based power transmission tower wind load vulnerability rapid analysis method provided by the present application, and the following is a detailed description of an embodiment of the clustering-based power transmission tower wind load vulnerability rapid analysis method provided by the present application.
The utility model provides a quick analytical equipment of transmission tower wind load vulnerability based on clustering which characterized in that, equipment includes processor and memory:
the memory is used for storing the computer program and sending the instructions of the computer program to the processor;
the processor executes a method for rapidly analyzing the wind load vulnerability of the power transmission tower based on the clustering according to the embodiment according to the instructions of the computer program.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.
Claims (10)
1. A method for rapidly analyzing wind load vulnerability of a power transmission tower based on clustering is characterized by comprising the following steps:
s100: establishing a power transmission tower sample library, wherein the power transmission tower sample library comprises
Seat transmission tower sample, note
A sample is obtained;
s200: obtaining samples of each transmission tower in said library
A key structural parameter, to
The key structure parameter is subjected to dimensionality reduction treatment by adopting a principal component analysis method to obtain
A principal component index;
s300: the said is obtained by Sturges empirical formula
A preliminary classification number of individual samples, said preliminary classification number and said
Calculating and determining an optimal classification number k by using an elbow discrimination method for each principal component index;
s400: utilizing k-means clustering algorithm to the optimal classification number k to perform the classification on the optimal classification number k
Classifying the samples to obtain k clustering results;
s500: selecting typical samples according to the k clustering results to obtain the number of the samples
A representative sample library of;
s600: establishing a finite element model of the typical sample library, and calculating the failure probability of the equipment under different wind strengths;
s700: fitting the failure probability of the equipment by using a lognormal distribution function to obtain the failure probability of the equipment
Vulnerability curves for the transmission tower samples.
2. The method for rapidly analyzing wind load vulnerability of power transmission tower based on clustering according to claim 1, wherein in step S200, the method is adopted
The key structural parameters specifically include:
the cross arm, the cross arm and the main material are of the same cross section size.
3. The method for rapidly analyzing wind load vulnerability of power transmission tower based on clustering according to claim 2, wherein in the step S200, the method comprises
The key structure parameter is subjected to dimensionality reduction treatment by adopting a principal component analysis method to obtain
The main component indexes specifically comprise:
will be described in
Each key structural parameter is respectively according to
Combining the linear combination relationship to obtain
A principal component index of
All the main component indexes are linearly uncorrelated, and
。
4. the method for rapidly analyzing wind load vulnerability of power transmission towers based on clustering according to claim 1, wherein in the step S300, the Sturges empirical formula is specifically:
in the formula:
for the purpose of the preliminary classification number,
the number of transmission towers.
5. The method for rapidly analyzing the wind load vulnerability of the power transmission tower based on clustering according to claim 1, wherein the step S300 specifically comprises:
obtaining a preliminary classification number of the power transmission tower by using a Sturges empirical formula;
taking the preliminary classification number as a reference classification number, sequentially increasing the number of the reference classification number, and respectively according to the reference classification number
Calculating a cluster distortion degree corresponding to each reference classification number by each principal component index;
drawing a line graph by taking the reference classification number as a horizontal axis and the clustering distortion degree as a vertical axis;
and determining the reference classification number corresponding to the position with the maximum change of the slope of the broken line in the broken line graph as the optimal classification number.
6. The method for rapidly analyzing the wind load vulnerability of the power transmission tower based on clustering according to claim 5, wherein the step S400 specifically comprises:
s401: generating k uniformly distributed initial clustering center points according to the optimal classification number k;
s402: calculating the Euclidean distance from each sample to each initial clustering center point;
s403: dividing the sample into classes represented by the initial clustering central points with the nearest distance to generate k classes;
s404: respectively calculating new clustering central points of the k classifications, and judging whether the new clustering central points are converged;
s405: if yes, outputting a clustering result containing k classifications, otherwise, executing step S402.
7. The method for rapidly analyzing wind load vulnerability of transmission towers based on clustering according to claim 1 or 6, wherein in the step S500, the number of the typical samples is:
selecting the
In a sample
One sample was taken as a representative sample.
8. The method for rapidly analyzing the wind load vulnerability of the power transmission tower based on clustering according to claim 7, wherein the step S500 specifically comprises:
according to the distance from the sample to the cluster center, respectively
Uniformly spaced selection among clusters
A number of samples consisting of
A representative sample library of;
the above-mentioned
Determined according to the following formula:
in the formula:
for a typical number of samples selected in each cluster,
is the number of samples of a typical sample library,
is as follows
The number of samples in a cluster of samples,
total number of samples.
9. The method for rapidly analyzing the wind load vulnerability of the power transmission tower based on clustering according to claim 1, wherein in the step S600, the calculating the failure probability of the equipment under different wind intensities further comprises:
calculating the number of failure power transmission towers under preset wind strength, and calculating the failure probability of equipment under different wind strengths according to an equipment failure probability calculation formula;
the equipment failure probability calculation formula is as follows:
in the formula:
in order to be a probability of failure,
in order to be able to determine the number of failed transmission towers,
number of samples of a typical sample library.
10. A cluster-based rapid analysis device for wind load vulnerability of a power transmission tower is characterized by comprising a processor and a memory, wherein the processor is used for:
the memory is used for storing a computer program and sending instructions of the computer program to the processor;
the processor executes a cluster-based rapid analysis method of wind load vulnerability of transmission towers according to any one of claims 1-9 according to instructions of the computer program.
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