CN114004515A - Singular value decomposition-based transformer substation equipment health monitoring sensor arrangement method - Google Patents
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Abstract
The application provides a transformer substation equipment health monitoring sensor arrangement method based on singular value decomposition, which comprises the following steps: modeling and modal analysis are carried out on a target structure, and a basic vibration mode of the target structure is calculated; selecting a basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape; determining a first mode matrix of a target structure according to a target mode shape and a target mode; deleting the unmeasured freedom degree of the node to obtain a second modal matrix of the target structure; performing singular value decomposition on the second modal matrix, and extracting n left singular vectors corresponding to non-zero singular values to form a matrix H; computing H.H of left singular vectorTThe row and column of the smallest diagonal elementAnd deleting, and repeating iterative calculation until the number of the sensors reaches the preset number. The invention can obtain information which can reflect the change of the structural parameters as much as possible by using as few sensors as possible under the influence of environmental noise.
Description
Technical Field
The application relates to the field of health monitoring of power equipment of a transformer substation and auxiliary important building structures, in particular to a method for arranging health monitoring sensors of the power equipment of the transformer substation based on singular value decomposition.
Background
The structural health monitoring is to collect characteristic information of a target structure by utilizing various nondestructive sensors in a broad sense, and then predict various responses of the structure through systematic analysis of the collected information, so as to achieve the purpose of accurately detecting and discriminating structural damage and performance change. At present, it can be said that the research of structural health monitoring and damage detection mainly relies on the test of structural dynamic characteristics for analysis, so the modal testing technology becomes the main means of damage detection. When the modal test is carried out, the arrangement problem of the measuring points needs to be determined, namely the number of the measuring points needs to be determined, and the arrangement positions of the measuring points also need to be known.
In recent years, people have extensively studied the optimal arrangement problem of sensors and actuators in large flexible structures (mainly space structures in aviation and aerospace), and a plurality of measuring point optimization calculation methods are proposed, and each calculation method has advantages and disadvantages. For large flexible space structures, the optimal arrangement of the measuring points is mainly based on the following reasons: one is to minimize various costs, including: equipment cost, data processing and transmission and minimum data channel occupation; secondly, the point distribution schemes can obtain better model parameter estimation from noisy measurement data; thirdly, structure control is improved through a large-scale structure model; fourthly, the structural characteristics and the change thereof can be effectively determined, and the overall performance evaluation system of the structure is improved; fifthly, for a large flexible structure, the early damage identification capability of the structure is improved by optimizing the arrangement of the measuring points.
However, the structure of substation equipment is different from the spatial structure, and a very important gap between the two is the uncertainty of the modeling level. Because the two requirements on the precision of the structure are extremely different, the space structure often requires precise modeling, the requirement on model errors is very strict, if the structure is different from a transformer substation equipment structure with larger inertia, the aviation and aerospace structures are in a relatively wider bandwidth range and are easy to excite and respond, and the transformer substation equipment has relatively loose requirements on modeling and allows model errors, and the two requirements belong to different subjects. At present, for health monitoring summary of substation equipment, a sensor arrangement method has many defects.
Disclosure of Invention
The application provides a transformer substation equipment health monitoring sensor arrangement method based on singular value decomposition, and aims to solve the problem that the existing transformer substation equipment health monitoring sensor arrangement method is insufficient.
A method for arranging health monitoring sensors of substation equipment based on singular value decomposition comprises the following steps:
modeling and modal analysis are carried out on a target structure, and a basic mode shape of the target structure is calculated, wherein the target structure comprises a plurality of nodes;
selecting the basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape, wherein the mode is obtained by modeling the target structure;
determining a first mode matrix of the target structure according to the target mode shape and the target mode;
deleting the unmeasured degree of freedom of the node to obtain a second modal matrix of the target structure;
performing singular value decomposition on the second modal matrix, and extracting n left singular vectors corresponding to non-zero singular values to form a matrix H;
computing H.H of the left singular vectorTAnd deleting the row and column where the minimum diagonal element is positioned, and repeating iterative calculation until the number of the sensors in the preset number is reached.
Further, when the target mode shape is selected, the order of the basic mode shape is less than 10.
Further, the first preset order is sixth order.
Further, the second preset order is sixth order.
Further, the unmeasured degrees of freedom include a degree of freedom of a corner of the target structure and a degree of freedom in which a measurement point cannot be arranged.
Further, each row of the matrix H represents the contribution of each candidate degree of freedom to the total degree of freedom of the target structure.
Further, the number of sensors is determined by the monitoring needs of the target structure and the requirements of substation equipment.
According to the technical scheme, the method for arranging the health monitoring sensors of the substation equipment based on singular value decomposition comprises the following steps: modeling and modal analysis are carried out on a target structure, and a basic vibration mode of the target structure is calculated; selecting a basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape; determining a first mode matrix of a target structure according to a target mode shape and a target mode; deleting the unmeasured freedom degree of the node to obtain a second modal matrix of the target structure; performing singular value decomposition on the second modal matrix, and extracting n left singular vectors corresponding to non-zero singular values to form a matrix; and calculating the left singular vector, deleting the row and column where the minimum diagonal element is positioned, and repeating iterative calculation until the number of the sensors reaches the preset number. The invention can obtain information which can reflect the change of the structural parameters as much as possible by using as few sensors as possible under the influence of environmental noise. In addition, on the basis of the existing sensor arrangement, data can be mainly acquired by adding a new sensor to some special parts of the structure or interested partial modes, the point distribution scheme is sensitive to the damage of the structure, the structure and the performance of the sensor are comprehensively considered, and the cost of equipment, data transmission processing and the like is minimized.
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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 embodiments will be briefly described 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 to obtain other drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for arranging health monitoring sensors of substation equipment based on singular value decomposition according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a steel model cantilever beam discrete model provided by an embodiment of the present application;
FIG. 3 is a schematic diagram illustrating changes of maximum values of off-diagonal elements of a MAC rectangle with the number of measured points in five different stiffness distributions according to an embodiment of the present application;
fig. 4 is a schematic diagram of a calculation result of a singular value decomposition method under different stiffness distributions according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following specific embodiments of the present application and the accompanying drawings. It should be apparent that the described embodiments are only some 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 technical solutions provided by the embodiments of the present application are described in detail below with reference to the accompanying drawings.
The embodiment of the application is an optimization method for sensor arrangement, which can optimize a newly arranged sensor and an existing sensor arrangement. The method and the device can obtain information capable of reflecting structural parameter changes as much as possible by using the sensors as few as possible under the influence of noise such as noise generated by wind vibration, temperature difference and noise caused by sensor measurement errors, and can obtain response closer to an actual structure through monitoring data measured by the optimized sensors.
Fig. 1 is a schematic flow chart of a method for arranging health monitoring sensors of substation equipment based on singular value decomposition according to an embodiment of the present application, and as shown in fig. 1, the method for arranging health monitoring sensors of substation equipment based on singular value decomposition includes:
and S1, modeling and modal analysis are carried out on the target structure, and the basic mode shape of the target structure is calculated, wherein the target structure comprises a plurality of nodes.
In order to more fully understand the characteristics of the present application and the practical applicability of the present application to engineering, the embodiments of the present application take the common pillar type devices in substation equipment as prototypes for explanation. Fig. 2 is a schematic diagram of a steel model cantilever beam discrete model provided in an embodiment of the present application, and the steel model cantilever beam (hereinafter referred to as a cantilever beam) shown in fig. 2 is used as an example model in a target structure, in an embodiment, the cantilever beam can be discrete into 30 equal-length planar beam units, and the cantilever beam has 31 nodes in total. Each node has two translational (horizontal and vertical) degrees of freedom and one angular degree of freedom, and only in-plane vibration is considered in calculation.
The cantilever beam has a cross-sectional area, a cross-sectional moment of inertia, and a length, e.g., the cross-sectional area of the cantilever beam is 7.5 x 10-4m2With a cross-sectional moment of inertia of 1.406 × 10-8m4The specific structural units and node numbers are shown in fig. 2. The target structure is not limited by the application and can be determined according to the actual engineering situation.
And after the target structure is selected, modeling the target structure and carrying out modal analysis. Modal analysis is a method for researching the dynamic characteristics of a structure and is generally applied to the field of engineering vibration. The modes refer to the natural vibration characteristics of the mechanical structure, and each mode has a specific natural frequency, a specific damping ratio and a specific mode shape. The process of analyzing these modal parameters is called modal analysis. And calculating the basic mode shape of the target structure according to the modeling and mode analysis results of the target structure.
The vibration mode refers to the vibration mode inherent to the elastic body or the elastic system. The relative position of the particles when vibrating, i.e. the vibration curve, can be described. Since the multi-particle system has multiple degrees of freedom, multiple vibration modes can occur, and multiple natural frequencies exist, wherein the vibration mode corresponding to the minimum natural frequency (also called basic frequency) is the basic vibration mode.
S2, selecting a basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape, wherein the mode is obtained by modeling a target object;
after modeling the target, a modality can be obtained. For the electrical equipment of the substation, generally, the first 10 orders of the main basic mode shape can be selected to meet the requirement, that is, when the target mode shape is selected, the order of the basic mode shape is less than 10, and preferably, the first preset order is six orders, and the second preset order is six orders.
S3, determining a first mode matrix of the target structure according to the target mode shape and the target mode;
according to the actual engineering condition and the structure form, the first p main basic vibration modes are selected, and a first mode matrix such as phi formed by the p basic vibration modes to be monitored is determinedr×pThe first mode matrix is the theoretical calculation result, where r is the number of structural degrees of freedom. In one embodiment, the first six-order vertical fundamental mode shape is selected as the target mode shape, and the first six-order mode shape is selected as the target mode shape for the test. In order to compare the distribution of the sensor arrangement when the stiffness of the cantilever beam changes, the cantilever beam can be divided into two parts. 1-19 total 19 units are used as the first part, 20-30 total 11 units are used as the second part, and the section moments of inertia of the two parts are respectively I2And I1Representing the ratio of the stiffness of the second part to the first part I2/I1The distribution of the sensors along the cantilever beam was calculated at 0.01, 0.1, 1, 10 and 100, respectively. And under the distribution condition of five different rigidities, carrying out sensor optimization distribution point selection on the cantilever beam.
S4, deleting the unmeasured freedom degree of the node to obtain a second modal matrix of the target structure;
deleting the unmeasured degrees of freedom of the nodes, wherein the number of the residual degrees of freedom is n, and obtaining a new target modal matrix of the target structure, namely a second modal matrix phin×pAnd the unmeasured freedom degrees comprise the rotation angle freedom degree of the target structure and the freedom degree of the measuring point which cannot be arranged. The first mode matrix is a theoretical calculation result, the second mode matrix is a matrix after removing the non-measurable freedom degree, wherein the rest freedom degree is closer to the achievable monitoring scheme, and the reduction from the first mode matrix to the second mode matrix can be understood as a pairThe first step of the sensor placement optimization scheme.
S5, performing singular value decomposition on the second modal matrix, and extracting n left singular vectors corresponding to non-zero singular values to form a matrix H;
with reference to step S4, in an embodiment, the horizontal displacement and the rotational degree of freedom of the node may be deleted, 30 degrees of freedom of vertical displacement are retained, and then singular value decomposition is performed on the first six-order modal shape of 30 candidate points (the 30 degrees of freedom of vertical displacement are candidate points). Singular value decomposition is a matrix decomposition method, and is used for solving the target mode phi by using singular valuen×pAnd processing is carried out, n left singular vectors corresponding to the non-zero singular values are extracted, the n vectors form a matrix H, and each row of the matrix H represents the contribution of each candidate degree of freedom to the total degree of freedom of the target structure.
S6 calculating H.H of left singular vectorTAnd deleting the row and column where the minimum diagonal element is positioned, and repeating iterative calculation until the number of the sensors in the preset number is reached.
In the embodiment of the application, the number of the sensors is determined by the monitoring requirement of the target structure and the requirement of the substation equipment. Under the influence of environmental noise, the information which can reflect the change of the structural parameters can be obtained as much as possible by using the least sensors. In the case of existing sensors of the target structure, a new sensor can be added to perform data intensive acquisition on some special parts or interested partial modalities of the target structure. In order to enhance the health monitoring of the target structure, the point distribution scheme should be selected according to a certain principle, for example, when the sensors are arranged, the monitored data should be sensitive to the damage of the target structure. For another example, the target structure and the performance of the sensor should be considered together, so that the cost of the equipment, data transmission processing, etc. is minimized.
In step S6, H · H of the left singular vector is calculatedTAnd deleting the row and column where the minimum diagonal element is positioned according to the size of the diagonal element. Each row of the matrix H of n left singular vectors represents the contribution of each candidate degree of freedom to the total R. Repeating iterative calculation according to the above method, and deleting each timeOne candidate station until the number of sensor stations that need to be kept.
It should be noted that in the embodiment of the present application, the singular value decomposition of the second mode matrix results in the decomposition into the sum of several components, each component representing the contribution of the rows of the H matrix to the overall matrix. The contribution of each row vector to the correlation coefficient can be measured according to the size of the diagonal elements. If a value is small, indicating that the corresponding row contribution is small, it may be deleted first. Deleting the smallest diagonal element can reduce the degree of freedom to achieve the optimization effect.
Referring to table 1, table 1 selects a reference table for the sensor stations. In Table 1, the selection direction of the measurement points is from left to right, and when the former six-order mode is the target mode, the I is taken2/I1For example, if 6 measuring points are arranged, the positions of the measuring points should be six points of 30, 25, 20, 15, 10 and 5, and if 9 measuring points are arranged, the positions of the measuring points should be nine points of 30, 25, 20, 15, 10, 5, 26, 6 and 16. The selection direction of the measuring points indicates the contribution sequence of each measuring point to the effective independence size of the target mode. In this example, assuming that 15 measurement points are reserved (here, 15 are only the number of assumptions, which is obtained by iterative reduction of the optimization algorithm, and table 1 only schematically shows this process), the selection scheme of the final measurement point obtained by calculation is shown in table 1:
table 1: sensor measuring point selection reference table
Fig. 3 is a schematic diagram of changes of maximum values of off-diagonal elements of a MAC rectangle with the number of measured points in five different stiffness distributions provided in the embodiment of the present application. The MAC matrix (modal association criterion) is also called a mode correlation coefficient, is a dot product between mode vectors, is a tool for evaluating the correlation of the mode vector space (geometry), and has a calculated scalar value between 0 and 1 or is expressed by percentage. And (4) calculating a mode shape correlation coefficient (MAC) so as to check the quality of experimental model data.
The variation of the maximum value of the off-diagonal elements of the MAC rectangle with the number of the measuring points under the five different rigidity distribution conditions is shown in FIG. 3. In FIG. 3, the horizontal direction represents the number of measurement points, the vertical direction represents the maximum value of the MAC rectangular non-focusing element, and each curve represents I2/I1I.e. the stiffness ratio. As shown in fig. 3, under different rigidity distribution conditions, when there are the same number of measuring points, it can be seen from the arrangement of the measuring points that the distribution density of the measuring points is higher at the portion with lower rigidity; the part with high rigidity has lower density of measuring point distribution; when the stiffness is uniformly distributed, the distribution of the measurement points is also substantially uniformly distributed.
Fig. 4 is a schematic diagram of a calculation result of a singular value decomposition method under different stiffness distributions according to an embodiment of the present application. The schematic of the layout of 12 stations for five different stiffness profiles is shown in FIG. 4, where the 12 stations are the first 12 station positions of Table 1. In Table 4, I is shown from the top to the bottom2/I1The measuring points are distributed at 0.01, 0.1, 1, 10 and 100, and black triangular symbols represent the positions of the measuring points.
The method fully considers the feasibility and the convenience of arranging the monitoring sensors on the power equipment and the target structure in the actual engineering, such as an important building structure, is simple, can quickly obtain the measuring point positions and the measuring point number of the sensors, and has an obvious optimization effect. The structural model reflected by the actual measurement information can be used for correcting the error of the analysis model, so that the actual performance of the structure is reflected by the actual measurement structural mode.
According to the technical scheme, the method for arranging the health monitoring sensors of the substation equipment based on singular value decomposition comprises the following steps: modeling and modal analysis are carried out on a target structure, and a basic vibration mode of the target structure is calculated; selecting a basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape; determining a first mode matrix of a target structure according to a target mode shape and a target mode; deleting the unmeasured freedom degree of the node to obtain a second modal matrix of the target structure; singular value decomposition is carried out on the second modal matrix, and n left singular vectors corresponding to non-zero singular values are extracted to form a matrixH; computing H.H of left singular vectorTAnd deleting the row and column where the minimum diagonal element is positioned, and repeating iterative calculation until the number of the sensors in the preset number is reached. The invention can obtain information which can reflect the change of the structural parameters as much as possible by using as few sensors as possible under the influence of environmental noise. In addition, on the basis of the existing sensor arrangement, data can be mainly acquired by adding a new sensor to some special parts of the structure or interested partial modes, the point distribution scheme is sensitive to the damage of the structure, the structure and the performance of the sensor are comprehensively considered, and the cost of equipment, data transmission processing and the like is minimized.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains.
Claims (7)
1. A method for arranging health monitoring sensors of substation equipment based on singular value decomposition is characterized by comprising the following steps:
modeling and modal analysis are carried out on a target structure, and a basic mode shape of the target structure is calculated, wherein the target structure comprises a plurality of nodes;
selecting the basic mode shape of a first preset order as a target mode shape, and selecting a mode of a second preset order as a target mode shape, wherein the mode is obtained by modeling the target structure;
determining a first mode matrix of the target structure according to the target mode shape and the target mode;
deleting the unmeasured degree of freedom of the node to obtain a second modal matrix of the target structure;
performing singular value decomposition on the second modal matrix, and extracting n left singular vectors corresponding to non-zero singular values to form a matrix H;
computing H.H of the left singular vectorTAnd deleting the row and column where the minimum diagonal element is positioned, and repeating iterative calculation until the number of the sensors in the preset number is reached.
2. The singular value decomposition based substation equipment health monitoring sensor arrangement method of claim 1, wherein the order of the base mode shape is less than 10 when the target mode shape is selected.
3. The singular value decomposition-based substation equipment health monitoring sensor arrangement method of claim 1, wherein the first preset order is six orders.
4. The singular value decomposition-based substation equipment health monitoring sensor arrangement method of claim 1, wherein the second preset order is six.
5. The singular value decomposition-based substation equipment health monitoring sensor arrangement method according to claim 1, wherein the non-measurable degrees of freedom comprise a degree of freedom of turning of the target structure and a degree of freedom of not arranging measurement points.
6. The singular value decomposition based substation equipment health monitoring sensor arrangement method of claim 1, wherein each row of said matrix H represents the contribution of each candidate degree of freedom to the total degree of freedom of the target structure.
7. The singular value decomposition based substation equipment health monitoring sensor arrangement method of claim 1, wherein the number of sensors is determined by the monitoring needs of the target structure and the requirements of substation equipment.
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