CN115291054A - Non-gradient positioning method based on wavelet image convolution - Google Patents
Non-gradient positioning method based on wavelet image convolution Download PDFInfo
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Abstract
A non-gradient positioning method based on wavelet image convolution belongs to the technical field of power equipment online monitoring, and firstly provides a wavelet image convolution time delay estimation method which visually presents the time domain and frequency domain relation between collected signals, realizes accurate time delay estimation between partial discharge signals in a complex environment and lays a foundation for further accurate space positioning; by introducing the mode search method, a new solution thought is provided for the partial discharge positioning optimization problem, higher positioning precision is ensured, meanwhile, the derivative of an objective function does not need to be calculated in the positioning process, higher operation speed and higher output real-time performance are achieved, and positioning ambiguity caused by movement of a receiving end is effectively avoided. The positioning method provided by the invention can realize effective evaluation of the external insulation state of the power equipment in the environment with low signal-to-noise ratio, improve the field maintenance level and assist in making a decision maintenance plan.
Description
Technical Field
The invention provides a wavelet image convolution-based non-gradient positioning method, and belongs to the technical field of power equipment online monitoring.
Background
Abnormal corona and partial discharge are important causes of insulation deterioration of power equipment, and seriously threaten the safe operation of the power equipment. With the continuous increase of the scale of the power grid and the access quantity of the power equipment, the routing inspection work of abnormal discharge of the equipment and the line also faces a larger pressure. Therefore, a more intuitive, accurate and rapid discharge positioning method is sought, early warning and technical support are provided for state maintenance, and the method has important practical significance.
At present, the common partial discharge positioning methods can be classified into an optical positioning method, an ultrahigh frequency positioning method, an ultrasonic positioning method and the like in terms of sensing principle. The ultrasonic method has the characteristics of non-invasion, strong signal penetrability, strong anti-interference performance and the like, so that the ultrasonic method becomes a more common signal coupling method in partial discharge positioning. According to the input characteristic quantity of the ultrasonic space positioning algorithm, the method can be divided into the following steps: time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), and signal strength (RSS). The TDOA algorithm is high in positioning accuracy, low in hardware cost and computing power requirements and more suitable for field application. The time delay estimation and the spatial location are the core elements for determining the accuracy of the TDOA algorithm, so most of the research is currently carried out around the above elements.
Accurate time delay estimation is an important premise for accurate positioning of discharge, but is limited by the existing ultrasonic sensing technology, signal processing technology and multi-path acquisition hardware cost, and the signal-to-noise ratio and resolution of the obtained ultrasonic signals are not ideal under the actual environmental noise condition. Therefore, the selection and optimization of the ultrasonic signal delay acquisition algorithm are very important. The traditional threshold value method, the generalized cross correlation method and the energy accumulation method can not eliminate the influence of environmental noise on a time delay estimation result.
In the aspect of spatial positioning, a traditional algorithm solves a distance equation set based on a least square method, a maximum likelihood estimation method and the like, but delay estimation errors often cause that a spherical curve determined by an equation is difficult to intersect at a unique point, so that an accurate estimated position is inconvenient to obtain. In order to solve the problem that a closed analytic solution is difficult to obtain, a learner converts the solution of a distance equation set into an optimization problem by considering, and searches an approximate solution through an intelligent optimization algorithm.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method is characterized in that a wavelet image convolution-based non-gradient positioning method is provided, and the anti-noise performance of a wavelet image convolution algorithm and the accuracy of a non-gradient positioning algorithm are utilized to perform online monitoring on abnormal discharge of the power equipment.
A non-gradient positioning method based on wavelet image convolution is characterized in that: comprises the following steps which are sequentially carried out,
establishing a mathematical model of local discharge source positioning, and establishing a relation among a local discharge source position, a receiving sensor position and an arrival time difference through a TDOA method;
secondly, collecting the ultrasonic signal waveform of the partial discharge source signal by adopting an ultrasonic sensor array unit, and acquiring coordinate values in the mathematical model in the first step;
estimating time difference between signals received by the ultrasonic sensor array unit by a wavelet image convolution method, and estimating time delay;
and step four, combining the time delay estimation obtained in the step three, converting the equation system solving problem into an optimization problem by adopting a non-gradient search algorithm-mode search method, obtaining an approximate solution of the partial discharge position, and finishing the determination of the partial discharge position.
The mathematical model of the first step is that when the number of the sensors is 4,
in the formula, the coordinates T (x, y, z) of the partial discharge source and the sensor coordinates are S respectively 1 (x 1 ,y 1 ,z 1 )，S 2 (x 2 ,y 2 ,z 2 )，S 3 (x 3 ,y 3 ,z 3 )，S 4 (x 4 ,y 4 ,z 4 )；
When the number n of the sensors is more than 4, an optimized mathematical model is established,
wherein f is an objective function; t is t ji ＝t j -t i Is a sensor S j And a sensor S i I =1,2,. · n-1, j = i +1, ·, n.
In the second step, an ultrasonic sensing array unit is adopted to collect partial discharge source signals, spatial three-dimensional positioning is carried out, and more than 4 sensors are adopted to form an array; two-dimensional positioning of a plane is carried out, and more than 3 sensors are adopted to form an array.
The method for estimating the convolution time delay of the wavelet image in the third step comprises the following specific steps,
step one, performing wavelet transformation on an acquired ultrasonic signal, measuring the time domain-frequency domain correlation of the acquired signal, and representing the correlation in a time-frequency graph form;
evaluating the corresponding relation of the two signals in the partial discharge occurrence time interval through a given convolution function average value; translating one signal and performing dot product with the other signal to obtain the maximum value of the average value of the convolution function, wherein the product of the offset corresponding to the maximum value and the sampling time interval is the time delay value between the two signals;
and step three, calculating time delay values among all the acquired signals to finish time delay estimation.
The mode searching method comprises axial searching and mode searching, wherein each iteration comprises one axial searching and one mode searching, when the iteration times meet a set value, the iteration stops performing axial searching of a single coordinate axis according to x, y and z dimensions, and after the axial searching of all axes is completed, the mode searching is performed through a vector determined by an original starting point and an end point of the axial searching; and after the specified times of search is finished, obtaining x, y and z coordinates which are the discharge source position to be estimated.
The specific method of axial search and mode searchTo, based on an n-dimensional optimized mathematical model, assume a starting point
The base of the linear space in which the contour lines are located is e 1 ,e 2 ,...,e n The step length and the reduction factor of the axial search are delta and beta respectively, and the acceleration factor of the mode search is alpha; firstly judging fitness function values at each beginning, then sequentially carrying out axial search in the x direction, the y direction and the z direction, searching the positive direction and the negative direction in each dimension, and determining a proper search result within a given step length range; performing mode search, determining the vector direction of the mode search, obtaining the optimal value of the iteration in the step length range, and finishing the iteration; with the search, the search step length is continuously reduced, so that the change range of the fitness function value is reduced, a function updating threshold condition is added, and a search program is restarted when the function is locally optimal; and when the iteration times meet the iteration condition, finishing the determination of x, y and z coordinates of the partial discharge position.
Through the design scheme, the invention can bring the following beneficial effects: a non-gradient positioning method based on wavelet image convolution visually presents the time domain-frequency domain relation among collected signals through a wavelet image convolution algorithm, realizes accurate time delay estimation among partial discharge signals in a complex environment, and lays a foundation for further accurate space positioning; by introducing a mode search method, a new solution thought is provided for the optimization problem of partial discharge positioning, higher positioning precision is ensured, meanwhile, the derivative of an objective function does not need to be calculated in the positioning process, higher operation speed and output real-time performance are achieved, and positioning fuzziness caused by movement of a receiving end is effectively avoided. In conclusion, the provided positioning method can effectively evaluate the external insulation state of the power equipment in the environment with low signal to noise ratio, improve the field maintenance level and assist in making a decision-making maintenance plan.
Drawings
The invention is further described with reference to the following figures and detailed description:
FIG. 1 is a schematic diagram of a partial discharge localization model according to the present invention.
Fig. 2 is a flow chart of the time delay estimation by the wavelet image convolution method according to the present invention.
FIG. 3 is a schematic diagram of the basic principle of the pattern search method of the present invention.
FIG. 4 is a flow chart of an algorithm implementation of the pattern search method of the present invention.
Detailed Description
A wavelet image convolution-based non-gradient positioning method is shown in figures 1-4 and comprises a proposed wavelet image convolution time delay estimation method and a non-gradient positioning method introducing positioning.
Firstly, a partial discharge mathematical model of an object to be detected is established, and a specific model diagram is shown in fig. 1. And listing a distance equation set or an optimization solving expression according to the sensor position and the partial discharge position information, and representing the relative relation in the space.
Assuming the coordinates T (x, y, z) of the partial discharge source, the sensor coordinates are S, respectively 1 (x 1 ,y 1 ,z 1 )，S 2 (x 2 ,y 2 ,z 2 )，S 3 (x 3 ,y 3 ,z 3 )，S 4 (x 4 ,y 4 ,z 4 ) Then, the distance relationship between each sensor and the local discharge source is expressed as:
when the number of sensors n is greater than 4, the above equation set has redundancy equations, and the problem can be transformed into an optimization problem:
wherein f represents an objective function; t is t ji ＝t j -t i Indicating the sensor S j And a sensor S i I =1,2,. · n-1, j = i +1, · n; to make full use of redundant information between sensors and avoid the problem of choosing the arrival time as a reference, the followingThe expression for solving the minimum value utilizes the estimation results among all sensors.
The non-gradient positioning method based on wavelet image convolution is characterized in that: the core of solving the optimization problem is in time delay estimation and space positioning, wherein the time delay estimation is the time difference t in the solving expression ji And determining the position of the partial discharge source to be detected by solving an equation system or an optimization problem in space positioning.
Secondly, in order to realize positioning, a sensor array is used for collecting partial discharge ultrasonic signals, and at least four sensors are needed to meet the observation quantity required in a partial discharge mathematical model for the three-dimensional positioning problem in space; for two-dimensional positioning of a plane, at least 3 sensors are required to form an array.
Secondly, for the ultrasonic signals acquired by the ultrasonic sensor array, the time delay estimation is carried out by a wavelet image convolution time delay estimation method, and the schematic diagram of the algorithm principle is shown in fig. 2. And providing an accurate time delay value for subsequent positioning. Processing collected partial discharge ultrasonic signals through wavelet transformation to obtain a time-frequency relation between the signals, then evaluating a corresponding relation of a partial discharge occurrence time interval through a given convolution function average value, and calculating a maximum value of the convolution function average value in a translation process, wherein the corresponding translation time is a time delay value between the two signals; calculating time delay values among all the acquired signals to finish time delay estimation; then, in order to solve the model optimization problem, a non-gradient search algorithm-mode search method is introduced to solve the local discharge optimization problem by combining the time delay estimation value obtained by the method, the mode search method is mainly divided into axial search and mode search, the axial search of a single coordinate axis is firstly carried out according to the dimensionality, and after the axial search of all the dimensionalities is completed, the mode search is carried out through the vector determined by the original starting point and the axial search end point; each iteration comprises one axial search and one mode search, and the iteration is stopped when the iteration number meets a set value. The basic principle diagram of the pattern search method is shown in fig. 3. Assume a starting point
The base of the linear space in which the contour lines are located is e 1 ,e 2 ,...,e n (ii) a The step length and the reduction factor of the axial search are delta and beta respectively; the acceleration factor of the pattern search is alpha, and the specific flow is shown in fig. 4; firstly judging fitness function values at each beginning, then sequentially carrying out axial search in the x direction, the y direction and the z direction, searching the positive direction and the negative direction in each dimension, and determining a proper search result within a given step length range; and performing mode search, determining the vector direction of the mode search according to the starting point and the axial search result of the previous step, obtaining the optimal value of the iteration in the step length range, and finishing the iteration.
With the search, the search step length is continuously reduced, so that the change range of the fitness function value is possibly small, a function updating threshold condition is added, and a search program is restarted when the function is locally optimal; and when the iteration times meet the iteration condition, finishing the determination of x, y and z coordinates of the partial discharge position.
Claims (6)
1. A non-gradient positioning method based on wavelet image convolution is characterized in that: comprises the following steps which are sequentially carried out,
establishing a mathematical model of local discharge source positioning, and establishing a relation among a local discharge source position, a receiving sensor position and an arrival time difference through a TDOA method;
secondly, collecting ultrasonic signal waveforms of the partial discharge source signals by adopting an ultrasonic sensor array unit, and acquiring coordinate values in the mathematical model in the first step;
estimating time difference between signals received by the ultrasonic sensor array unit by a wavelet image convolution method, and estimating time delay;
and step four, combining the time delay estimation obtained in the step three, converting the equation system solving problem into an optimization problem by adopting a non-gradient search algorithm-mode search method, obtaining an approximate solution of the partial discharge position, and finishing the determination of the partial discharge position.
2. The wavelet image convolution-based non-gradient localization method according to claim 1, characterized in that: the mathematical model of the first step is that, when the number of the sensors is 4,
in the formula, the coordinates T (x, y, z) of the partial discharge source and the sensor coordinates are S respectively 1 (x 1 ,y 1 ,z 1 )，S 2 (x 2 ,y 2 ,z 2 )，S 3 (x 3 ,y 3 ,z 3 )，S 4 (x 4 ,y 4 ,z 4 )；
When the number n of the sensors is more than 4, an optimized mathematical model is established,
wherein f is an objective function; t is t ji ＝t j -t i Is a sensor S j And a sensor S i I =1,2,. · n-1, j = i +1, ·, n.
3. The wavelet image convolution-based non-gradient localization method according to claim 1, characterized in that: in the second step, an ultrasonic sensing array unit is adopted to collect partial discharge source signals, spatial three-dimensional positioning is carried out, and more than 4 sensors are adopted to form an array; two-dimensional positioning of a plane is carried out, and more than 3 sensors are adopted to form an array.
4. The wavelet image convolution-based non-gradient positioning method according to claim 1, characterized in that: the method for estimating the convolution time delay of the wavelet image in the third step comprises the following specific steps,
step one, performing wavelet transformation on the acquired ultrasonic signals, measuring the time domain-frequency domain correlation of the acquired signals, and representing the correlation in a time-frequency diagram form;
evaluating the corresponding relation of the two signals in the local discharge occurrence time interval through a given convolution function average value; translating one signal and performing dot product with the other signal to calculate the maximum value of the average value of the convolution function, wherein the product of the offset corresponding to the maximum value and the sampling time interval is the time delay value between the two signals;
and step three, calculating time delay values among all the acquired signals to finish time delay estimation.
5. The wavelet image convolution-based non-gradient localization method according to claim 1, characterized in that: the step four-mode search method comprises axial search and mode search, each iteration comprises one axial search and one mode search, and the iteration is stopped when the iteration times meet a set value; respectively carrying out axial search of a single coordinate axis according to x, y and z dimensions, and carrying out mode search through the original starting point and a vector determined by the axial search end point after completing the axial search of all axes; and after the specified times of search is finished, obtaining x, y and z coordinates which are the discharge source position to be estimated.
6. The wavelet image convolution-based non-gradient localization method according to claim 5, wherein: the specific method of the axial search and the mode search is that an initial point is assumed based on an n-dimensional optimization mathematical model
The base of the linear space in which the contour lines are located is e 1 ,e 2 ,...,e n The step length and the reduction factor of the axial search are delta and beta respectively, and the acceleration factor of the mode search is alpha; firstly judging fitness function values at each beginning, then sequentially carrying out axial search in the x direction, the y direction and the z direction, searching the positive direction and the negative direction in each dimension, and determining a proper search result within a given step length range; performing mode search, determining the vector direction of the mode search, obtaining the optimal value of the iteration in the step length range, and finishing the iteration; the search step size is continuously reduced as the search progressesReducing the variation range of the fitness function value, additionally arranging a function updating threshold condition, and restarting a search program when the function is locally optimal; and when the iteration times meet the iteration condition, finishing the determination of x, y and z coordinates of the partial discharge position.
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