CN110376290A - Acoustic emission source locating method based on multidimensional Density Estimator - Google Patents
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Abstract
The invention discloses a kind of acoustic emission source locating methods based on multidimensional Density Estimator.Firstly, the then data to acoustic emission sensor are combined, multiple groups then data are obtained；Equation group is just determined according to different then data combination buildings is corresponding.Each equation group is solved, multiple groups closed solutions are obtained, the closed solutions comprising imaginary root is screened out, r can be obtained0A Primary Location result.Secondly, excluding the abnormal positioning result in Primary Location result, r Primary Location result is finally obtained.Again, the multidimensional Density Estimator function of r Primary Location result building acoustic emission source coordinate θ is utilizedFinally, seeking multidimensional Density Estimator functionMaximum point, which is optimal acoustic emission source positioning result.The method of the present invention positioning accuracy is high.
Description
Technical Field
The invention relates to an acoustic emission source positioning method based on multi-dimensional nuclear density estimation.
Technical Field
The acoustic emission positioning technology is widely applied to the fields of structural integrity monitoring, material damage mechanism research, mine risk early warning and the like. However, due to complicated experimental conditions and a noisy construction environment, an acoustic emission waveform including arrival time information detected by an acoustic emission sensor in an acoustic emission detection (positioning) process is often influenced by an interference signal to generate abnormal arrival times. In addition, the subjectivity of artificial arrival time picking and the limitation of the existing arrival time picking algorithm also cause the acquired arrival time data to be often mixed with abnormal data. And the accuracy of the positioning result is seriously influenced by the abnormal data. For this reason, the invention patent with application number CN201510973875.4 proposes a signal source positioning method for uniform velocity field, which can obtain a more ideal positioning result when the number of abnormal values is small, but the probability of positioning failure of the method is greatly increased when the number of abnormal values is large. The invention patent with the application number of CN201610571666.1 provides a method for recognizing microseismic or acoustic emission abnormal arrival time data based on minimum distance, and the method can better determine the abnormal arrival time data under the condition that only one abnormal value exists. However, in a real engineering environment, whether or not an abnormal value is included and the number of abnormal values are often not predetermined. The invention patent with application number CN201610571029.4 further provides a method for determining the arrival time of microseism or acoustic emission anomaly, which uses Logistic probability distribution to determine the anomaly value, and the method further improves the accuracy of determining the data of the arrival time of anomaly, but the method adopts a conjugate gradient method or a marquardt method (iterative method) to obtain the initial positioning result, which greatly reduces the calculation efficiency. In addition, the criterion of the abnormal arrival time data is difficult to accurately obtain, and the data of the initial positioning result is difficult to obey a certain specific distribution due to different environmental noises and the number and the size of the abnormal arrival time, so that the method is not reasonable for the assumption that each parameter of the initial positioning result obeys Logistic distribution, so that a larger error still exists in the determination of the abnormal value, and the calculation accuracy of the subsequent sound emission source coordinate is influenced. Therefore, further research is still urgently needed for acoustic emission source localization problems that contain abnormal arrival time data.
Disclosure of Invention
The invention aims to solve the technical problem that the existing acoustic emission positioning technology is easily influenced by abnormal arrival time data, and provides an acoustic emission source positioning method based on multi-dimensional nuclear density estimation.
The technical scheme provided by the invention is as follows:
an acoustic emission source positioning method based on multi-dimensional nuclear density estimation comprises the following steps:
step 1, combining arrival time data of each acoustic emission sensor in an acoustic emission detection system to obtain multiple groups of arrival time data; obtaining a plurality of preliminary positioning results based on the plurality of groups of arrival time data;
step 2, constructing a multi-dimensional kernel density estimation function of the acoustic emission source coordinate theta by using the obtained multiple primary positioning results
Step 3, solving a multidimensional kernel density estimation functionThe maximum point is the optimal acoustic emission source positioning result.
In the step 1, based on the plurality of sets of arrival time data, a method disclosed in the prior art, such as an analytic positioning algorithm or a numerical positioning method disclosed in the invention patent with application number CN201610571666.1 (the method selects 6 arrival time numbers each time to obtain a positioning result), or a conjugate gradient method or a marquardt method disclosed in the invention patent with application number CN201610571029.4, may be used to obtain a plurality of preliminary positioning results.
Further, in the step 1, the meter is reducedCalculating amount and improving calculation efficiency, the invention also provides a method for obtaining a preliminary positioning result, namely, a set equation set is constructed according to each set of arrival time data, and unknowns in the set equation set are coordinates (X, Y and Z) of an acoustic emission source, the average wave speed v of an acoustic emission signal propagation medium and the triggering time t of the acoustic emission signal; respectively solving each set of the equations to obtain a plurality of closed-form solutions, screening out the closed-form solutions containing the virtual root, and using the rest r0Combined solution to obtain acoustic emission source r0And (5) obtaining a preliminary positioning result.
Further, in the step 1, each set of arrival-time data includes arrival-time data of 5 acoustic emission sensors; the set of equations constructed from a set of arrival time data is:
wherein, (X, Y, Z) is the coordinate of the acoustic emission source, v is the average wave velocity of the acoustic emission signal propagation medium, t is the triggering time of the acoustic emission signal, v and t are unknown numbers, and the rest are known; t is tiFor the ith arrival time data in the set of arrival time data, (x)i,yi,zi) Is tiCorresponding acoustic emission sensor SiThe coordinates of (a).
Further, the closed form solution of the set of equations is defined as:
wherein,
p＝a3b4c5-a3b5c4-a4b3c5+a4b5c3+a5b3c4-a5b4c3
furthermore, the unknown parameter ω can be obtained by solving the following one-dimensional cubic equation:
Aω3+Bω2+Cω+D＝0
wherein, A, B, C and D are constants, and their expressions are:
and,
wherein m isi(i＝1,2,3)、ni(i＝1,2,3)、w、p、ai(i＝3,4,5)、bi(i＝3,4,5)、ci(i＝3,4,5)、di(i＝3,4,5)、ei(i＝3,4,5)、xi,1(i＝2,3,4,5)、yi,1(i＝2,3,4,5)、zi,1(i＝2,3,4,5)、ti,1(i＝2,3,4,5)、Li,1(i＝2,3,4,5)、A、B、C、D、Q1、Q2Are all intermediate variables. The inventionThe triggering time t of the acoustic emission signal is not solved.
Further, in the step 3, firstly, each preliminary positioning result obtained in the step 2 is calculated, and the euclidean distance between the preliminary positioning result and the origin is calculated; then based on the calculated Euclidean distance, r is eliminated by combining a quartile method0And obtaining r initial positioning results finally according to the abnormal positioning results in the initial positioning results.
Further, r is excluded0And obtaining r initial positioning results finally according to the abnormal positioning results in the initial positioning results.
Further, the method for eliminating the abnormal positioning result comprises the following steps: first to r0Calculating the Euclidean distance from each initial positioning result to the origin point respectively; then based on the calculated Euclidean distance, r is eliminated by combining a quartile method0And obtaining r initial positioning results finally according to the abnormal positioning results in the initial positioning results.
Further, the euclidean distance from the jth preliminary positioning result to the origin is:
wherein (X)j,Yj,Zj) As the jth primary positioning result, j is 1,2, …, r0。
Further, based on the calculated Euclidean distance, r is excluded by combining a quartile method0The abnormal positioning result in the initial positioning result is specifically as follows: if sj＞q3+1.5(q3-q1) Or sj＜q1-1.5(q3-q1) If so, the jth preliminary positioning result is considered as an abnormal positioning result and is eliminated; wherein q is1Is r0The first quartile of Euclidean distance, q, from the initial positioning result to the origin3Is r0A third quartile of Euclidean distance from the initial positioning result to the origin, j being 1,2, …, r0. The existing quartile position determination methods are of several kinds, and the invention can adopt any one of the quartile position determination methodsA method.
Further, in step 2, a multi-dimensional (multi-component) kernel density estimation function of the coordinates θ of the acoustic emission sourceThe specific expression form is as follows:
wherein θ ═ θ1,θ2,θ3) (X, Y, Z) is a multivariate random vector of the probability density function f (θ), i.e., the acoustic emission source coordinates; theta1、θ2And theta3X, Y and Z, respectively; thetaj,1、θj,2And thetaj,3Respectively represent Xj、YjAnd Zj；(θj,1,θj,2,θj,3)＝(Xj,Yj,Zj) The method comprises the steps that j is the jth multivariate random sample of a probability density function f (theta), namely the jth preliminary positioning result, j is 1,2, …, r, r is the number of the preliminary positioning results finally obtained in the step 1; d is an element position index in the variable theta, 1,2 and 3; k (-) is a kernel function.
Further, the kernel function adopts a probability density function of standard normal distribution (in the multidimensional kernel density estimation, the kernel function adopts the probability density function of standard normal distribution, that is, normal information diffusion is performed), and the expression is as follows:
wherein h isdFor bandwidth, the concrete expression is:
wherein sigmadThe scale parameter is expressed in the following specific form:
where med (-) represents the median.
Further, in step 3, the function is estimated by multidimensional kernel densityAnd (3) searching the maximum value of the target function by adopting an iteration method, taking the average value of r primary positioning results obtained in the step (3) as initial acoustic emission source coordinates (X, Y and Z) in the searching process, continuously correcting the coordinates (X, Y and Z) to find the optimal acoustic emission source coordinates, terminating iteration when an iteration termination condition is met, and obtaining the final corrected result, namely the optimal acoustic emission source coordinates.
Further, the iteration termination condition is: when the variable quantity of the objective function value obtained by two adjacent iterative computations is smaller than a preset value, the step length of X, Y and Z correction is smaller than the preset value or the iteration number exceeds the preset value.
Has the advantages that:
1) the method gives a closed-form solution of acoustic emission source parameters under a set equation set, does not invert the triggering time, uses five arrival time data for positioning each time, is one less than the traditional method, reduces the calculation amount, and can ensure the positioning precision each time;
2) according to the method, the abnormal positioning result in the primary positioning result is eliminated through the quartile method, so that the fitting of the multidimensional probability kernel density function is better, and the over-fitting phenomenon is avoided;
3) the multi-dimensional nuclear density estimation method does not utilize prior knowledge of data distribution of the primary positioning result by adopting multi-dimensional nuclear density estimation, does not need to carry out any additional assumption on the data distribution, starts from the data of the primary positioning result, obtains more accurate density estimation, and avoids errors caused by unreasonable assumed distribution. The method ensures the accuracy and robustness of the obtained positioning result from the statistical angle of non-parameter estimation, so that a more ideal positioning result can be obtained even if the time-out error is serious;
4) the method adopts a multi-dimensional nuclear density estimation model, considers the correlation between the acoustic emission parameters X, Y and Z, and has higher accuracy;
5) the method takes the average value of a plurality of preliminary positioning results with small deviation as an iteration initial value, and adopts an iteration method to search the maximum value of the multidimensional kernel density function, so that the efficiency of searching the extreme value of the function can be improved while the search is prevented from getting into local optimum;
6) compared with the traditional method, the method has very obvious stability, is more suitable for the practical engineering practice problem, and better solves the technical problems of unstable positioning result and low positioning precision caused by the fact that time data in the acoustic emission positioning field contains abnormal values.
Drawings
FIG. 1 is a flow chart of method steps according to an embodiment of the present invention.
FIG. 2 is a comparison of positioning results of the method of the present invention with other methods.
Detailed description of the invention
An acoustic emission source is preset with coordinates S (110, 160, 180) and is surrounded by 9 acoustic emission sensors with coordinates a (0,0,0), B (300,0,0), C (300, 0), D (0,300,0), E (0,0,300), F (300,0,300), G (300,300,300), H (0,300,300), I (300,150,150). The units are all mm. The wave velocity is unknown. In the test, a group of arrival time data is generated by a simulation method, the influence of environmental noise on positioning is simulated by adding an error with a variance of 0.2 mu s in the obtained arrival time data, and in addition, a large error of +/-5 mu s is randomly added to one arrival time data to simulate the interference of an abnormal value. The set of arrival time data generated by the above random process is: 38.38, 42.90, 40.89, 50.75, 53.10, 53.13, 55.27, 59.41, 61.55, in μ s.
The method is explained in detail by this example. For the sake of clarity, the method of the present invention is illustrated in the following five steps:
(1) closed form solution of the set of equations is defined:
in this example, there are 9 total arrival time data, and each time 5 arrival time data are selected, a set of the determined equations can be formed,can be obtained by different combinationsEach set of the defined equations is solved to obtain multiple closed-form solutions, and the closed-form solutions with virtual root are excluded from the rest r0(r083) to obtain r of acoustic emission source0(r083) preliminary positioning results, as shown in table 1. This example shows the calculation of the closed-form solution of only one set of equations for the construction of the selected arrival time data 38.38, 42.90, 40.89, 50.75 and 59.41 (in mus) as follows
Firstly, the formula
Is calculated to obtain
Second formula of
Is calculated to obtain
And can then calculate
p＝a3b4c5-a3b5c4-a4b3c5+a4b5c3+a5b3c4-a5b4c3＝1.18×1015
In addition, the unknown parameter ω can be obtained by solving the following cubic equation
Aω3+Bω2+Cω+D＝0
Wherein, the specific expressions of the coefficients A, B, C and D are respectively
And,
calculated, the only real solution of omega excluding the imaginary root is 2.90 x 107。
Finally, a preliminary localization result (acoustic emission source coordinates) of the acoustic emission source can be obtained from the set of equations:
table 1: 83 groups of screened localization results
(2) Calculation of Euclidean distance of acoustic emission source to origin
According to the formula
Calculating the Euclidean distance s from the jth primary positioning result to the originjThe specific calculation results are shown in table 1.
(3) Method for eliminating abnormal group by quartile method
The specific formula of the quartile method for eliminating the abnormal positioning result in the preliminary positioning result is as follows:
wherein q is1Is the first quartile of data, q3Is the third quartile of data.
R is calculated according to the quartile method0(r083) a first quartile and a third quartile of Euclidean distances of the preliminary positioning results to the origin, which are q respectively1＝260.21×103，q3＝266.49×103. The criteria from which the anomaly groups can be derived are:
according to the criterion, 13 groups with abnormity are excluded, and r (r is 70) primary positioning results are remained, and the specific results are shown in table 1.
(4) Calculation of scale parameters
Scale parameter σdThe specific expression form of (A) is as follows:
where r is 70, calculated to give:
σ1＝1.78×10-3,σ2＝1.49×10-3,σ3＝2.09×10-3。
(5) calculation of a bandwidth matrix
The bandwidth matrix H is a diagonal matrix, H1/2The vector elements of the main diagonal of (a) may be expressed as:
calculating a normal scale parameter sigma according to the step (4)dCan obtain hdAre respectively as follows:
h1＝9.39×10-4,h2＝7.86×10-4,h3＝11.04×10-4
(6) constructing a multi-dimensional kernel density estimation function
Multidimensional kernel density estimation functionComprises the following steps:
wherein, the kernel function k (·) adopts a probability density function of standard normal distribution, and the expression is as follows:
finally, the expression of the multidimensional kernel density estimation function can be obtained as follows:
(7) calculation of optimal positioning results
Searching the maximum value of a multi-dimensional nuclear density estimation function by adopting an iteration method, selecting an average value (110.38,156.52,180.68) (unit: mm) of 70 groups of initial positioning results as initial acoustic emission source coordinates (X, Y, Z) in the iteration searching process, and continuously correcting the coordinates (X, Y, Z) to find an optimal solution, wherein the deviation between the initial value and the true value is large at the initial searching stage, so that the step length of X, Y and Z correction is large; the X, Y and Z correction steps become smaller and smaller as the real value is continuously approached, and when the variation of the objective function value obtained by two adjacent iterative computations is less than 10-6Or both acoustic source coordinates X, Y and the step size of the Z correction are less than 10-6m, or the number of iterations exceeds 25, the iteration terminates. The result of the last correction (110.29160.09179.89) (unit: mm) is the optimal acoustic source coordinates, which fit well with the real coordinates S (110, 160, 180) (unit: mm) with high positioning accuracy.
The method has the following three advantages that (1) a closed-type solution of the coordinates of the acoustic emission source under a set equation is given, the least arrival time data can be used each time during positioning, inversion does not need to be carried out on the triggering time, and the calculation efficiency is improved. (2) A multi-dimensional kernel density estimation model is adopted, and the correlation advantage among parameters is considered; (3) by adopting the parameter-free estimation, the prior knowledge of data is not needed, the prior distribution of data is not needed to be assumed, the applicability is wider, and the accuracy is higher.
The New positioning method (New) disclosed by the invention is respectively compared with a two-step weighted least square method (2WLS), a non-iterative unknown wave velocity system acoustic emission source analytic positioning method (NIUV) and a comprehensive analytic method (CAS), and the positioning result is shown in figure 2. Compared with the traditional method, the method has higher positioning accuracy, and can better solve the problems of unstable positioning result and low positioning accuracy caused by overlarge picking error in acoustic emission positioning.
Claims (10)
1. An acoustic emission source localization method based on multi-dimensional nuclear density estimation is characterized by comprising the following steps:
step 1, combining arrival time data of each acoustic emission sensor in an acoustic emission detection system to obtain multiple groups of arrival time data; obtaining a plurality of preliminary positioning results based on the plurality of groups of arrival time data;
step 2, constructing a multi-dimensional kernel density estimation function of the acoustic emission source coordinate theta by using the obtained multiple primary positioning results
Step 3, solving a multidimensional kernel density estimation functionThe maximum point is the optimal acoustic emission source positioning result.
2. The method for positioning an acoustic emission source based on multi-dimensional nuclear density estimation according to claim 1, wherein in the step 1, a set of predetermined equations is constructed according to each set of arrival time data, and the unknowns in the set of predetermined equations are coordinates of the acoustic emission source, an average wave speed of a propagation medium of the acoustic emission signal, and a trigger time of the acoustic emission signal; respectively solving each set of the equations to obtain a plurality of closed-form solutions, screening out the closed-form solutions containing the virtual root, and using the rest r0Combined solution to obtain r0And (5) obtaining a preliminary positioning result.
3. The method according to claim 2, wherein each set of arrival time data in step 1 comprises arrival time data of 5 acoustic emission sensors; the set of equations constructed from a set of arrival time data is:
wherein (X, Y, Z) is the coordinate of the acoustic emission source, v is the average wave velocity of the acoustic emission signal propagation medium, and t is the acoustic emission signalThe triggering time of the number, v and t are unknown numbers, and the rest are known; t is tiFor the ith arrival time data in the set of arrival time data, (x)i,yi,zi) Is tiCorresponding acoustic emission sensor SiThe coordinates of (a).
4. The method of claim 2, wherein r is excluded from the multi-dimensional nuclear density estimation-based acoustic emission source localization0And obtaining r initial positioning results finally according to the abnormal positioning results in the initial positioning results.
5. The method of claim 4, wherein the method of excluding outlier localization results comprises: first to r0Calculating the Euclidean distance from each initial positioning result to the origin point respectively; then based on the calculated Euclidean distance, r is eliminated by combining a quartile method0And obtaining r initial positioning results finally according to the abnormal positioning results in the initial positioning results.
6. The method of claim 5, wherein the Euclidean distance from the origin of the jth preliminary localization result to the origin is:
wherein (X)j,Yj,Zj) As the jth primary positioning result, j is 1,2, …, r0。
7. The method of claim 6, wherein r is excluded by using a quartile method based on the calculated Euclidean distance0The abnormal positioning result in the initial positioning result is specifically as follows: if sj＞q3+1.5(q3-q1) Or sj＜q1-1.5(q3-q1) If so, the jth preliminary positioning result is considered as an abnormal positioning result and is eliminated; wherein q is1Is r0The first quartile of Euclidean distance, q, from the initial positioning result to the origin3Is r0A third quartile of the Euclidean distance of the preliminary positioning result to the origin.
8. The method for acoustic emission source localization according to claim 1, wherein in step 2, the multi-dimensional kernel density estimation functionThe specific expression form is as follows:
wherein θ ═ (X, Y, Z) is the acoustic emission source coordinates; theta1、θ2And theta3X, Y and Z, respectively; thetaj,1、θj,2And thetaj,3Respectively represent Xj、YjAnd Zj；(Xj,Yj,Zj) For the jth primary positioning result, j is 1,2, …, r and r are the number of the initial positioning results finally obtained in the step 1; d is 1,2,3 is an element position index in the variable theta; k (-) is a kernel function.
9. The method of claim 8, wherein the kernel function is a probability density function of a standard normal distribution, and the expression is as follows:
wherein h isdFor bandwidth, the concrete expression is:
wherein sigmadThe scale parameter is expressed in the following specific form:
where med (-) represents the median.
10. The method according to claim 8, wherein in step 3, the function is estimated using multi-dimensional kernel densityAnd (3) searching the maximum value of the target function by adopting an iteration method, taking the average value of r primary positioning results obtained in the step (3) as initial acoustic emission source coordinates (X, Y and Z) in the searching process, continuously correcting the coordinates (X, Y and Z) to find the optimal acoustic emission source coordinates, terminating iteration when an iteration termination condition is met, and obtaining the final corrected result, namely the optimal acoustic emission source coordinates.
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| CN112098947A (en) * | 2020-09-27 | 2020-12-18 | 中南大学 | CTLS-based acoustic emission source positioning method, system and storage medium |
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Application publication date: 20191025 Assignee: Hunan creative Blasting Engineering Co.,Ltd. Assignor: CENTRAL SOUTH University Contract record no.: X2022980003448 Denomination of invention: Acoustic emission source location method based on multidimensional kernel density estimation Granted publication date: 20200804 License type: Common License Record date: 20220402 |