A method for locating a sound emission source of a curved layered medium based on a shortest path principle

Abstract

The application provides a curved surface layered medium acoustic emission source positioning method based on a shortest path principle, first constructs a refraction path control equation of an acoustic emission source to a sensor position, secondly calculates a refraction point position according to the shortest path principle and orthogonal constraint, and finally solves the position of an optimal acoustic emission source under the refraction path through Taylor first-order expansion to realize acoustic emission source positioning. The method can solve the positioning deviation problem caused by acoustic wave refraction in a complex medium, is easy to implement and has high positioning precision.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, specifically to a method for locating acoustic emission sources in curved layered media based on the shortest path principle. Background Technology

[0002] Acoustic emission source localization technology, as an important non-destructive testing technique, has wide applications in structural damage detection, disaster risk assessment, and early warning. To achieve high-precision acoustic emission source localization, scholars have proposed various localization methods and applied them to different fields. However, most traditional acoustic emission source localization methods assume a homogeneous medium and that sound waves propagate in a straight line, using a fixed wave velocity as the input parameter. But in actual engineering environments and application scenarios, the propagation medium is often non-homogeneous and discontinuous, with more prevalent media stratification. If the traditional assumption of straight-line sound wave propagation is still used, the final localization result will be severely inaccurate. Patent CN106442743A proposes an acoustic emission source localization method considering the refraction of sound waves at the interface of two media. This method uses the law of sound wave refraction to establish a set of spatiotemporal equations relating the sound source and the measuring point. Based on the known coordinates of the sensor location, the time difference of the sound wave signal arrival, and the propagation velocity of the sound wave in the two media, the position coordinates of the acoustic emission source can be obtained. The inventors of this application have found through research that this method is only applicable to the positioning problem of horizontally layered media interfaces. In order to further solve the positioning deviation caused by acoustic wave refraction in complex media and the problem of local convergence or non-convergence of iteration, and to improve the efficiency and accuracy of refraction point calculation, a new acoustic emission source positioning method applicable to curved layered media still needs further research. Summary of the Invention

[0003] Existing acoustic emission source localization methods are only applicable to horizontal layered localization at the interface of a medium. In order to further solve the technical problems of localization deviation caused by acoustic wave refraction in complex media and the local convergence or non-convergence of iteration, and to improve the efficiency and accuracy of refraction point calculation, this invention provides an acoustic emission source localization method based on the shortest path principle for curved layered media. This method can solve the problem of localization deviation caused by acoustic wave refraction in complex media, is easy to implement, and has high localization accuracy.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A method for locating acoustic emission sources in curved layered media based on the shortest path principle includes the following steps:

[0006] S1. Construct the refraction path control equations from the acoustic emission source to the sensor position. The constructed refraction path control equations are as follows:

[0007]

[0008] Among them, t i φ represents the time from the location of the acoustic emission source to the acoustic emission sensor; v1 and v2 represent the wave velocities in different media, respectively; t0 represents the sensor synchronization time; (φ m ,r m ,h m ) is the refraction point s m The cylindrical coordinates of u; (φ,r,h) are the cylindrical coordinates of the acoustic emission source u; (φ i ,r i ,h i ) is the sensor s i Cylindrical coordinates; i = 1, 2, ..., N;

[0009] S2. Calculate the location of the refraction point based on the shortest path principle and orthogonal constraints;

[0010] S3. Solve for the position of the optimal acoustic emission source u under the refraction path by Taylor first-order expansion to achieve acoustic emission source localization.

[0011] Furthermore, in step S2, the objective function constructed based on the shortest path principle is:

[0012]

[0013] Where, τ i This represents the propagation time of the sound wave from the location of the sound emission source to the sound emission sensor under the shortest path.

[0014] Furthermore, in step S2, the orthogonal constraint relationship is as follows:

[0015]

[0016] Among them, (x i ,y i ,h i (x, y, h) represents the coordinates of the sensor, and (x, y, h) represents the coordinates of the acoustic emission source.

[0017] Furthermore, in step S2, the refraction point s m Refraction angle φ in cylindrical coordinates m The refined search range is:

[0018]

[0019] Wherein, the search boundary φ p By falling within the interval [φ, φ i The refraction point (x) p ,y p Converted to cylindrical coordinates, in, b = -2rm 2 y i , Similarly, the search boundary φ c By using the critical point (x) c ,y c Converted to cylindrical coordinates, Where, a′=(x i -x) 2 +(y i -y) 2 b′=2x(x i -x)+2y(y i -y),

[0020] Furthermore, in step S3, the least-squares solution of the correction term Δθ for the unknown variable θ(φ,r,h,t0) containing the cylindrical coordinates of the acoustic emission source is expressed as:

[0021] Δθ=(A T A+λdiag(A T A)) -1 A T b

[0022] Among them, A T A is the Hessian matrix; T represents the transpose of the matrix; λ is a damping factor greater than 0, which is automatically adjusted during iteration; diag(·) represents an Nth-order equation with the elements in parentheses as the main diagonal elements and all elements on the main diagonal being 0. in, This represents the actual observed value at that time. This represents the calculated value at that time; A is the gradient matrix, represented as... in,

[0023]

[0024]

[0025] Compared with existing technologies, the method for locating acoustic emission sources in curved layered media based on the shortest path principle provided by this invention has the following advantages:

[0026] (1) This method uses the shortest path principle to solve the positioning deviation problem caused by sound wave refraction, and has high positioning accuracy and is easy to implement;

[0027] (2) This method linearizes the control equations and adds an adaptive step-size damping term to avoid the problem of local convergence or non-convergence.

[0028] (3) This method considers orthogonal constraints and refines the search interval in the solution of refraction points, which improves the efficiency and accuracy of refraction point calculation. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the process for locating acoustic emission sources in curved layered media based on the shortest path principle provided by the present invention. Detailed Implementation

[0030] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific illustrations.

[0031] Please refer to Figure 1 As shown, this invention provides a method for locating acoustic emission sources in curved layered media based on the shortest path principle, comprising the following steps:

[0032] S1. Construct the refraction path control equations from the acoustic emission source to the sensor position. The constructed refraction path control equations are as follows:

[0033]

[0034] Among them, t i φ represents the time from the location of the acoustic emission source to the acoustic emission sensor; v1 and v2 represent the wave velocities in different media, respectively; t0 represents the sensor synchronization time; (φ m ,r m ,h m ) is the refraction point s m The cylindrical coordinates of u; (φ,r,h) are the cylindrical coordinates of the acoustic emission source u; (φ i ,r i ,h i ) is the sensor s i Cylindrical coordinates; i = 1, 2, ..., N;

[0035] S2. Calculate the location of the refraction point based on the shortest path principle and orthogonal constraints;

[0036] S3. Solve for the position of the optimal acoustic emission source u under the refraction path by Taylor first-order expansion to achieve acoustic emission source localization.

[0037] In a specific embodiment, the objective function constructed based on the shortest path principle in step S2 is:

[0038]

[0039] Where, τ i This represents the propagation time of the sound wave from the location of the sound emission source to the sound emission sensor under the shortest path.

[0040] By minimizing the objective function, the angular component φ of the refraction point is obtained. m for:

[0041]

[0042] Among them, T c This represents the calculated time from the location of the acoustic emission source to the acoustic emission sensor. Let φ... m Substitute h m Regarding φ m From the expression, the cylindrical coordinates s of the refraction point are obtained. m =[φ m ,r m ,h m ].

[0043] In a specific embodiment, the orthogonal constraint relationship in step S2 is as follows:

[0044]

[0045] Among them, (x i ,y i ,h i (x, y, h) represents the coordinates of the sensor, and (x, y, h) represents the coordinates of the acoustic emission source.

[0046] In a specific embodiment, in step S2, the refraction point s m Refraction angle φ in cylindrical coordinates m The refined search range is:

[0047]

[0048] Wherein, the search boundary φ p By falling within the interval [φ, φ i The refraction point (x) p ,y p Converted to cylindrical coordinates, in, b = -2r m 2 y i , Similarly, the search boundary φ c By using the critical point (x) c ,y c Converted to cylindrical coordinates, Where, a′=(x i -x) 2 +(y i -y) 2 b′=2x(x i -x)+2y(y i -y),

[0049] In a specific embodiment, the least squares solution of the correction term Δθ of the unknown variable θ(φ,r,h,t0) containing the cylindrical coordinates of the acoustic emission source in step S3 is expressed as:

[0050] Δθ=(A T A+λdiag(A T A)) -1 A T b

[0051] Among them, A T A is the Hessian matrix; T represents the transpose of the matrix; λ is a damping factor greater than 0, which is automatically adjusted during iteration; diag(·) represents an Nth-order equation with the elements in parentheses as the main diagonal elements and all elements on the main diagonal being 0. in, This represents the actual observed value at that time. This represents the calculated value at that time; A is the gradient matrix, represented as... in,

[0052] To further and better understand the technical solution of the present invention, the principle of the curved layered medium acoustic emission source localization method based on the shortest path principle provided by the present invention will be described in detail below:

[0053] Use (φ) m ,r m ,h m ) represents the refraction point s m The cylindrical coordinates (φ, r, h) represent the cylindrical coordinates of the acoustic emission source u to be determined. i ,r i ,h i (i = 1, 2, ..., N) represents the sensor s i The cylindrical coordinates, where N represents the number of sensors, and t i This represents the time between the location of the acoustic emission source and the acoustic emission sensor.

[0054] First, based on the sensor coordinates and the time it receives the acoustic emission signal, the following control equations are established:

[0055]

[0056] Where v1 and v2 represent wave velocities in different media, and t0 represents the synchronization time of the sensor.

[0057] The time calculated by equation (1) often deviates from the observed time. The deviation can be expressed as:

[0058]

[0059] Using a first-order Taylor expansion to linearly approximate equation (2), it can be expressed as:

[0060]

[0061] The matrix form of the above linear expression is:

[0062] AΔθ=b (4)

[0063] Where Δθ is the correction term for the unknown variable θ(φ,r,h,t0); in, This represents the actual observed value at that time. This represents the calculated value at that time; A is the gradient matrix, represented as... in,

[0064] The least squares solution of the correction term Δθ is expressed as:

[0065] Δθ=(A T A+λdiag(A T A)) -1 A T b (5)

[0066] Among them, A T A is the Hessian matrix; T represents the transpose of the matrix; λ is a damping factor greater than 0, which is automatically adjusted with each iteration; diag(·) represents an Nth-order equation with the elements within the brackets as the main diagonal elements and all elements on the main diagonal being 0. If the residual of equation (3) in one iteration is significantly reduced compared to the previous iteration, the value of λ should be appropriately reduced (λ = λ / β) to make the algorithm closer to the Gauss-Newton algorithm. The constant β is a step control factor greater than 1. If the residual of equation (3) in a certain iteration is not reduced enough compared to the previous iteration, or even increases compared to the previous iteration, the value of λ should be increased (λ = λβ) to make the step size closer to the gradient descent direction. Each component of the Hessian matrix can be effectively scaled by λ to provide Taylor second-order information, avoiding the problems of slow convergence in the direction of small gradients and non-convergence in the direction of large gradients.

[0067] After obtaining the correction term Δθ, the initial value θ0 of the cylindrical coordinate λ of the acoustic emission source can be iteratively updated as follows:

[0068] θ=θ0+Δθ (6)

[0069] Generally, due to the large deviation between the initial value and the true value, iterative correction is difficult to approximate the true value. Therefore, equations (5) and (6) need to be calculated repeatedly until the correction term is less than a certain threshold, or the number of iterations exceeds a certain threshold, at which point the iteration terminates. The specific iteration termination thresholds are set as follows:

[0070]

[0071] In theory, the location of the refraction point can be obtained using Fermat's principle.

[0072] The propagation paths of sound waves through refracting surfaces in different media are as follows:

[0073]

[0074] Where, τ i φ represents the propagation time of the sound wave from the location of the sound emission source to the sound emission sensor under the shortest path. m and h m All of these are unknown quantities, and there are implicit orthogonal constraints between them. The specific expressions of the orthogonal constraint relationships will be derived in detail below.

[0075] The normal vector n1 of plane M1 is solved by the following formula:

[0076] n1(h m ,φ m )=L×J (9)

[0077] Where L represents the vector from sensor S to acoustic emission source U, i.e., L = US; J represents the vector from refraction point R to acoustic emission source U, i.e., J = UR; and U represents the coordinates of the acoustic emission source, denoted as U = [xyh]. T =[rcos(φ) rsin(φ) h] T R represents the coordinates of the refraction point to be determined, expressed as R = [x m y m h m ] T =[r m cos(φ m ) r m sin(φ m h m ] T S represents the coordinates of the acoustic emission sensor, denoted as S0. i =[x i y i h i ] T =[r i cos(φ i ) r i sin(φ i hi ] T .

[0078] The normal vector n2 of plane M2 is solved by the following formula:

[0079] n2(h m ,φ m )=[x m y m 0] T =[r m cos(φ m ) r m sin(φ m ) 0] T (10)

[0080] Since planes M1 and M2 are orthogonal, their normal vectors are also orthogonal, that is:

[0081] n1(h m ,φ m )×n2(h m ,φ m )=0 (11)

[0082] By solving equation (11), the unknown quantity φ is obtained. m with h m The orthogonal constraint relationship between them is:

[0083]

[0084] Substituting equation (12) into equation (8), we obtain the result only regarding the angular component φ. m The objective function is:

[0085]

[0086] Minimize the objective function of equation (13) above to obtain the angular component φ of the refraction point. m for:

[0087]

[0088] Among them, T c This represents the calculated time from the location of the acoustic emission source to the acoustic emission sensor. Then φ... m Substituting into equation (14), we obtain the height component h of the refraction point. m Thus, the cylindrical coordinates of the refraction point are obtained as s. m =[φ m ,r m ,h m ].

[0089] As can be seen from the properties of wave propagation, the solution to equation (14) must lie between the angular component φ of the acoustic emission source and the angular component φ of the sensor. i Between. However, in the entire interval [φ,φ] i During the search within the region, equation (14) still tends to get stuck in a local optimum and leads to an incorrect refraction path. To avoid this, the critical angle φ at the exit angle should be considered. p The constraint is at 90°.

[0090] Assume the coordinates of the critical point are (x p ,y p The sensor's coordinates are (x...). i ,y i The vector L1 between the refraction point and the sensor is represented as:

[0091] L1 = [x p -x i y p -y i (15)

[0092] The vector L2 from the center of the circle to the point of refraction is expressed as:

[0093] L2 = [x p y p (16)

[0094] When the exit angle is 90°, vectors L1 and L2 are perpendicular to each other, that is:

[0095]

[0096] Furthermore, the refraction point is located at a radius of r m On the circle, the following equation should be satisfied:

[0097]

[0098] Combining equations (17) and (18), we can obtain:

[0099]

[0100] in, b = -2r m 2 y i ,

[0101] y p We can obtain the result by solving equation (19):

[0102]

[0103] y pSubstituting into equation (18) yields x p :

[0104]

[0105] The above process yields two solutions, but only one solution falls within the interval [φ, φ]. i Within ], by using the unique solution (x p ,y p Convert to cylindrical coordinates φ p The search boundary is obtained.

[0106] In addition, it is necessary to determine the angle φ of the acoustic emission wave propagating in a straight line. c The straight line between the acoustic emission source and the sensor can be represented as:

[0107]

[0108] By combining equations (18) and (22), we can obtain:

[0109]

[0110] Where, a′=(x i -x) 2 +(y i -y) 2 b′=2x(x i -x)+2y(y i -y),

[0111] Solving equation (23) yields the refraction point (x). c ,y c The coordinates of φ are used to obtain another search boundary. This is achieved through the critical angle φ. c and φ p Determined angle of refraction φ m The refined search range is:

[0112]

[0113] Experimental example:

[0114] Assume a cylindrical specimen with an inner diameter of 50 mm and a hollow cylindrical specimen with an outer inner diameter of 50 mm and an outer diameter of 100 mm, with a specimen height of 100 mm. The cylindrical coordinates of the eight sensors are (0,100,0), (90,100,0), (180,100,0), (270,100,0), (45,100,100), (135,100,100), (225,100,100), and (315,100,100). Simultaneously, the cylindrical coordinates of the virtual acoustic emission source are (0.588,36.1,50.0). The internal medium wave velocity is set to 3500 m / s, and the external medium wave velocity is set to 4900 m / s. This experiment generates a set of arrival data through simulation, adding a 0.2 μs Gaussian random error to the arrival data to simulate the impact of environmental noise on positioning accuracy.

[0115] Using the steps and formulas described in the above embodiments, the calculated coordinates of the acoustic emission source cylinder are (0.5938, 35.8, 50.4). The positioning error of the acoustic emission source using the method described in the above embodiments is 0.526 mm, indicating that the technical solution provided by the present invention is feasible and has higher positioning accuracy.

[0116] Compared with existing technologies, the method for locating acoustic emission sources in curved layered media based on the shortest path principle provided by this invention has the following advantages:

[0117] (1) This method uses the shortest path principle to solve the positioning deviation problem caused by sound wave refraction, and has high positioning accuracy and is easy to implement;

[0118] (2) This method linearizes the control equations and adds an adaptive step-size damping term to avoid the problem of local convergence or non-convergence.

[0119] (3) This method considers orthogonal constraints and refines the search interval in the solution of refraction points, which improves the efficiency and accuracy of refraction point calculation.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for locating acoustic emission sources in curved layered media based on the shortest path principle, characterized in that, Includes the following steps: S1. Construct the refraction path control equations from the acoustic emission source to the sensor position. The constructed refraction path control equations are as follows: in, This represents the time from the location of the acoustic emission source to the acoustic emission sensor; These represent wave velocities in different media; Indicates the synchronization time of the sensor; Point of refraction Cylindrical coordinates; Acoustic emission source Cylindrical coordinates; For sensors Cylindrical coordinates; ; S2. Calculate the location of the refraction point based on the shortest path principle and orthogonal constraints; S3. Solve for the optimal acoustic emission source under the refraction path using Taylor first-order expansion. The location of the acoustic emission source is determined; among which, In step S2, the objective function constructed based on the shortest path principle is: in, This represents the propagation time of the sound wave from the location of the sound emission source to the sound emission sensor under the shortest path. In step S2, the orthogonal constraint relationship is as follows: in, Indicates sensor coordinates, Indicates the coordinates of the acoustic emission source; In step S3, the unknown variable includes the cylindrical coordinates of the acoustic emission source. Correction items The least squares solution is expressed as: in, It is a Hessian matrix; Represents the transpose of a matrix; The damping factor is greater than 0 and is automatically adjusted with each iteration. This represents a set of elements whose main diagonal elements are all zeros, with the elements within the parentheses being zeros. Order equation; ,in, , This represents the actual observed value at that time. This indicates the calculated value at that time; It is the gradient matrix, represented as ,in, , ， ， 。 2. The method for locating acoustic emission sources in curved layered media based on the shortest path principle according to claim 1, characterized in that, In step S2, the refraction point Angle of refraction in cylindrical coordinates The refined search range is: Among them, search boundary By falling within the interval point of refraction Converted to cylindrical coordinates , ,in, , , Similarly, the search boundary By critical point Converted to cylindrical coordinates , ,in, , , .

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