A method for locating a sound emission source of a stiffened plate structure based on numerical simulation and hybrid optimization algorithm

Abstract

This invention discloses a method for locating acoustic emission sources in stiffened plate structures based on numerical simulation and hybrid optimization algorithms, belonging to the field of structural health monitoring technology. The method includes: establishing a high-precision finite element numerical model of the stiffened plate structure to be tested, determining the mesh size and excitation signal, and performing transient dynamic analysis to ensure that the model can accurately describe various propagation behaviors of sound waves in the structure; using mesh nodes on the structural surface as virtual sound source points, setting multiple virtual sensor observation points on the structure, and constructing a propagation relationship database with a "position-time of arrival" mapping; arranging a sensor array on the surface of the structure to be monitored, collecting real acoustic emission signals, extracting the arrival time of each sensor channel, and forming a measured time difference of arrival (TDOA) vector; and employing a two-stage hybrid optimization strategy, first performing global coarse localization, and then using the result as initial value for local fine localization, ultimately giving the sound source location.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and non-destructive testing technology, and specifically relates to a method for locating acoustic emission sources in complex reinforced structures, such as aerospace structural shells. Background Technology

[0002] Acoustic emission technology is an important method for structural health monitoring. By detecting and analyzing the elastic waves generated by the rapid release of energy within materials, it is possible to locate and assess damage sources. Commonly used location methods include time difference of arrival (TDOA) methods, time reversal methods, and data-driven methods. Among these, the TDOA-based location method is the core method and is widely used due to its simplicity and low cost.

[0003] Traditional time-difference-of-arrival (TDOA) positioning methods are based on the assumptions that "sound waves propagate in a straight line" and "wave velocity is constant," and are effective when the structure is simple and the material is homogeneous. However, when applied to stiffened plate structures commonly found in aerospace, shipbuilding, and other engineering fields, these assumptions deviate significantly from physical reality: the presence of stiffeners causes sound waves to reflect, refract, and undergo mode conversion, resulting in a noticeably tortuous propagation path; simultaneously, the composite structure formed by the plate and stiffeners causes uneven spatial distribution of wave velocity and exhibits significant dispersion effects. These factors lead to a sharp decrease in the accuracy of time-difference-of-arrival positioning methods based on fixed wave velocity models, or even their failure.

[0004] While some studies have attempted to locate and measure structures under unknown wave speed conditions, most remain constrained by the assumptions of constant wave speed and linear propagation, failing to fundamentally solve the positioning challenges of stiffened plate structures. A patent titled "Adaptive Threshold Cross-Correlation Positioning System and Algorithm for Stiffened Plates in Spacecraft" (Publication No. CN111474244A) is based on the time-of-flight method for positioning. It relies on the assumption that "stress waves propagate at a constant or known wave speed along an approximately linear path." This premise can be approximately satisfied in simple homogeneous plate structures, but cannot be guaranteed in complex stiffened plate structures. Another patent titled "A Method for Locating Acoustic Emission Sources of Wind Turbine Blades Based on Whale Optimization Algorithm" (Publication No. CN120577767A) uses an optimization method to solve the time-of-flight positioning equation and search for the optimal sound source location. However, it still fundamentally relies on prior wave speeds, and the optimization process is prone to getting trapped in local optima in complex multi-peak error surfaces, posing challenges to convergence and real-time performance in engineering applications. The invention patent titled "A Method for Locating Acoustic Emission Sources Based on Step-by-Step Time Reversal Technology and Time-Domain Spectral Units" (Publication No. CN114674930A) employs a time-reversal focusing method, based on the principle of wave reversibility, theoretically requiring no prior knowledge of the wave velocity. However, its significant drawback lies in its extremely high computational cost and extreme sensitivity to material parameters, boundary conditions, and damping settings in the model, making efficient and stable online monitoring difficult to achieve in practical engineering. The invention patent titled "A Method and System for Locating Acoustic Emission Sources Based on a Hybrid Model" (Publication No. CN120334853A) combines sound velocity partitioning calibration (physical model) with random forest prediction (data model) for weighted localization. However, the accuracy of its physical model relies on a large number of precise offline calibration experiments, while the machine learning model requires sufficient training samples to ensure generalization ability.

[0005] Meanwhile, with the rapid development of computer hardware technology, the continuous reduction in the cost of high-performance computing platforms, and the ongoing advancements in finite element simulation software and technology, high-fidelity dynamic simulation of complex structures has become both possible and inevitable. Currently, in high-end manufacturing fields such as aerospace, shipbuilding, and automotive, establishing accurate structural finite element models and conducting large-scale transient dynamic analysis has become a routine method for design verification and performance evaluation. The continuously improving accuracy of simulation models ensures the accurate characterization of wave propagation behavior in complex structures, such as reflection, refraction, and dispersion. However, existing acoustic emission localization methods have failed to fully utilize this technological advancement. How to combine high-precision simulation models with measured data to construct a novel localization method that does not rely on simplification assumptions has become a pressing technical problem to be solved in this field.

[0006] To address the above issues, this invention proposes a method for locating acoustic emission sources in stiffened plate structures based on numerical simulation and a hybrid optimization algorithm. This method fully utilizes existing simulation technology to construct a high-precision "position-time of arrival" (TDOA) mapping database, and uses a hybrid optimization algorithm to match and invert the measured TDOA data with the database, thereby achieving high-precision location of the acoustic emission source. This effectively overcomes the fundamental flaw of traditional methods that rely on unreasonable assumptions, and effectively solves the problems of accuracy, efficiency, and applicability in locating acoustic emission sources in complex stiffened plate structures. Summary of the Invention

[0007] This invention first constructs a database describing the propagation of waves in a specific structure based on high-precision numerical simulation. Then, it uses a hybrid optimization algorithm to match the measured data with the theoretical results in the database, thereby retrieving the location of the sound source.

[0008] To achieve the above objectives, the technical solution of the present invention includes the following steps: Step S1: Establish a high-precision finite element model of the structure to be tested. The finite element model has accurate geometry, the mesh size is determined based on the acoustic emission signal frequency band, boundary conditions and connection relationships are set according to actual working conditions, material properties (elastic modulus, Poisson's ratio, density, etc.) are assigned, and reasonable excitation signals and transient dynamic calculation and analysis types are set. Step S2: Construct a propagation relationship database. Using sampling strategies based on experience, geometric features, wavelength, and positioning accuracy, a limited number of representative virtual sound source points and virtual sensor observation points are selected from the surface mesh nodes of the finite element model. Based on the reciprocity theorem, excitation is applied only to the sensor positions. The dynamic response of all virtual sound source points is obtained through transient analysis, and the first arrival time is extracted, thus constructing a "position-first arrival time" information matrix from the virtual sound source points to each sensor. A rapid estimation model for the theoretical first arrival time at any position on the structural surface is established using radial basis function interpolation. The reciprocity theorem used in this step is applicable to linear elastic structural systems. For isotropic, anisotropic, and stiffened plate structures composed of composite materials, the reciprocity theorem holds strictly as long as the material is in a linear elastic working state and the structure satisfies the small deformation assumption. For composite laminates, under the premise of linear elasticity and interlayer continuity, existing research has shown that a reciprocity theorem similar to that of three-dimensional elastic theory can be established. Step S3: Signal Acquisition and TDOA Extraction. An array of sensors coinciding with the virtual observation point is arranged on the surface of the structure to be monitored. Real acoustic emission signals are acquired, the arrival time of each sensor channel is extracted, and the Time Difference of Arrival (TDOA) vector with a specific sensor as a reference is calculated. Step S4: Hybrid Optimization Localization. A two-stage hybrid optimization algorithm is used to invert the sound source location: First, a coarse global localization is performed using the Particle Swarm Optimization (PSO) algorithm to initially pinpoint the area where the sound source is located; then, using the PSO results as initial values, a fine local search is performed using the Levenberg-Marquardt (LM) method to finally obtain a high-precision localization result. During the optimization process, the theoretical first arrival time and TDOA corresponding to any candidate point are quickly calculated using the interpolation model.

[0009] The technical solution provided by this invention makes full use of numerical models to accurately depict the physical process of wave propagation, fundamentally eliminating the assumptions of "sound waves propagate in a straight line" and "constant wave speed". It adopts a hybrid optimization strategy that has both global convergence and local fast convergence capabilities, which can ensure that while finding the global optimal solution, it has a fast convergence speed. At the same time, it has strong adaptability to structural complexity and sensor layout changes, and has wide applicability. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating the logic of a method for locating acoustic emission sources in a stiffened plate structure based on numerical simulation and a hybrid optimization algorithm, according to the present invention.

[0011] Figure 2 This is a schematic diagram showing the geometry of a stiffened plate structure and the location of the sensor array.

[0012] Figure 3 This is a mesh diagram of a finite element model of a stiffened plate structure. Detailed Implementation (1) Specific Implementation Example 1 The invention will be described in detail below with reference to an embodiment of an aluminum alloy plate with cross-shaped reinforcement. The plate measures 500 mm × 500 mm and has a thickness of 3 mm. The reinforcement height is 100 mm and the thickness is 3 mm. An acoustic emission sensor is arranged at the center of each of the eight partitions, for a total of eight sensors. Figure 2 As shown. See the attached instruction manual. Figure 1 The diagram illustrates a flowchart of a method for locating acoustic emission sources in stiffened plate structures based on numerical simulation and hybrid optimization algorithms, according to the present invention.

[0014] S1: Establish a high-precision finite element model of the structure to be monitored.

[0015] The software platform for establishing the finite element model can be a commercial simulation platform such as ANSYS or ABAQUS, which can establish a three-dimensional solid model or a mid-surface model based on the structural characteristics.

[0016] S101: Create mid-surface models of the flat plate and stiffeners in finite element software (such as ANSYS), and assign aluminum alloy material properties, including the elastic modulus. Gpa, Poisson's ratio ,density kg / m 3 .

[0017] S102: Mesh discretization is performed using SHELL163 shell elements, with the mesh being quadrilateral shell elements. The center frequency of acoustic emission signals generated by collisions with foreign objects in aerospace structures is considered to be concentrated in... The bending wave group velocity in the plate is approximately kHz. m / s, then the minimum wavelength m; to ensure accuracy, take Then the maximum grid size m, therefore set the grid size m.

[0018] S103: The excitation signal is a 5-cycle Hanning window modulated sine wave, with a center frequency of... kHz, its time-domain expression is .

[0019] S104: An explicit dynamic solver is used, with the time step automatically set by the software. The wave propagation speed and structural dimensions in the stiffened plate structure are taken into account, and the total calculation time is not less than 200 μs.

[0020] S2: Construct a "location-first arrival time" database from virtual sound source points to each sensor.

[0021] S201: For each sensor location Apply the same excitation signal as S1 to the corresponding node and perform 8 independent transient dynamic analyses.

[0022] S202: After each analysis, use the software's output function to record all surface nodes ( The displacement or velocity time history of the node is calculated. For each node, the moment when its response first exceeds a threshold (e.g., 5% of the maximum amplitude) is extracted and denoted as . (from sensor) i To the node j (First arrival time).

[0023] S203: According to the reciprocity theorem, from node... j To the sensor i First arrival time This allows for the construction of a "location-first arrival time" information matrix. Each row of data contains 3 columns of coordinates and 8 columns of the first arrival time of the corresponding 8 sensors, and the matrix is ​​stored as a database file.

[0024] S3: Collect real acoustic emission signals and extract the arrival time of each sensor channel.

[0025] In the actual structure, eight identical acoustic emission sensors were placed at the same locations as in the numerical model. Acoustic emission sources were generated by conducting a pencil lead breakage experiment. Signals were recorded using a data acquisition system with a minimum sampling rate of 1 MHz. The arrival time of each channel was automatically acquired using the AIC pickup method for the discrete signal of each channel. (length is) N Calculate the AIC function

[0026] Minimize AIC k The corresponding time is the arrival time. And calculate the TDOA vector with sensor 1 as the reference.

[0027] S4: A two-stage hybrid optimization algorithm is used to invert the sound source location. S401: Establish the objective function:

[0028] in, To determine the coordinates of the sound source location, the constraint that it lies on the surface of the structure must be satisfied (i.e., the point lies on the surface mesh of the finite element model). To read directly from the database (if) (This can be obtained as a node) or through interpolation.

[0029] S402: Uses particle swarm optimization for global search.

[0030] S4021: Set population size Maximum iteration Inertial weight The learning factor decreases linearly from 0.9 to 0.4. .

[0031] S4022: Initialize particle position (random within the structure surface) and velocity.

[0032] Assume there is a total The quadrilateral unit, the first i Area of ​​each unit Total area Generate random numbers Iterate through the cells and accumulate the cell areas. When the accumulated area first exceeds [a certain value], [the text continues with further steps]. r When the quadrilateral cell is selected, let the coordinates of its four vertices be in the following order: , , , The initial position of the particle is calculated using bilinear interpolation parameterization.

[0033] in, These are two independent random numbers.

[0034] Set the initial velocity of all particles to zero. Regardless of the method used to initialize particle position and velocity, surface constraint processing must be performed after each subsequent position update to ensure that the particle position is on the structure surface.

[0035] S4023: For each particle, if its position is exactly a node, the first arrival time is obtained directly by looking up the table; otherwise, its quadrilateral cell is located and bilinear interpolation is performed to obtain the first arrival time, and then the fitness is calculated. .

[0036] S4024: Update the optimal individual particle. and global optimal .

[0037] S4025: Updates particle velocity and position using the standard PSO formula, ensuring the updated state... It remains located on the surface of the structure.

[0038]

[0039] S4026: Iteration to convergence condition (global optimal solution changes less than 10 for 10 consecutive iterations) -3 If the maximum number of iterations is reached (mm) or the maximum number of iterations is reached, output the globally optimal solution.

[0040] S403: The Levenberg-Marquardt (LM) method is used for local fine search.

[0041] S4031: with initial value .

[0042] S4032: Set the differential step size mm, initial value of damping factor .

[0043] S4033: For the current Calculate the residual vector ( , ).

[0044] S4034: Calculate the Jacobian matrix using the central difference method J For each row, for the first Line (corresponding sensor) i The elements are calculated using the following formula.

[0045]

[0046]

[0047] in, Obtained by table lookup / interpolation, since the sound source location must be located on the structural surface, the disturbance point must be on the structural surface when performing the difference.

[0048] S4035: Solve the LM equation get .

[0049] S4036: If Then accept the update. and reduce (as ordered) (If it becomes 0.1 times its original value), otherwise increase it. (as ordered) (The step size is increased to 10 times the original value), and the step size is calculated again.

[0050] S4037: When Stop when mm or the maximum number of iterations is reached, and output the final localization result. (2) Specific Implementation Example 2 Based on Example 1, this embodiment uses finite point sampling and RBF interpolation to compress the database size and achieve fast querying of continuous space.

[0052] S2: Construct a "location-first arrival time" database from virtual sound source points to each sensor.

[0053] S201: Select virtual sound source points. Based on geometric characteristics: maintain the spacing between virtual sound source points in the reinforced attachment area (within 10 mm of the reinforcement). mm, in the flat plate region, the distance between sound source points can be increased. mm, this effectively reduces the number of virtual sound source points, ultimately choosing A virtual sound source point. Additionally, 200 points are selected as a validation set, which are not used in the interpolation model construction but only for interpolation validation.

[0054] S202: First-arrival time calculation (still using the reciprocity theorem). Following steps S201-S202 of Example 1, perform 8 transient analyses to extract the travel times of all surface nodes (including the 4200 virtual sound source points and verification points) from the overall response. This forms the "location-first-arrival time" information matrix for the virtual sound source points. Information matrix of verification points

[0055] S203: Establish the RBF interpolation model. For each sensor i Establish an independent interpolation model and select the radial basis function of the thin plate spline: Using linear polynomial additional terms.

[0056] Construct a system of interpolation equations:

[0057] in, , , , , , Sensors corresponding to virtual sound source points i The first arrival time vector. Solving for the coefficients yields... and .

[0058] S204: Interpolation Model Accuracy Verification For each point in the validation set Predicting first arrival time using an interpolation model

[0059] With actual timekeeping Compare and calculate the root mean square error (RMSE). If the error index exceeds a preset threshold (e.g., RMSE > 0.2 μs), it indicates that the interpolation model accuracy is insufficient and model optimization is required. Optimization measures include one or more of the following: 1) Encrypt sampling points: Increase the number of virtual sound source points in local areas with large errors (such as near reinforcement or where curvature changes abruptly), recalculate numerically, and update the interpolation model.

[0060] 2) Change the type of radial basis function: Try different basis functions, such as Gaussian function, multiple quadratic function, inverse multiple quadratic function or compactly supported radial basis function, and choose the function type that performs best on the validation set.

[0061] 3) Increase the polynomial order: If a linear polynomial is insufficient to capture the overall trend of the time-travel field, a quadratic polynomial term can be introduced, such as... The polynomial basis matrix is ​​increased accordingly. Given the number of columns and the number of orthogonal conditions, the interpolation coefficients are recalculated.

[0062] 4) Other interpolation methods, such as Kriging interpolation, moving least squares (MLS) or thin plate splines (without polynomials), as alternatives to RBF interpolation, also fall within the scope of protection of this invention.

[0063] S205: Database Storage Store the coordinates of the virtual sound source point and the interpolation coefficients of each sensor. and RBF parameters (such as) type).

[0064] S4: A two-stage hybrid optimization algorithm is used to invert the sound source location. Similar to S4 in Example 1, but the theoretical first arrival time calculation is changed to call the RBF interpolation model, and it must be ensured that the query point is located on the structure surface. The most obvious effect is that the database size is compressed from 40000×11 to 4200×11, while the positioning accuracy decreases only slightly, significantly improving practicality and computational efficiency.

[0065] The hybrid optimization framework of this invention is not limited to a specific combination of PSO and LM; any combination of algorithms capable of achieving "global exploration followed by local refinement" is acceptable. For example, global search can employ genetic algorithms, differential evolution algorithms, simulated annealing, etc., while local refinement search can employ Gauss-Newton methods, quasi-Newton methods (such as BFGS), trust region methods, etc. These alternative solutions also fall within the scope of protection of the claims of this invention.

Claims

1. A method for locating acoustic emission sources in stiffened plate structures based on numerical simulation and hybrid optimization algorithms, characterized in that, Includes the following steps: Step S1: Establish a high-precision finite element model of the structure to be monitored. The model has accurate geometry. The mesh size is determined based on the acoustic emission signal frequency band. Accurate boundary conditions and connection relationships are set according to the actual working conditions. The constitutive relations of the material (e.g., elastic modulus, Poisson's ratio, density, etc.) are set. The excitation source is also set. Step S2: Select a finite number of nodes in the surface mesh of the finite element model as virtual sound source points, set multiple virtual sensor observation points on the structural surface, and extract the first arrival time of the wave generated by each virtual sound source point to each sensor through transient dynamic analysis, and construct a propagation relationship database; construct an interpolation model to realize the rapid estimation of the first arrival time of the wave to each sensor observation point when the non-node position of the structural surface is used as a virtual sound source point; Step S3: Arrange a sensor array on the surface of the structure to be monitored, collect real acoustic emission signals, extract the arrival time of each sensor channel, and form a measurement time difference of arrival (TDOA) vector; the sensor positions coincide with the virtual observation points, and the number of sensors is not less than the number of virtual observation points set. Step S4: Using a hybrid optimization algorithm, with the measured TDOA vector as the observation value and the propagation relationship database as the forward model, the sound source location coordinates are inverted and solved; the hybrid optimization algorithm includes a global search stage followed by a local fine search stage.

2. The method according to claim 1, characterized in that, In step S1, the minimum mesh size of the finite element model satisfy ,in The wavelength corresponding to the frequency of the sound source signal of interest. n The value is generally 6 to 10; the excitation source signal is a sine wave modulated by a window function; the analysis type is transient dynamic analysis, and damping is generally not required.

3. The method according to claim 1, characterized in that, In step S2, the propagation relation database is constructed using an efficient method based on the reciprocity theorem: Step S21: Apply an excitation source signal to each virtual sensor observation point and perform... M Sub-independent transient dynamic analysis, in which M The total number of virtual sensors set; Step S22: In each analysis, record the displacement, velocity, or acceleration response time histories of a finite number of mesh nodes (virtual sound source points) on the structural surface, and extract the first arrival time of each node. ,in i For sensor serial number index, j The virtual sound source node index; the first arrival time is defined as the time when the sensor node's response signal envelope first exceeds a preset threshold; Step S23: According to the reciprocity theorem, from the excitation source to the sensor i Propagation from location to surface nodes j First arrival time , equal to from surface nodes j propagation to sensor i First arrival time at the location This allows for the efficient construction of the first-arrival time matrix from the virtual sound source to each sensor.

4. The method according to claim 1, characterized in that, The selection of the limited number of virtual sound source points in step S2 follows one or a combination of the following rules: Rule A: Based on geometric features and empirical sampling criteria, increase the density of sampling points near reinforcement and in areas with large curvature, and increase the density of sampling points in areas prone to collisions; Rule B: Wavelength-based sampling criteria, sampling interval d Not greater than ,in The wavelength corresponding to the frequency of the sound source signal of interest; Rule C: Based on the adoption criteria of positioning accuracy, the minimum sampling density that meets the accuracy requirements is determined by progressively increasing the density of sampling points.

5. The method according to claim 1, characterized in that, The interpolation model described in step S2 is a radial basis function interpolation model, for the sensor i The time from the sound source point at any location on the structural surface to its first arrival point can be expressed as: ； in The coordinates of the point to be queried. The coordinates of the virtual sound source point are set by the user. For radial basis functions, It is a low-order polynomial. Represents the weighting coefficient, i.e., the first... j A virtual sound source point to the sensor i The contribution of the first arrival time to the final result is determined by interpolation conditions, and the weighting coefficients and polynomial coefficients are solved.

6. The method according to claim 1, characterized in that, The global search phase in step S4 employs the Particle Swarm Optimization (PSO) algorithm, where the particle positions... and speed Update using the following formula: ； in, k Indicates the number of iterations. This is the inertia weighting coefficient. , As a learning factor, , for Uniformly distributed random numbers within an interval. For the first i The particle up to the [number]th k The historical best position in the next iteration. For the entire particle swarm up to the [number]th k The global optimal position in the next iteration.

7. The method according to claim 1, characterized in that, The local fine search stage described in step S4 uses the Levenberg-Marquardt (LM) algorithm to solve for the sound source location. This algorithm solves a nonlinear least squares function problem iteratively. ； in M This represents the number of sensors, with sensor 1 serving as the reference sensor. For the first i The measured time difference of arrival between the first sensor and the second sensor. The position of the sound source is calculated using the interpolation model described in step S2. To the i First arrival time of each sensor, Location of the sound source Time to first arrival at the selected reference sensor; In the k In this iteration, the current point is calculated first. residual vector at And Jacobi matrix Then, solve the following system of linear equations to obtain the iteration step size. , ； in: for Jacobian matrix ( d The number of coordinates of the sound source location is usually 3, but 2 in a plane. Its elements Indicates the first i The residuals for the first... j Partial derivatives of each position coordinate; for The residual vector; The damping factor is a positive real number used to control the switching of the algorithm's behavior: when When the value is large, the algorithm approximates the steepest descent method, ensuring the stability of convergence; when... When the size is small, the algorithm approximates the Gauss-Newton method, achieving fast local convergence; Represents the identity matrix; for The iteration step size vector represents the amount of correction to the sound source position in this iteration; Solving for the results Then, the algorithm evaluates the candidate points. The objective function value is determined, and the damping factor is adaptively adjusted based on the decrease in the objective function. If the objective function value decreases, then reduce To accelerate convergence; if the objective function value increases, then increase The step size is then recalculated until a step size that reduces the objective function or the preset iteration conditions are met.

8. The method according to claim 7, characterized in that, The Jacobian matrix A central difference method is used for numerical approximation. For example, the location of the sound source on the surface of the plate structure is not considered. z Coordinates, position coordinates Jacobian matrix Line (corresponding sensor) i The elements of ) are calculated using the following formulas: ； ； ； in The difference step size is a sufficiently small positive number (e.g., 0.1 mm). The points obtained by the interpolation model described in step S2 are... To the sensor i The first arrival time.

9. The method according to claim 1, characterized in that, The arrival time of each sensor channel mentioned in step S3 is picked up using the Akaike Information Criterion (AIC) method. For a length of... N discrete signals x [1], x [2],..., x [ N Its AIC function is defined as follows: ； in For discrete signals, it represents the first to the second... k One sampling point; The signal represents the first k +1 to the number k One sampling point; Represents the variance of the sequence. k The dividing point is chosen so that its value range avoids signal boundaries. This minimizes the AIC value. k The corresponding time is the arrival time of the channel. .

10. The method according to claim 1, characterized in that, Step S3 involves extracting the arrival time of each sensor channel, which can be achieved using any one of the following methods: short-time averaging / long-time averaging, energy ratio method, wavelet transform modulus maxima method, or higher-order statistical method.

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