Flexible array ultrasound full free-form profile inversion method without prior position

Abstract

The application discloses a flexible array ultrasonic full free contour inversion method without prior position, and belongs to the technical field of ultrasonic nondestructive testing. In view of the problem that the existing method depends on external equipment or prior geometric constraint and has poor universality, the application only utilizes the equal-interval transverse arrangement characteristics of an array, parameterizes the array contour with a Bezier curve full free parameter, and all the longitudinal coordinates of control points are to-be-optimized variables; a double-objective function containing an imaging envelope energy, a curvature penalty term and a circular phase variance is constructed, a multi-objective optimization algorithm is adopted to obtain a Pareto optimal solution set, and the optimal solution is selected after normalization to determine the spatial position of each array element. The application realizes full free inversion, does not need prior values of array element positions, improves contour reconstruction precision and image quality, and is suitable for health monitoring and nondestructive testing of complex curved surface structures.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic nondestructive testing technology, specifically relating to a flexible array ultrasonic fully free profile inversion method that does not require prior position. Background Technology

[0002] Flexible array ultrasonic transducers, due to their bendability, can fit well with complex curved surfaces such as aircraft skin, pipes, and blades, and have become a cutting-edge method for in-service structural health monitoring and industrial non-destructive testing. However, the true spatial position of each array element is unknown after the array is attached, and directly using the assumption of equidistant planes for imaging will lead to phase distortion, focus shift, and a severe decrease in resolution.

[0003] Existing solutions can be mainly divided into three categories: First, they are supplemented with external devices such as fiber optic shape sensors or laser trackers, which have high accuracy but increase system complexity, cost and operation difficulty; second, they are based on parameter estimation of ultrasonic echo waveforms, such as using direct waves or interface reflection waves, but these methods often require clear waveform features and simple geometric models, and have poor robustness when facing unknown complex surfaces; third, they are based on end-to-end prediction of deep learning, which requires massive amounts of labeled data and whose generalization ability is limited by the training conditions.

[0004] In recent years, methods for array self-calibration using image quality optimization have attracted attention. Ingram et al. used phase coherence for shape estimation, and Noda et al. used image entropy as the optimization objective. However, these methods usually restrict the array shape to a specific parametric function or require fixing certain array element positions as a spatial reference, which limits the versatility and adaptability of the methods. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a flexible array ultrasonic fully free contour inversion method that does not require prior positions. This method overcomes the shortcomings of existing methods that rely on external hardware or prior geometric constraints. This invention does not preset any prior values ​​for array element positions. Instead, it utilizes the inherent equidistant lateral arrangement information of the array. By equating the array contour to the coordinates of all control points of a Bézier curve and jointly optimizing the imaging energy and phase circular variance, the array shape reconstruction under complex curved surfaces is achieved.

[0006] The technical solution adopted in this invention is as follows: A flexible array ultrasonic fully free contour inversion method without prior position, comprising the following steps:

[0007] S1. Full matrix data acquisition and signal extraction: A flexible array ultrasonic transducer is used to acquire full matrix capture data, and the signals of each channel are analyzed and processed to extract the amplitude envelope and instantaneous phase information of the signals.

[0008] S2. Fully Free Parameterization of Bézier Curves: The spatial contour of the flexible array is represented by fully free parameterization using Bézier curves. The ordinates of all control points on the curve are set as variables to be optimized. No prior values ​​of array element positions are preset. The distribution of the lateral coordinates of the control points is determined only based on the inherent equidistant horizontal arrangement characteristics of the array, and then the spatial coordinates of each array element are mapped to obtain the spatial coordinates.

[0009] S3. Region of Interest Determination: Generate a low-resolution fully focused image based on the initial uniform contour, and select the region of interest containing the defect or the structure to be tested in the image;

[0010] S4. Construct a dual-objective optimization function: one is the negative value of the imaging envelope energy with an additional curvature penalty term, and the other is a circular phase variance index based on direction statistics.

[0011] S5. Multi-objective optimization solution: Using the variable to be optimized as the decision variable, a multi-objective optimization algorithm is used to solve the bi-objective function and obtain the Pareto optimal solution set.

[0012] S6. Optimal Solution Selection: The Pareto optimal solution is normalized, the distance from each solution to the ideal point is calculated, and the optimal solution is selected. Based on the optimal solution, the spatial position of all array elements is determined, and the flexible array profile inversion is completed.

[0013] Furthermore, in step S1, the analytical processing includes performing Hilbert transform on the signals of each channel of the full matrix data to obtain analytical signals, and then extracting the amplitude envelope and instantaneous phase from the analytical signals; and setting the front end segment of the initial direct wave signal to zero to eliminate direct wave interference.

[0014] Furthermore, in step S2, the Bézier curve is defined by multiple control points. The horizontal coordinates of the control points are equidistantly distributed within the range of the horizontal coordinates of the array elements. The vertical coordinates of all control points are independent variables to be optimized, and the values ​​of the variables are limited to a preset range. The vertical coordinates of each array element are obtained by linear mapping of the curve parameters and calculation using Bernstein polynomials, thereby determining the complete spatial coordinates of the array elements.

[0015] Furthermore, in step S3, the initial uniform contour is a preset straight contour, the low-resolution full-focus image is used to initially locate the defect or the structure to be tested, the region of interest is determined by rectangular selection, and subsequent optimization calculations are only carried out within this region.

[0016] Furthermore, in step S4, the negative objective function of the imaging envelope energy is used to characterize the image brightness and contrast, the curvature penalty term is used to suppress contour distortion and ensure contour smoothness, and the circular phase variance index is used to measure the degree of phase coherence and avoid the calculation deviation of the periodic phase by the linear variance.

[0017] Furthermore, in step S5, the multi-objective optimization algorithm adopts the non-dominated sorting genetic algorithm NSGA-II, with minimizing the bi-objective function as the optimization objective. The population size, maximum number of generations and Pareto ratio parameters are set, and the Pareto optimal solution set is obtained by iterative solution.

[0018] Furthermore, in step S6, normalization is performed separately for the two objective functions to eliminate the difference in dimensions; the ideal point is the point corresponding to the optimal value of both objective functions, the optimal solution closest to the ideal point is selected, the corresponding control point ordinate vector is output, and then the precise spatial position of all array elements is calculated.

[0019] This invention also provides a flexible array ultrasound fully free contour inversion system without prior position, used to implement the flexible array ultrasound fully free contour inversion method described above without prior position. The system includes:

[0020] Data acquisition and analysis module: used to acquire full matrix data of flexible array ultrasound, complete signal analysis and processing, and extract amplitude envelope and instantaneous phase;

[0021] Contour parameterization module: used to achieve fully free parameterization of the flexible array contour using Bézier curves, set the variables to be optimized, and map and calculate the spatial coordinates of the array elements;

[0022] Region of Interest (ROI) Selection Module: Used to generate low-resolution full-focus images and select regions of interest containing defects or structures to be tested.

[0023] Bi-objective function construction module: used to construct a bi-objective optimization function that includes imaging envelope energy and circular phase variance, with an additional curvature penalty term;

[0024] Multi-objective optimization solution module: Used to solve bi-objective functions using multi-objective optimization algorithms and output Pareto optimal solution set;

[0025] The optimal solution selection and contour output module is used to normalize the optimal solution set and select the optimal solution, determine the spatial position of the array elements, and output the flexible array inversion contour.

[0026] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the flexible array ultrasonic fully free contour inversion method without prior position as described above.

[0027] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for flexible array ultrasonic fully free contour inversion without prior position.

[0028] Compared with the prior art, the beneficial effects and advantages of the present invention are as follows:

[0029] True fully free inversion: No need to know the exact position of any array element in advance, the ordinates of all control points are completely free within a reasonable range, there is no dependence on the initial state, and the scope of application is wider.

[0030] Hybrid objective function design: It adopts two physically complementary indicators, imaging energy (defect echo intensity) and circular phase variance (waveform coherence), and combines them with curvature regularization term to ensure both image brightness and contrast, as well as contour smoothness, avoiding the overfocusing problem that may be introduced by simply using energy indicators.

[0031] Circular phase variance is more in line with the principles of physics: phase is a periodic quantity, and circular variance can accurately measure the central tendency of directional data, avoiding the averaging effect produced by linear variance in phase, thus improving the sensitivity and accuracy of optimization.

[0032] Multi-objective optimization and automatic decision-making: After obtaining the Pareto front using the NSGA-II algorithm, the most representative compromise solution is automatically determined by the normalized minimum distance method without manual intervention. Attached Figure Description

[0033] Figure 1 This is a flowchart of the overall process of the present invention;

[0034] Figure 2 A schematic diagram of Bézier curve parameterization and fully free control points;

[0035] Figure 3 Select an interface diagram for ROI;

[0036] Figure 4 A schematic diagram illustrating the Pareto front distribution and the selection of the optimal solution;

[0037] Figure 5 Comparison of shape estimation results under different surface models, where (a) is a circular surface with large curvature and (b) is a random cubic Bézier surface;

[0038] Figure 6 The simulation model diagrams are shown, where (a) is a large curvature circular surface and (b) is a random cubic Bézier surface. Detailed Implementation

[0039] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0040] Example 1

[0041] like Figure 1 As shown, a flexible array ultrasound fully free contour inversion method without prior location is proposed, comprising the following steps:

[0042] Step 1: Full matrix data acquisition and signal extraction:

[0043] Utilizing A flexible array ultrasonic transducer with individual elements acquires full-matrix capture data. The Hilbert transform of each channel signal is used as the imaginary part. Using the imaginary unit, we obtain the analytic signal:

[0044]

[0045] Then extract the amplitude envelope. and instantaneous phase .

[0046] Step 2: Fully Free Parameterization of Bézier Curves:

[0047] by The Bézier curves at each control point describe the spatial profile of the array, and the parametric equations of the curves are:

[0048]

[0049] In the formula, Here are the coordinates of the control points, and the x-coordinate of the control points. Within the x-coordinate range of the array element Fixed inner equidistant spacing:

[0050]

[0051] The ordinates of all control points As variables to be optimized, they constitute a vector. The variable search range is set to , without any Fixed at a known real location.

[0052] For the x-coordinate of the k-th element The corresponding curve parameters are obtained through linear mapping. :

[0053]

[0054] Array element vertical coordinate Calculated using Bernstein polynomials:

[0055]

[0056] Step 3: Determine the region of interest:

[0057] Low-resolution full-focus imaging is performed using an initial uniform contour, and the user selects the region of interest containing the defect or the structure under test on the image using a rectangular selection box. .

[0058] Step 4: Construct a dual-objective optimization function:

[0059] It consists of two items:

[0060] First objective function A curvature penalty term is added to the negative value of the imaging envelope energy:

[0061]

[0062] In the formula, The pixel values ​​of the fully focused image within the ROI are normalized to the [0,1] interval; The average curvature of the Bézier curve; For curvature penalty weights.

[0063] Second objective function A circular phase variance index based on direction statistics:

[0064]

[0065] In the formula, For array element pairs At the imaging point The instantaneous phase of the analytic signal at that location; This represents the total number of pixels within the ROI. The scaling factor is determined by presampling.

[0066] Step 5: Multi-objective optimization solution

[0067] by As decision variables, with To optimize the objective, the non-dominated sorting genetic algorithm NSGA-II was used to obtain the Pareto optimal solution set. and the corresponding target vector .

[0068] Step Six: Optimal Solution Selection

[0069] Normalize each objective dimension separately:

[0070]

[0071] Calculate the Euclidean distance from each solution to the ideal point:

[0072]

[0073] Choose the solution with the smallest distance:

[0074]

[0075] Its corresponding This is the ordinate vector of the optimal control point, from which the spatial positions of all array elements can be obtained. .

[0076] The basic principle of this invention is as follows: the deformable contour of the flexible array is expressed using a Bézier curve, with the ordinates of all control points on the curve serving as optimization variables without any fixed constraints related to the actual position. Simultaneously, the imaging envelope energy and circular phase variance within the region of interest are used as two complementary optimization objectives, with a curvature smoothing term added. A multi-objective genetic algorithm is then used to search the variable space for the contour configuration that optimizes image quality. Finally, the contour with the best overall performance is automatically selected from the Pareto front, completing the array's self-calibration. The completely free variables in step 2 and the definition of the circular variance in step 4 are the core innovations of this invention. They enable the method to truly break free from dependence on any prior positional information and improve the physical accuracy of phase evaluation.

[0077] Example 2

[0078] A flexible array ultrasound fully free contour inversion method that does not require prior location includes the following steps:

[0079] Step 1: FMC Data Acquisition and Signal Processing

[0080] Using A flexible array of individual elements is used for full matrix acquisition to obtain a three-dimensional data volume. Perform a Hilbert transform on each A-scan signal to obtain the analytic signal and its corresponding amplitude envelope. To eliminate direct wave interference, ... The initial signal is forced to zero.

[0081] Step 2: Parameterization of Fully Free Bézier Curves

[0082] like Figure 2 As shown, n = 5, x-coordinate of control point The array elements are evenly spaced within the x-coordinate range [-5.7, 4.8] mm. The y-coordinates of all five control points are... As variables to be optimized, none are fixed at their actual positions. The search range for variables is uniformly set to [1.5, 10] mm. For any element's x-coordinate, the corresponding curve parameter t is obtained through linear mapping, and then the element's y-coordinate is calculated using Bernstein polynomials:

[0083]

[0084] Thus, the spatial coordinates of the array elements are determined solely by the variable vector. Decide.

[0085] Step 3: Selecting the Region of Interest

[0086] To reduce computational load and focus on key structures, a low-resolution fully focused image is generated using an initial flat profile (with all control points having reasonable initial ordinate values). In the image interface, the Region of Interest (ROI) containing the defect or the structure under test is selected using a rectangular bounding box, such as... Figure 3 As shown, all subsequent image quality assessments are performed only within this ROI.

[0087] Step 4: Construct a dual-objective optimization function

[0088] For a given optimization variable :

[0089] Reconstruct the element coordinates and use a vectorized full-focusing algorithm to calculate the envelope overlay image within the ROI. The summation and negation of the energy within the ROI of the normalized image is used as the primary objective.

[0090]

[0091] Calculate the instantaneous phase circular variance of each pixel within the ROI:

[0092]

[0093] Then, average all pixels within the ROI to obtain the original APV value. Use the 90th percentile obtained from presampling as the scaling factor. To achieve the second objective .

[0094] To suppress potential large curvature oscillations, the average value of the discrete curvature of the Bézier curve is calculated. And it is added to the first objective with a weight of 0.08, that is, the final first objective is .

[0095] Step 5: Multi-objective optimization and Pareto decision making

[0096] The NSGA-II algorithm (using the gamultiobj function in MATLAB) was employed, with a population size of 80, a maximum generation count of 100, and a Pareto ratio of 0.4. After evolution, a set of target vectors corresponding to Pareto optimal solutions was obtained. .like Figure 4 As shown, respectively for and Normalization is performed, the Euclidean distance from each solution to the ideal point (0,0) is calculated, and the solution with the smallest distance is selected as the optimal individual, whose variable is the final control point ordinate.

[0097] Step 6: Contour Output and Imaging Verification

[0098] The precise spatial positions of all array elements are calculated using the optimal control points, enabling high-resolution full-focus imaging, such as... Figure 5 As shown in (a), this is a comparison of the initial surface, the fitted surface, and the actual surface of a large-curvature circular surface. The fitted curve can accurately focus on the location of the defect, and the curve profile and... Figure 6 In (a), the true contour error is 0.23 times the wavelength. Figure 5 (b) Comparison of the initial surface, fitted surface, and true surface of a random cubic Bézier surface. The fitted curve can accurately focus on the location of the defect, and the curve profile and... Figure 6 In (b), the true contour error is 0.25 times the wavelength. Experiments show that this method significantly improves image structural similarity even without fixing any starting point.

Claims

1. A flexible array ultrasonic fully free contour inversion method without prior position, characterized in that, Includes the following steps: S1. Full matrix data acquisition and signal extraction: A flexible array ultrasonic transducer is used to acquire full matrix capture data, and the signals of each channel are analyzed and processed to extract the amplitude envelope and instantaneous phase information of the signals. S2. Fully Free Parameterization of Bézier Curves: The spatial contour of the flexible array is represented by fully free parameterization using Bézier curves. The ordinates of all control points on the curve are set as variables to be optimized. No prior values ​​of array element positions are preset. The distribution of the lateral coordinates of the control points is determined only based on the inherent equidistant horizontal arrangement characteristics of the array, and then the spatial coordinates of each array element are mapped to obtain the spatial coordinates. S3. Region of Interest Determination: Generate a low-resolution fully focused image based on the initial uniform contour, and select the region of interest containing the defect or the structure to be tested in the image; S4. Construct a dual-objective optimization function: one is the negative value of the imaging envelope energy with an additional curvature penalty term, and the other is a circular phase variance index based on direction statistics. S5. Multi-objective optimization solution: Using the variable to be optimized as the decision variable, a multi-objective optimization algorithm is used to solve the bi-objective function and obtain the Pareto optimal solution set. S6. Optimal Solution Selection: The Pareto optimal solution is normalized, the distance from each solution to the ideal point is calculated, and the optimal solution is selected. Based on the optimal solution, the spatial position of all array elements is determined, and the flexible array profile inversion is completed.

2. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S1, the analytical processing includes performing Hilbert transform on the signals of each channel of the full matrix data to obtain analytical signals, and then extracting the amplitude envelope and instantaneous phase from the analytical signals; and setting the front end of the initial direct wave signal to zero to eliminate direct wave interference.

3. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S2, the Bézier curve is defined by multiple control points. The x-coordinates of the control points are equidistantly distributed within the x-coordinate range of the array elements. The y-coordinates of all control points are independent variables to be optimized, and the values ​​of the variables are limited to a preset range. The y-coordinates of each array element are obtained by linear mapping of the curve parameters and calculation using Bernstein polynomials, thereby determining the complete spatial coordinates of the array elements.

4. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S3, the initial uniform contour is a preset straight contour, and the low-resolution full-focus image is used to initially locate the defect or the structure to be tested. The region of interest is determined by rectangular selection, and subsequent optimization calculations are only carried out within this region.

5. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S4, the negative objective function of imaging envelope energy is used to characterize image brightness and contrast, the curvature penalty term is used to suppress contour distortion and ensure contour smoothness, and the circular phase variance index is used to measure the degree of phase coherence and avoid the calculation deviation of periodic phase by linear variance.

6. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S5, the multi-objective optimization algorithm adopts the non-dominated sorting genetic algorithm NSGA-II, with the goal of minimizing the bi-objective function. The population size, maximum number of generations and Pareto ratio parameters are set, and the Pareto optimal solution set is obtained by iterative solution.

7. The flexible array ultrasonic fully free contour inversion method without prior position as described in claim 1, characterized in that, In step S6, normalization is performed separately for the two objective functions to eliminate the difference in dimensions; the ideal point is the point where both objective functions take the optimal value. The optimal solution closest to the ideal point is selected, and the corresponding control point ordinate vector is output. Then, the precise spatial position of all array elements is calculated.

8. A flexible array ultrasonic fully free contour inversion system without prior position, used to implement the flexible array ultrasonic fully free contour inversion method without prior position as described in any one of claims 1-7, characterized in that, include: Data acquisition and analysis module: used to acquire full matrix data of flexible array ultrasound, complete signal analysis and processing, and extract amplitude envelope and instantaneous phase; Contour parameterization module: used to achieve fully free parameterization of the flexible array contour using Bézier curves, set the variables to be optimized, and map and calculate the spatial coordinates of the array elements; Region of Interest (ROI) Selection Module: Used to generate low-resolution full-focus images and select regions of interest containing defects or structures to be tested. Bi-objective function construction module: used to construct a bi-objective optimization function that includes imaging envelope energy and circular phase variance, with an additional curvature penalty term; Multi-objective optimization solution module: Used to solve bi-objective functions using multi-objective optimization algorithms and output Pareto optimal solution set; The optimal solution selection and contour output module is used to normalize the optimal solution set and select the optimal solution, determine the spatial position of the array elements, and output the flexible array inversion contour.

9. An electronic device, comprising a memory and a processor, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements a flexible array ultrasonic fully free contour inversion method without prior position as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a flexible array ultrasonic fully free contour inversion method without prior location as described in any one of claims 1-7.

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