An Optimization Arrangement Method of Piezoelectric Sensors for Ultrasonic Guided Wave Damage Monitoring

Abstract

The present invention discloses an optimized layout method for piezoelectric sensors used in ultrasonic guided wave damage monitoring, belonging to the technical field of structural health monitoring. It can, under the condition of a certain number of piezoelectric sensors, obtain a monitoring coverage area as large as possible by adjusting the sensor positions. First, discrete control points are set in the area to be monitored of the entire structure. Then, the proportion of the damage influence area in the form of an ellipse defined by every two sensors covering the control points is taken as the coverage rate optimization target. Finally, the artificial bee colony intelligent algorithm is used for iterative solution to obtain the optimal layout form of the sensors. The present invention can effectively solve the problem of optimizing the layout of piezoelectric sensors on a planar structure, and plays an important role in expanding the monitoring area and improving the reliability of ultrasonic guided wave damage monitoring.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring, and in particular relates to a method for optimizing the arrangement of piezoelectric sensors for ultrasonic guided wave damage monitoring. Background Art

[0002] When aircraft structures are in service, they will inevitably be damaged by uncertain factors, such as impact damage caused by hail and tool drops. These damages can lead to interface debonding, delamination, cracks, etc., which seriously weaken the strength and stability of the structure. Therefore, it is necessary to perform structural health monitoring on the structure to ensure the safety of the aircraft in service.

[0003] The structural health monitoring system uses the drive and sensor units integrated in the aircraft structure to obtain information related to the state of the structure online, especially the characteristics, degree, location and development trend of the structural damage, so that decision makers can make timely decisions to prevent the deterioration of structural performance and failure damage, which is of vital importance to reducing maintenance costs and improving structural safety. After the unremitting efforts of many researchers, considerable research progress has been made in the field of structural health monitoring. In recent years, damage identification technology based on piezoelectric sensors and ultrasonic guided waves is considered to be a very promising method and has been widely studied. When piezoelectric materials are in a strain state under mechanical stress, polarization and electric field will be caused inside them. This process of converting mechanical energy into electrical energy is called the positive piezoelectric effect. In contrast to the positive piezoelectric effect, when piezoelectric materials are polarized under the action of an electric field, strain will be generated. This process of converting electrical energy into mechanical energy is called the inverse piezoelectric effect. The inverse piezoelectric effect and the positive piezoelectric effect of piezoelectric materials can be used to excite and receive ultrasonic guided waves in the structure respectively. By analyzing the ultrasonic guided wave signal and extracting the damage-related signal, information about the damage state can be obtained. Traditional piezoelectric sensor layout methods usually use a large number of sensors to be evenly distributed in the structure to be monitored, resulting in a certain waste of resources. Optimizing and reasonably configuring the layout of piezoelectric sensors through optimization algorithms can help improve sensor utilization, reduce the number of sensors, reduce the complexity of the entire monitoring system, and alleviate the additional impact of the monitoring system on structural performance.

[0004] Therefore, the optimal arrangement of piezoelectric sensors is a key issue that needs to be urgently solved in structural health monitoring technology based on ultrasonic guided waves, which is of great value for the practical application of ultrasonic guided waves in aircraft structural damage monitoring and identification. Summary of the invention

[0005] The present invention provides an optimized layout method for piezoelectric sensors used in ultrasonic guided wave damage monitoring. When the number of piezoelectric sensors is fixed, by adjusting the sensor positions, a monitoring coverage area as large as possible can be obtained, enabling timely detection of damage in the area to be monitored and avoiding the situation where some areas and parts cannot be effectively monitored due to the sensor layout.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] An optimized layout method for piezoelectric sensors used in ultrasonic guided wave damage monitoring, comprising the following steps:

[0008] Step 1: Establish a coordinate system on the surface of the planar structure, and determine the geometric dimensions of the area to be monitored in the structure and the coordinate information of the inner and outer boundaries;

[0009] Step 2: Set discrete control points in the area to be monitored in the structure to define the coverage rate. The number and distribution of the control points can be user-defined;

[0010] Step 3: Determine the number of piezoelectric sensors available for layout. The user can define a preliminary layout scheme for the sensors or randomly generate an initial layout scheme within the allowable range;

[0011] Step 4: Take the proportion of the damage influence area of the sensing path between each two sensors covering the control points as the coverage rate optimization target, and construct a combinatorial optimization problem for sensor layout;

[0012] Step 5: To avoid the above combinatorial optimization problem falling into a local solution, use an artificial bee colony intelligent algorithm with global optimization ability for iterative solution, and gradually optimize the initial layout scheme to obtain the optimal layout scheme of the sensors, maximizing the coverage rate.

[0013] In the above steps, the combinatorial optimization problem of sensor layout described in Step 4 includes:

[0014] (1) Define the objective function for optimized sensor layout:

[0015] (a) The coverage rate CR is the number of discrete control points covered by the damage influence areas of three or more sensing paths, and it is used as the objective function of the optimization problem to be maximized:

[0016]

[0017] Where, when the kth control point is covered by the damage influence areas of three or more sensing paths, CR k = 1, otherwise CR k = 0; K is the total number of discrete control points in the total area to be monitored;

[0018] (b) If the area affected by the damage of the sensing path formed by the k-th control point, the i-th sensor, and the j-th sensor satisfies then it is considered that the area affected by the damage of the sensing path formed by the k-th control point, the i-th sensor, and the j-th sensor is covered, denoted as CR ijk = 1, where (x i , y i ) and (x j , y j ) are the central coordinates of the i-th sensor and the j-th sensor respectively, and (x k , y k ) is the central coordinate of the k-th control point. The eccentricity β determines the degree of influence of the damage on the ultrasonic guided wave signal on the sensing path, which is specified by the user before optimization;

[0019] (2) The sensor arrangement needs to satisfy the following constraint conditions:

[0020] (a) The number of sensors N s is specified by the user before optimization and remains unchanged during the optimization process;

[0021] (b) The distance D ij between the centers of the i-th sensor and the j-th sensor needs to satisfy D max > D ij > D min , where (x i , y i ) and (x j , y j ) are the central coordinates of the i-th sensor and the j-th sensor respectively, and D max and D min are specified by the user before optimization;

[0022] (c) The positions where the sensors are arranged need to be inside or on the boundary of the area to be monitored of the structure.

[0023] For the above combined optimization problem, general mathematical optimization algorithms are prone to falling into local solutions. To solve this problem, the optimization algorithm adopted needs to have good global solution ability and be able to avoid the iterative solution of the combined optimization problem of sensor arrangement from falling into local solutions. The present invention adopts an artificial bee colony intelligent algorithm that simulates the behavior of bees collecting honey to solve the combined optimization problem of sensor arrangement in step five. Through the local optimization behavior of each artificial bee individual, the global optimal value finally emerges in the bee colony, with a relatively fast convergence speed. The condition for terminating the iterative solution of the artificial bee colony intelligent algorithm adopted in step five is that the coverage rate CR of the objective function reaches the specified coverage rate CR aim , that is, CR ≥ CR aim, or the number of iterative solutions ITER reaches the specified number of iterations ITER max , that is, ITER ≥ ITER max , CR aim and ITER max are specified by the user before optimization.

[0024] Beneficial effects: The present invention provides an optimized layout method for piezoelectric sensors used in ultrasonic guided wave damage monitoring. When arranging piezoelectric sensors, the influence of damage on the propagation of ultrasonic guided wave signals on the sensing path is considered, the concept of monitoring area coverage rate is defined, and the goal is to maximize the coverage rate of the sensors. The optimization layout of the sensors is transformed into a combinatorial optimization problem and solved by an artificial bee colony intelligent algorithm with global optimization ability, providing an effective means for the optimized layout of piezoelectric sensors. Description of the drawings

[0025] Figure 1 is the schematic diagram of the corresponding sensor coverage rate in the embodiment of the present invention;

[0026] In the figure, 01 is the planar structure area, 02 is the discrete control points, 03 is the piezoelectric sensor, and 04 is the sensing path damage influence area;

[0027] Figure 2 is the schematic diagram of the planar structure and discrete control point examples in the embodiment of the present invention;

[0028] Figure 3 is the schematic diagram of the randomly generated initial layout scheme of the sensors in the embodiment of the present invention;

[0029] Figure 4 is the coverage rate evolution diagram obtained by iterative calculation of the artificial bee colony intelligent algorithm in the embodiment of the present invention;

[0030] Figure 5 is the schematic diagram of the optimal layout scheme of the sensors obtained by iterative calculation of the artificial bee colony intelligent algorithm in the embodiment of the present invention. Detailed implementation manners

[0031] The present invention will be described in detail below in conjunction with the drawings and specific implementation manners:

[0032] As Figure 1The figure shows a schematic diagram of the optimized layout of the piezoelectric sensor corresponding to the present invention, which includes a plane structure area 01 to be monitored, discrete control points 02, piezoelectric sensors 03, and a sensing path damage influence area 04; the number and distribution of the discrete control points 02 can be user-defined. In the present invention, the coverage rate CR of the structure to be monitored area refers to the number of discrete control points 02 covered by three or more sensing path damage influence areas 04. The present invention takes the maximization of the coverage rate CR as the optimization goal, constructs a combinatorial optimization problem for sensor layout, and uses an artificial bee colony intelligent algorithm with global optimization ability to perform iterative solution, and gradually optimizes from the initial layout scheme to obtain the optimal layout scheme of the sensor.

[0033] As Figure 2 shown, the monitored planar structure is a square area with a side length of 100 mm. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring includes the following steps:

[0034] Step 1: Set the coordinate origin at the lower left corner of this area, with the x-axis along the lower boundary to the right and the y-axis along the left boundary upward. The coordinates of each corner point of the boundary are as Figure 2 shown;

[0035] Step 2: Set discrete control points in the structure to be monitored area to define the coverage rate. A total of 900 control points are set, and the intervals of the control points are the same, as Figure 2 shown;

[0036] Step 3: Assume that the number of piezoelectric sensors available for layout is 20. Within the allowable range, that is, inside or on the boundary of the structure to be monitored area, as Figure 3 shown, randomly generate the coordinates of these 20 sensors as the initial layout scheme. The coordinate information of each sensor in the initial layout scheme is shown in Table 1. According to the initial layout scheme, calculate the coverage rate CR at this time to be 78.67%, and the uncovered control points are also marked in Figure 3 ;

[0037] Table 1 Coordinates of the initial layout scheme of piezoelectric sensors in the example

[0038] Sensor number 1 2 3 4 5 6 7 8 9 10 x (mm) 89.75 0.26 36.48 15.68 71.45 1.37 18.31 0.00 65.85 42.61 y (mm) 66.06 15.84 5.01 90.18 72.93 50.38 51.50 97.73 61.23 85.55 Sensor number 11 12 13 14 15 16 17 18 19 20 x (mm) 1.86 100.00 0.54 69.82 88.59 81.16 18.25 89.31 100.00 26.44 y (mm) 24.21 19.46 26.88 13.99 15.43 98.31 3.05 18.85 25.38 92.78

[0039] Step 4: Take the proportion of the control points covered by the sensing path damage influence area between every two sensors as the coverage rate optimization goal, and construct a combinatorial optimization problem for sensor layout:

[0040] First, define the objective function for optimizing the sensor layout as follows:

[0041] (a) The coverage rate CR is the number of discrete control points covered by three or more sensing path damage influence areas, and it is used as the objective function of the optimization problem to be maximized:

[0042]

[0043] Among them, when the k-th control point is covered by damage influence areas of three or more sensing paths, CR k = 1, otherwise CR k = 0; K is the total number of discrete control points in the total area to be monitored. In this example, K = 900.

[0044] (b) Between the k-th control point and the damage influence area formed by the i-th sensor and the j-th sensor, if is satisfied, it is considered that the k-th control point is covered by the damage influence area formed by the i-th sensor and the j-th sensor, denoted as CR ijk = 1, where (x i , y i ) and (x j , y j ) are the center coordinates of the i-th sensor and the j-th sensor respectively, (x k , y k ) is the center coordinate of the k-th control point, and the eccentricity β determines the influence degree of the damage on the ultrasonic guided wave signal on the sensing path. In this example, the eccentricity β is set to 1.03;

[0045] Then, the following constraint conditions that the sensor layout needs to meet are defined:

[0046] (a) The number N of sensors s remains unchanged during the optimization process. In this example, N s = 20;

[0047] (b) The distance D between the centers of the i-th sensor and the j-th sensor ij , needs to satisfy D max > D ij > D min , where (x i , y i ) and (x j , y j ) are the center coordinates of the i-th sensor and the j-th sensor respectively. In this example, D max = 80mm, D min = 10mm;

[0048] (c) The positions where the sensors are arranged need to be inside or on the boundary of the area to be monitored of the structure;

[0049] Step 5: Use the artificial bee colony intelligent algorithm with global optimization ability for iterative solution. Gradually optimize from the initial layout plan to obtain the optimal layout plan of the sensors, maximizing the coverage rate. In the artificial bee colony algorithm, set the total number of bees in the bee colony to 80, and the total number of iterations ITER max = 40. The termination condition for the iterative solution of the artificial bee colony intelligent algorithm adopted is that the number of iterative solutions ITER reaches the specified number of iterations ITER max , that is, ITER ≥ ITER max ; The specific process is as follows:

[0050] (a) Initialization: Randomly generate a set of nectar sources within the allowable range of the structural size (the information contained in the nectar source is the position of the sensor). The number of nectar sources is half of the number of bees, that is, 40. Each nectar source contains a set of horizontal and vertical coordinates of a total of N S = 20 sensors;

[0051] (b) Scout bee search: The scout bees search for new and better nectar sources near the nectar sources. For each nectar source, randomly generate a candidate nectar source within its neighborhood, and calculate the objective functions of the original nectar source and the candidate nectar source respectively, that is, the coverage rate CR. If the objective function of the candidate nectar source is higher than that of the original nectar source, the original nectar source will be replaced by the candidate nectar source, otherwise the original nectar source remains unchanged;

[0052] (c) Onlooker bee search: Sum up the objective functions corresponding to all nectar sources, and use the ratio of the objective function of each nectar source to the sum of the objective functions as the probability of selecting the corresponding nectar source. Randomly generate a random number between 0 and 1, and select a nectar source by the roulette method. Generate a candidate nectar source within its neighborhood, and calculate the objective functions of the original nectar source and the candidate nectar source respectively, that is, the coverage rate CR. If the objective function of the candidate nectar source is higher than that of the original nectar source, the original nectar source will be replaced by the candidate nectar source, otherwise the original nectar source remains unchanged;

[0053] (d) Repeat the search processes in (b) and (c) until the total number of iterations reaches the pre-set value, that is, ITER ≥ ITER max .

[0054] In this example, the iterative optimization curve of the artificial bee colony intelligent algorithm for the coverage rate is as Figure 4 shown. It can be seen from the figure that after 40 times of iterative optimization, the coverage rate of the sensors has reached 97.56%, and the coverage rate has been significantly improved. The sensor layout plan obtained after optimization by the present invention is as Figure 5 shown. The un-covered control points are also marked in Figure 5 . The coordinates of each optimized sensor are shown in Table 2

[0055] Table 2 Coordinates of the optimized layout plan of piezoelectric sensors in the example

[0056] Sensor number 1 2 3 4 5 6 7 8 9 10 x (mm) 40.79 0.00 100.00 41.23 9.12 74.58 0.00 19.35 23.64 0.59 y (mm) 62.70 22.26 100.00 83.00 83.53 93.91 0.00 3.80 100.00 96.34 Sensor number 11 12 13 14 15 16 17 18 19 20 x (mm) 67.42 100.00 47.87 28.13 81.77 100.00 41.19 96.62 68.17 100.00 y (mm) 34.36 58.21 16.81 22.75 82.44 15.38 8.66 3.54 60.96 36.61

[0057] The above are only the preferred embodiments of the present invention and should not be construed as limitations on the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention, and all of them fall within the protection scope of the present invention.

Claims

1. A method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring, characterized in that, it includes the following steps: Step 1: Establish a coordinate system on the surface of the planar structure to determine the geometric dimensions of the area to be monitored in the structure and the coordinate information of the inner and outer boundaries; Step 2: Set discrete control points in the area to be monitored in the structure to define the coverage rate; Step 3: Determine the preliminary layout plan of the sensors; Step 4: Take the proportion of the damage influence area of the sensing path between every two sensors covering the control points as the coverage rate optimization target, and construct a combined optimization problem for sensor layout, including: (1) Define the objective function for optimizing the layout of sensors: (a) The coverage rate CR is the number of discrete control points covered by the damage influence areas of three or more sensing paths, and it is maximized as the objective function of the optimization problem: Among them, when the k-th control point is covered by damage influence areas of three or more sensing paths, CR k = 1, otherwise CR k = 0; K is the total number of discrete control points in the total area to be monitored; (b) If it satisfies between the k-th control point and the sensing path damage influence area formed by the i-th sensor and the j-th sensor then it is considered that the k-th control point covers the sensing path damage influence area formed by the i-th sensor and the j-th sensor, denoted as CR ijk = 1, where (x i , y i ) and (x j , y j ) are the center coordinates of the i-th sensor and the j-th sensor respectively, and (x k , y k ) is the center coordinate of the k-th control point. The eccentricity β determines the influence degree of the damage on the ultrasonic guided wave signal on the sensing path, which is specified by the user before optimization; (2) Define the constraint conditions that need to be satisfied for sensor layout: (a) The number N of sensors s is specified by the user before optimization and remains unchanged during the optimization process; (b) The distance D between the centers of the i-th sensor and the j-th sensor ij , it is required that D max > D ij > D min , where (x i , y i ) and (x j , y j ) are the center coordinates of the i-th sensor and the j-th sensor respectively, D max and D min are specified by the user before optimization; (c) The positions where the sensors are arranged need to be inside or on the boundary of the area to be monitored in the structure; Step 5: Use the artificial bee colony intelligent algorithm with global optimization ability to perform iterative solution, and gradually optimize from the initial layout plan to obtain the optimal layout plan of the sensors, maximizing the coverage rate; the termination condition for the iterative solution of the adopted artificial bee colony intelligent algorithm is that the coverage rate CR of the objective function reaches the specified coverage rate CR aim , that is, CR ≥ CR aim , or the number of iterative solutions ITER reaches the specified number of iterations That is 2. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 1, characterized in that, the number and distribution of the control points in Step 2 are user-defined.

3. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 1 or 2, characterized in that, the coverage rate of the area to be monitored in the structure in Step 2 refers to the proportion of the number of discrete control points covered by the damage influence areas of three or more sensing paths to the total number of discrete control points.

4. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 1, characterized in that, in Step 3, the user defines the preliminary layout plan of the sensors or randomly generates an initial layout plan within the allowable range.

5. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 1, characterized in that, in Step 4, the shape of the damage influence area of the sensing path between every two sensors is an ellipse, its foci are these two sensors, the line connecting the two sensors is the sensing path, and the eccentricity of the ellipse is determined by the degree of influence of the damage on the ultrasonic guided wave signal on the sensing path.

6. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 1, characterized in that, Step 5 specifically includes the following steps: (a) Initialization: Randomly generate a group of nectar sources within the allowable range of the structure size. The information contained in the nectar sources is the position of the sensors. The number of nectar sources is half of the number of bees. Each nectar source contains a set of horizontal and vertical coordinates of the sensors; (b) Scout bee search: The scout bees search for new and better nectar sources near the nectar sources. For each nectar source, a candidate nectar source is randomly generated within its domain, and the objective functions of the original nectar source and the candidate nectar source, that is, the coverage rate CR, are calculated respectively. If the objective function of the candidate nectar source is higher than that of the original nectar source, the original nectar source will be replaced by the candidate nectar source, otherwise the original nectar source remains unchanged; (c) Follow-the-bee search: Sum up the objective functions corresponding to all nectar sources, and use the ratio of the objective function of each nectar source to the sum of the objective functions as the probability of selecting the corresponding nectar source. Randomly generate a random number between 0 and 1, and select a nectar source by the roulette wheel method. Generate a candidate nectar source within its neighborhood, and calculate the objective functions of the original nectar source and the candidate nectar source respectively, that is, the coverage rate CR. If the objective function of the candidate nectar source is higher than that of the original nectar source, the original nectar source will be replaced by the candidate nectar source; otherwise, the original nectar source remains unchanged. (d) Repeat the search process in steps (b) and (c) until the target function coverage rate CR reaches the specified coverage rate CR aim , that is, CR ≥ CR aim , or the number of iterative solutions ITER reaches the specified number of iterations ITER max , that is, ITER ≥ ITER max .

7. The method for optimizing the layout of piezoelectric sensors for ultrasonic guided wave damage monitoring according to claim 6, characterized in that The CR aim and ITER max are specified by the user before optimization.

Images