Steel plate internal damage detection method based on guided waves and PINNs

Abstract

The invention discloses a steel plate internal damage detection method based on guided waves and PINNs, and the method comprises the following steps: firstly establishing a rectangular plane coordinate system, selecting a guided wave application position and a guided wave receiving point on the surface of a steel plate, applying guided waves to the steel plate, and selecting M time points of free vibration of the steel plate, the method comprises the following steps: carrying out guided wave receiving on a steel plate, calculating out-of-plane displacements of the steel plate at all guided wave receiving points, constructing a PINNs model and a DNN model, training the PINNs model and the DNN model at the same time by using the out-of-plane displacements, coordinates and time of the steel plate at all guided wave receiving points, detecting the steel plate by using the PINNs model and the DNN model, and positioning the damage position of the steel plate. According to the method, the wave equation is approximately solved through the physical information neural network, a complex finite difference method formula is avoided, so that the calculation cost is reduced, compared with a three-dimensional wave equation, the adopted physical equation based on the plate-shell theory is simpler, the calculation cost is reduced, the accuracy of positioning the internal damage of the steel plate is improved, and the accuracy of positioning the internal damage of the steel plate is improved. The internal damage position of the steel plate can be positioned.

Description

Technical Field

[0001] The present invention relates to the technical field of steel plate damage detection, and in particular to a steel plate internal damage detection method based on guided wave and PINNs. Background Art

[0002] Steel bridge decks are widely used due to their light weight, high strength, convenient construction, and good durability. However, under repeated vehicle loads, the original internal defects of steel bridge decks expand and develop into serious internal damage, which greatly affects the service life of steel bridge decks. Therefore, it is extremely important to detect internal damage of steel bridge decks.

[0003] The prior art uses the output γ of the neural network (machine learning method) to characterize the change of material parameters, then multiplies γ with the parameters characterizing the material in the wave equation, and then uses a numerical method (finite difference method) to solve the wave equation to obtain the predicted displacement field. The loss function of the neural network is the average of the square difference between the predicted displacement field and the actual displacement field. The neural network is then trained by back propagation of the loss function to obtain the final γ, and the damage position can be located according to the value of γ.

[0004] The existing technology has limited physical information coupling due to the finite difference solver embedded in the algorithm. At the same time, the finite difference method formula of the wave equation is relatively complex, resulting in high computational costs. In addition, the existing technology generally locates the damage position based on one-dimensional and two-dimensional wave equations, but the accuracy of locating steel plate damage using three-dimensional wave equations is low. Summary of the invention

[0005] The purpose of the present invention is to provide a method for detecting internal damage of steel plates based on guided waves and PINNs in response to the above-mentioned problems. The wave equation is approximately solved by a physical information neural network, thereby avoiding complex finite difference method formulas and reducing calculation costs. The physical equation based on plate and shell theory is simpler than the complex three-dimensional wave equation, which further reduces the calculation cost and improves the accuracy of locating internal damage of steel plates, and can locate the internal damage position of the steel plate.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is as follows:

[0007] According to one aspect of the present invention, a method for detecting internal damage of a steel plate based on guided waves and PINNs is provided, comprising the following steps:

[0008] S1. Establish a plane rectangular coordinate system with the surface of the steel plate as the reference plane;

[0009] S2. Select a waveguide application position on the surface of the steel plate, arrange a plurality of waveguide receiving points at equal intervals based on the waveguide application position, and simultaneously obtain the coordinates of each waveguide receiving point;

[0010] S3, applying guided waves to the steel plate, and when the guided wave application is completed and the steel plate is in free vibration, M time points in the process of the steel plate in free vibration are selected, and the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points is calculated using a physical equation based on plate and shell theory;

[0011] S4, constructing a PINNs model and a DNN model, wherein the PINNs model is used to solve physical equations, and the DNN model is used to train parameters of the steel plate that characterize changes in material properties, and the PINNs model and the DNN model are simultaneously trained using the out-of-plane displacement, coordinates, and time of the steel plate at all waveguide receiving points corresponding to each of the M time points;

[0012] S5. Use the trained PINNs model and DNN model to detect the steel plate, obtain parameters that characterize changes in material properties of the steel plate, and locate the location of the steel plate damage based on the parameters.

[0013] Preferably, in step S3, the waveguide is ultrasonic wave, and the ultrasonic wave is expressed by the following formula:

[0014]

[0015] Where A is the amplitude; f c is the center frequency; N c is the number of peaks; H(t) is the Heaviside function.

[0016] Preferably, the Heaviside function H(t) can be expressed by the following formula:

[0017]

[0018] Preferably, in step S3, based on the plate-shell theory, the out-of-plane displacement of the steel plate at each waveguide receiving point is calculated by the following formula:

[0019]

[0020] Where u is the out-of-plane displacement of a particle on the surface of the plate; x and y are the coordinates of the particle; t is time; ρ is the density of the plate; and D is the bending stiffness of the plate.

[0021] Preferably, the bending stiffness D of the steel plate is:

[0022]

[0023] Among them, E is the elastic modulus, v is the Poisson's ratio, and h is the thickness of the thin plate.

[0024] Preferably, in step S4, the PINNs model includes an input layer, a hidden layer and an output layer, the number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 100, and the number of neurons in the output layer is 1.

[0025] Preferably, the loss function of the PINNs model is:

[0026] f(θ)=f r (θ)+λf d (θ)

[0027]

[0028] f r (θ) is the physical constraint loss; f d (θ) is the data loss term; u(x i ,y i ,t i ) is the measured true value; u θ (x i ,y i ,t i ) is the predicted value; N is the total number of particles; θ is the weight and bias term of the PINNs model; (γ β ) i is the output of the DNN model; λ is the weight.

[0029] Preferably, in step S4, the DNN model includes an input layer, a hidden layer and an output layer, the number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 40, and the number of neurons in the output layer is 1.

[0030] Preferably, the loss function of the DNN model is:

[0031]

[0032] Among them, β is the weight and bias term of the DNN model.

[0033] Preferably, in step S4, the training method of the PINNs model and the DNN model is:

[0034] The PINNs model and the DNN model are first trained simultaneously by the optimizer Adam. After 20,000 iterations, the LBFGS optimizer is used to train the PINNs model and the DNN model simultaneously.

[0035] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0036] 1. The present invention adopts PINNs to approximately solve the physical equations based on plate and shell theory instead of using traditional numerical methods.

[0037] 2. Traditional damage diagnosis methods often rely on extracting damage indexes from signals, which may lead to loss of diagnostic information or reduced accuracy. The present invention uses physical information neural networks combined with acoustic waves to measure parameters that characterize material properties to directly locate the damage location.

[0038] 3. The present invention uses PINNs to directly embed known physical laws (plate and shell theory) into the network's loss function, thereby ensuring that the prediction results of the neural network conform to the physical laws of the problem.

[0039] 4. The PINNs in the present invention can be used not only for forward problems (i.e. predicting output given input), but also for solving complex reverse problems (such as inferring physical parameters from observed data). It not only predicts the displacement field of the system (forward problem), but also can infer material properties and damage locations from observed data (reverse problem). BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic flow chart of the method of the present invention;

[0041] Figure 2 It is a waveguide waveform diagram of the present invention;

[0042] Figure 3 It is a training flow chart of two models of the present invention;

[0043] Figure 4 It is a schematic diagram of the network structure of the PINNs model of the present invention;

[0044] Figure 5 It is a schematic diagram of the network structure of the DNN model of the present invention;

[0045] Figure 6 is a schematic structural diagram of a steel plate of the present invention;

[0046] Figure 7 is a schematic diagram of the side structure of the steel plate of the present invention;

[0047] Figure 8 is a cloud diagram of the final γ value of the present invention;

[0048] Fig. 9 It is a schematic diagram of the loss function values ​​of the two models of the present invention. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are only for the purpose of enabling the reader to have a thorough understanding of one or more aspects of the invention, and these aspects of the present invention can be realized even without these specific details.

[0050] See also Figures 1 to 9 The present invention provides a method for detecting internal damage of steel plates based on guided waves and PINNs. The technical solution is as follows:

[0051] A method for detecting internal damage of a steel plate based on guided waves and PINNs comprises the following steps:

[0052] S1. Establish a plane rectangular coordinate system with the surface of the steel plate as the reference plane.

[0053] Specifically, the upper surface of the steel plate is used as a reference plane, and a plane rectangular coordinate system is established with the reference plane to obtain the coordinates of each point on the steel plate. For example, a certain corner of the steel plate is used as the origin of the coordinates, and the side of the steel plate passing through the origin is used as the X-axis or Y-axis, and another perpendicular line perpendicular to the side is used as the Y-axis or X-axis to establish a plane rectangular coordinate system to better obtain the coordinates of the steel plate.

[0054] S2. Select a waveguide application position on the surface of the steel plate, arrange multiple waveguide receiving points on the surface of the steel plate at equal intervals based on the waveguide application position, and obtain the coordinates of each waveguide receiving point, wherein the range of the waveguide receiving points is ensured to cover the damaged position.

[0055] Specifically, when the approximate range of the damaged part of the steel plate cannot be known, a waveguide application position is selected at the edge of the entire steel plate, and the waveguide application position is diffused outward to arrange multiple waveguide receiving points on the surface of the steel plate at equal intervals. The waveguide receiving points are arranged in the form of a grid, and the coordinates of each waveguide receiving point are obtained through the established rectangular coordinate system.

[0056] When the approximate range of the steel plate damage is known, the waveguide application position is selected on the boundary of the range, and multiple waveguide receiving points are arranged at equal intervals in the form of a grid within the range. The coordinates of the waveguide receiving points are then obtained according to the coordinate system, thereby narrowing the detection range and reducing the amount of calculation and improving the calculation accuracy.

[0057] S3. Apply guided wave to the steel plate. When the guided wave application is completed and the steel plate is in free vibration, M time points in the process of free vibration of the steel bridge deck are intercepted, and the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points is calculated.

[0058] Specifically, a waveguide generator is placed at the waveguide application position selected on the steel plate, and the waveguide generator is used to apply waveguide to the steel plate. In this embodiment, the waveguide is ultrasonic wave, and the ultrasonic wave generation satisfies the following formula:

[0059]

[0060] Where A is the amplitude; f c is the center frequency; N c is the number of peaks; H(t) is the Heaviside function.

[0061] The Heaviside function H(t) can be expressed as follows:

[0062]

[0063] In this embodiment, A is set to 0.5, f c The value is 30KHz, N c The value is 5, and the sampling frequency is 1.25MHz. The final waveguide is as follows Figure 2 As shown. The guided wave starts to act on the steel plate from t = 0. After the guided wave is applied, the steel plate begins to vibrate freely. When the steel plate is vibrating freely, M time points (M ≥ 2) are intercepted during the free vibration of the steel plate, and the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points is calculated. Based on the Kirchhoff-Love plate theory, the control equation of the flexural motion of an isotropic homogeneous thin plate under free vibration can be expressed as:

[0064]

[0065] Among them, u is the out-of-plane displacement of the particle on the surface of the thin plate; x and y are the coordinates of the particle; t is time; ρ is the density of the thin plate; D is the bending stiffness of the steel plate. The bending stiffness D of the steel plate is:

[0066]

[0067] Among them, E is the elastic modulus, v is the Poisson's ratio, and h is the thickness of the thin plate.

[0068] The control equation can be simplified to:

[0069]

[0070] Where α is:

[0071]

[0072] α is only related to the material properties of the steel plate (elastic modulus, density, thickness, etc.), and will change in the damaged area of ​​the steel plate. Therefore, the damaged area can be located according to the change of α value.

[0073] The out-of-plane displacement of the steel plate at each waveguide receiving point can be calculated using the control equation.

[0074] S4. Construct a PINNs model and a DNN model, and use the out-of-plane displacement, coordinates, and time of the steel plate at all waveguide receiving points corresponding to each of the N time points to simultaneously train the PINNs model and the DNN model.

[0075] Specifically, a PINNs model and a DNN model are constructed. The PINNs model is a physical information neural network used to solve the simplified control equation. The DNN model is a deep neural network used to train the parameter γ. γ is used to characterize the change of the material property α. The two models PINNs and DNN are trained simultaneously. The whole method flow is as follows Figure 3 shown.

[0076] like Figure 4 As shown in the figure, the PINNs model includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 100, and the number of neurons in the output layer is 1. The activation function is sin. The input data of the input layer are the coordinates x and y of the waveguide receiving point on the surface of the steel plate, and the time t. The output of the output layer of PINNs is the out-of-plane displacement of the steel plate at the waveguide receiving point. The loss function of the PINNs model is expressed by the following formula:

[0077] f(θ)=f r (θ)+λf d (θ)

[0078]

[0079] f r (θ) is the physical constraint loss; f d (θ) is the data loss term; u(x i ,y i ,t i ) is the measured true value; u θ (x i ,y i ,t i ) is the predicted value; N is the total number of particles; θ is the weight and bias term of the PINNs model; (γ β ) i is the output of the DNN model; λ is the weight. In this embodiment, λ is 100.

[0080] like Figure 5As shown in the figure, the DNN model includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 40, and the number of neurons in the output layer is 1. Except for the activation function of the last hidden layer, which is an exponential function, the activation functions of the rest are sin. The input data of the input layer are the coordinates x and y of the waveguide receiving point on the steel plate surface, and the time t. The output of DNN is γ β , γ β It is used to characterize the change of material property α. The loss function of the DNN model is expressed as follows:

[0081]

[0082] Among them, β is the weight and bias term of the DNN model.

[0083] In this embodiment, the PINNs model and the DNN model are first trained simultaneously by the optimizer Adam. After 20,000 iterations, the LBFGS optimizer is used to train the PINNs model and the DNN model simultaneously. The entire method flow is as follows: Figure 1 shown.

[0084] S5. Use the trained PINNs model and DNN model to detect the steel plate.

[0085] Specifically, the trained PINNs model and DNN model are used to detect internal damage of the steel plate. After the model is trained, there will be M γ values ​​for each waveguide receiving point. Finally, the average of γ at each waveguide receiving point is taken as the final γ value of each waveguide receiving point. The γ cloud map is obtained based on the γ value. The γ value changes in the damaged area, thereby locating the damage location.

[0086] This application prepares a steel plate, such as Figure 6 and Figure 7 As shown, the side length of the steel plate is 200mm and the thickness is 3mm. An artificial damage is made, the damage is a rectangle with a length and width of 10mm and a depth of 2mm, and the upper surface of the damage is 1mm away from the upper surface of the steel plate. The experiment is carried out with the steel plate with known damage. The experimental process is as follows:

[0087] Take the lower left corner of the steel plate as the origin to make a plane rectangular coordinate system, and the two right-angled sides passing through the origin are the X-axis and the Y-axis. Frame an 80*80mm square area at the damage location, and the damage location is located at the center of the square area. Select the ultrasonic emission position on the left side of the square area, and the coordinates of the ultrasonic emission position are (60, 105) mm (the black dot in the figure is the transmitter, and point O is the origin). The shaded area is the square area, and a waveguide receiving point is arranged every 1mm in the shaded area. The waveguide receiving points are arranged in a grid, with a total of 6561 waveguide receiving points.

[0088] The guided wave acts on the steel plate from t = 0 and ends at t = 0.166ms. Therefore, after 0.166ms, the steel plate vibrates freely. The out-of-plane displacement of the steel plate at 6561 guided wave receiving points at t = [0.1676, 0.1696, 0.1716, 0.1736]ms is extracted for training the model. The interval between the four time points is 0.002ms. The displacements at these moments and the coordinates of the corresponding points and the corresponding time are input into PINNs and DNN to train the model.

[0089] Experimental results: The PINNs model and the DNN model were first trained simultaneously using the Adam optimizer. After 20,000 iterations, the LBFGS optimizer was used to train the PINNs model and the DNN model simultaneously. The maximum number of iterations of the LBFGS optimizer was set to 10,000. Since the data of four time points were extracted at equal intervals before, there would be four γ values ​​for each waveguide receiving point after the final model training. Finally, the average of the γ values ​​of each waveguide receiving point was taken as the final γ value of each waveguide receiving point.

[0090] The results are as follows Figure 8 As shown, Figure 8 is the cloud map of the final γ value. The black dotted frame is the actual damaged area of ​​the steel plate. The γ value changes in the damaged area, thereby locating the location of the damage. Fig. 9 As shown, Fig. 9 The change in the loss function value during the model parameter update process. After the parameter update 20,000 times, the loss function has converged, so the optimizer LBFGS has not been triggered.

[0091] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A steel plate internal damage detection method based on guided wave and PINNs, characterized in that: The following steps are involved: S1. Establish a plane rectangular coordinate system with the surface of the steel plate as the reference plane; S2. Select a waveguide application position on the surface of the steel plate, arrange a plurality of waveguide receiving points at equal intervals based on the waveguide application position, and simultaneously obtain the coordinates of each waveguide receiving point; S3, applying guided waves to the steel plate, and when the guided wave application is completed and the steel plate is in free vibration, M time points in the process of the steel plate in free vibration are selected, and the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points is calculated using a physical equation based on plate and shell theory; S4, constructing a PINNs model and a DNN model, wherein the PINNs model is used to solve physical equations, and the DNN model is used to train parameters of the steel plate that characterize changes in material properties, and the PINNs model and the DNN model are simultaneously trained using the out-of-plane displacement, coordinates, and time of the steel plate at all waveguide receiving points corresponding to each of the M time points; S5. Use the trained PINNs model and DNN model to detect the steel plate, obtain parameters that characterize changes in material properties of the steel plate, and locate the location of the steel plate damage based on the parameters.

2. According to claim 1, a steel plate internal damage detection method based on guided wave and PINNs is characterized in that: In step S3, the guided wave is an ultrasonic wave, and the ultrasonic wave is expressed by the following formula: Where A is the amplitude; f c is the center frequency; N c is the number of peaks; H(t) is the Heaviside function.

3. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 2, characterized in that: The Heaviside function H(t) can be expressed as follows:

4. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 1, characterized in that: In step S3, based on the plate-shell theory, the out-of-plane displacement of the steel plate at each waveguide receiving point is calculated by the following formula: Where u is the out-of-plane displacement of a particle on the surface of the plate; x and y are the coordinates of the particle; t is time; ρ is the density of the plate; and D is the bending stiffness of the plate.

5. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 4, characterized in that: The bending stiffness D of the steel plate is: Among them, E is the elastic modulus, v is the Poisson's ratio, and h is the thickness of the thin plate.

6. The method for detecting internal damage of steel plates based on guided wave and PINNs according to claim 1, characterized in that: In step S4, the PINNs model includes an input layer, a hidden layer and an output layer. The number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 100, and the number of neurons in the output layer is 1.

7. A steel plate internal damage detection method based on guided wave and PINNs according to claim 6, characterized in that: The loss function of the PINNs model is: f(θ)=f r (θ)+λf d (i) f r (θ) is the physical constraint loss; f d (θ) is the data loss term; u(x i ,y i ,t i ) is the measured true value; u θ (x i ,y i ,t i ) is the predicted value; N is the total number of particles; θ is the weight and bias term of the PINNs model; (γ β ) i is the output of the DNN model; λ is the weight.

8. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 1, characterized in that: In step S4, the DNN model includes an input layer, a hidden layer and an output layer. The number of neurons in the input layer is 3, the number of layers in the hidden layer is 3, the number of neurons in the hidden layer is 40, and the number of neurons in the output layer is 1.

9. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 8, characterized in that: The loss function of the DNN model is: Among them, β is the weight and bias term of the DNN model.

10. The method for detecting internal damage of steel plates based on guided waves and PINNs according to claim 1, characterized in that: In step S4, the training method of the PINNs model and the DNN model is: The PINNs model and the DNN model are first trained simultaneously by the optimizer Adam. After 20,000 iterations, the LBFGS optimizer is used to train the PINNs model and the DNN model simultaneously.

Images