A steel plate internal damage detection method based on guided waves and PINNs

Abstract

The application discloses a kind of steel plate internal damage detection method based on guided wave and PINNs, the method includes the following steps, first, establish plane rectangular coordinate system, guided wave is applied to the surface of steel plate and guided wave receiving point is selected, guided wave is applied to the steel plate, select M time points of free vibration of the steel plate, and calculate the out-of-plane displacement of the steel plate at all guided wave receiving points, PINNs model and DNN model are constructed, PINNs model and DNN model are trained simultaneously using the out-of-plane displacement of the steel plate at all guided wave receiving points, coordinates and time, the steel plate is detected using PINNs model and DNN model, and the position of the steel plate damage is located.The application solves wave equation by physical information neural network, avoids complex finite difference method formula, thereby reduces the cost of calculation, and the physical equation based on plate shell theory is simpler than three-dimensional wave equation, reduces the cost of calculation, and improves the accuracy of internal damage positioning of the steel plate, and the internal damage position of the steel plate can be located.

Description

Technical Field

[0001] This invention relates to the field of steel plate damage detection technology, and in particular to a method for detecting internal damage in steel plates based on guided waves and PINNs. Background Technology

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

[0003] Current technology uses the output γ of a neural network (machine learning method) to characterize changes in material parameters. Then, γ is multiplied by the material parameters in the wave equation, and the wave equation is solved numerically (finite difference method) to obtain the predicted displacement field. The loss function of the neural network is the average of the squared differences between the predicted and actual displacement fields. The neural network is then trained through backpropagation using the loss function to obtain the final γ. The damage location can then be determined based on the value of γ.

[0004] Existing technologies, due to the embedding of finite difference solvers in the algorithms, have limited coupling with physical information. Furthermore, the finite difference method formula for the wave equation is quite complex, leading to high computational costs. Moreover, existing technologies generally locate damage based on one-dimensional and two-dimensional wave equations, but the accuracy of damage location in steel plates using three-dimensional wave equations is low. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned problems by providing a method for detecting internal damage in steel plates based on guided waves and PINNs. This method uses a physical information neural network to approximate the wave equation, avoiding the complex finite difference method formula, thereby reducing computational costs. Furthermore, the physical equation based on plate and shell theory is simpler than the complex three-dimensional wave equation, which further reduces computational costs and improves the accuracy of locating internal damage in steel plates, enabling the accurate location of internal damage.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] According to one aspect of the present invention, a method for detecting internal damage in steel plates based on waveguides 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, and arrange multiple waveguide receiving points at equal intervals based on the waveguide application position, while obtaining the coordinates of each waveguide receiving point.

[0010] S3. Apply guided waves to the steel plate. When the application of guided waves ends and the steel plate is in free vibration, select M time points during the free vibration process of the steel plate, and use the physical equations based on plate and shell theory to calculate the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points.

[0011] S4. Construct a PINNs model and a DNN model. The PINNs model is used to solve the physical equations, and the DNN model is used to train the parameters that characterize the changes in material properties of the steel plate. The PINNs model and the DNN model are trained simultaneously 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 the parameters that characterize the changes in the material properties of the steel plate, and locate the location of the damage in the steel plate based on the parameters.

[0013] Preferably, in step S3, the guided wave is an ultrasonic wave, which is represented by the following formula:

[0014]

[0015] Where A is the amplitude; f c The center frequency; N c t represents 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 plate and 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 thin plate; x and y are the coordinates of the particle; t is time; ρ is the density of the thin plate; and D is the bending stiffness of the steel plate.

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

[0022]

[0023] Where E is the elastic modulus, v is Poisson's ratio, and h is the thickness of the sheet.

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

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

[0026] f(θ)=f r (θ)+λf d (θ)

[0027]

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

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

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

[0031]

[0032] Where β represents the weights and biases of the DNN model.

[0033] Preferably, in step S4, the training methods for the PINNs model and the DNN model are as follows:

[0034] 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.

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

[0036] 1. This invention uses PINNs to approximate the solution of physical equations based on plate and shell theory, rather than using traditional numerical methods.

[0037] 2. Traditional damage diagnosis methods often rely on extracting damage indices from signals, which may lead to the loss of diagnostic information or a decrease in accuracy. This invention uses a physical information neural network combined with acoustic wave measurements to obtain parameters characterizing material properties to directly locate the damage site.

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

[0039] 4. In this invention, PINNs can be used not only for forward problems (i.e., predicting output given input) but also for solving complex inverse problems (such as inferring physical parameters from observation data). It not only realizes the prediction of the displacement field of the system (forward problem) but also infers material properties and damage location from observation data (inverse problem). Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0041] Figure 2 This is a waveform diagram of the guided wave of the present invention;

[0042] Figure 3 This is a flowchart of the training process for the two models of this invention;

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

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

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

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

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

[0048] Figure 9 This is a schematic diagram of the loss function values ​​for the two models in this invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 merely to provide the reader with a thorough understanding of one or more aspects of the invention, and these aspects of the invention can be achieved even without these specific details.

[0050] Please see Figures 1 to 9 This invention provides a method for detecting internal damage in steel plates based on guided waves and PINNs, the technical solution of which is as follows:

[0051] A method for detecting internal damage in steel plates based on guided waves and PINNs includes 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 Cartesian coordinate system is established based on this 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 coordinate system, and the edge of the steel plate passing through the origin is used as the X-axis or Y-axis. Then, another perpendicular line to that edge is used as the Y-axis or X-axis to establish a Cartesian coordinate system, so as to better obtain the coordinates of the steel plate.

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

[0055] Specifically, when the approximate extent of the damage to the steel plate cannot be determined, a waveguide application position is selected at the edge of the entire steel plate, and multiple waveguide receiving points are arranged at equal intervals on the surface of the steel plate from this waveguide application position. The waveguide receiving points are arranged in a grid, and the coordinates of each waveguide receiving point are obtained through an established Cartesian coordinate system.

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

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

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

[0059]

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

[0061] The heaviside function H(t) can be expressed by the following equation:

[0062]

[0063] In this embodiment, A is set to 0.5, and f c The value is 30kHz, N c The value is set to 5, and the sampling frequency is 1.25MHz. The final guided wave is as follows: Figure 2 As shown. A guided wave acts on the steel plate starting at t=0. After the guided wave application ends, the steel plate begins to vibrate freely. During the free vibration of the steel plate, M time points (M≥2) are captured, 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 governing equation for the flexural motion of an isotropic homogeneous thin plate under free vibration can be expressed as:

[0064]

[0065] Where u is the out-of-plane displacement of a 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; and D is the bending stiffness of the steel plate. The bending stiffness D of the steel plate is:

[0066]

[0067] Where E is the elastic modulus, v is Poisson's ratio, and h is the thickness of the sheet.

[0068] The governing equations 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 based on 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 governing equations.

[0074] S4. Construct the PINNs model and the DNN model. Simultaneously train the PINNs model and the DNN model using 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.

[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 governing equations. The DNN model is a deep neural network used to train the parameter γ. γ is used to characterize the variation of the material property α. Both models, PINNs and DNN, are trained simultaneously. The entire methodology is as follows: Figure 3 As shown.

[0076] like Figure 4 As shown, the PINNs model consists of an input layer, hidden layers, and an output layer. The input layer has 3 neurons, the hidden layer has 3 layers and 100 neurons, and the output layer has 1 neuron. The activation function is sin. The input data for the input layer are the coordinates (x and y) of the waveguide receiver point on the steel plate surface, and time (t). The output of the PINNs output layer is the out-of-plane displacement of the steel plate at the waveguide receiver 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) represents the physical constraint loss; f d (θ) represents the data loss term; u(x) i ,y i ,t i ) represents the measured true value; u θ (x i ,y i ,t i ) represents the predicted value; N represents the total number of particles; θ represents the weights and biases of the PINNs model; (γ) represents the predicted value; β ) i λ represents the output of the DNN model; λ is the weight, which is 100 in this embodiment.

[0080] like Figure 5As shown, the DNN model consists of an input layer, hidden layers, and an output layer. The input layer has 3 neurons, the hidden layers have 3 layers and 40 neurons, and the output layer has 1 neuron. Except for the last hidden layer, which uses an exponential activation function, all other activation functions are sine functions. The input data for the input layer consists of the coordinates (x and y) of the waveguide receiving point on the steel plate surface, and time (t). The output of the DNN is γ. β γ β It is used to characterize the change in material property α. The loss function of the DNN model is expressed by the following formula:

[0081]

[0082] Where β represents the weights and biases of the DNN model.

[0083] In this embodiment, the PINNs model and the DNN model are first trained simultaneously using the Adam optimizer. 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 As shown.

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

[0085] Specifically, the trained PINNs and DNN models are used to detect internal damage in the steel plate. After the models are trained, each waveguide receiver point will have M γ values. Finally, the average γ value of each waveguide receiver point is taken as the final γ value for that point. Based on the γ values, a γ contour map is obtained. The γ value changes in the damage area, thus locating the damage location.

[0086] This application involves preparing a steel plate, such as Figure 6 and Figure 7 As shown, the steel plate has a side length of 200mm and a thickness of 3mm. An artificial damage is created, a rectangle with dimensions of 10mm x 10mm and a depth of 2mm. The upper surface of the damage is 1mm from the upper surface of the steel plate. An experiment is conducted using this steel plate with known damage. The experimental procedure is as follows:

[0087] A Cartesian coordinate system is established with the lower left corner of the steel plate as the origin. The two legs of the right angle passing through the origin are the X-axis and Y-axis, respectively. An 80*80mm square area is defined around the damage location, with the damage location at the center of this square area. An ultrasonic wave transmission position is selected to the left of the square area, with coordinates (60, 105)mm (the black dot in the diagram represents the transmitter, and point O is the origin). The shaded area represents the square area. A guided wave receiver is placed every 1mm within the shaded area, arranged in a grid pattern, for a total of 6561 guided wave receivers.

[0088] The guided wave acts on the steel plate from t=0 and terminates at t=0.166ms. Therefore, after 0.166ms, the steel plate undergoes free vibration. The out-of-plane displacements of the steel plate at 6561 guided wave receiving points at t=[0.1676, 0.1696, 0.1716, 0.1736]ms are extracted for model training, with an interval of 0.002ms between the four time points. These displacements, their corresponding point coordinates, and the corresponding times are then input into PINNs and a DNN to train the model.

[0089] Experimental Results: The PINNs and DNN models were initially trained simultaneously using the Adam optimizer. After 20,000 iterations, the LBFGS optimizer was then used to train both models simultaneously, with a maximum iteration count of 10,000. Because data was extracted at four equally spaced time points, each waveguide receiver point would have four γ values ​​after the final model training. The average γ value for each waveguide receiver point was then taken as the final γ value for that point.

[0090] The results are as follows Figure 8 As shown, Figure 8 The image shows the cloud map of the final γ value. The area within the black dashed box represents the actual damage zone of the steel plate. The γ value changes within this damage zone, thus pinpointing the location of the damage. Figure 9 As shown, Figure 9 This represents the change in the loss function value during model parameter updates. The loss function converged after 20,000 parameter updates, therefore the optimizer LBFGS was not triggered.

[0091] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for detecting internal damage in steel plates based on guided waves and PINNs, characterized in that, Includes the following steps: 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, and arrange multiple waveguide receiving points at equal intervals based on the waveguide application position, while obtaining the coordinates of each waveguide receiving point. S3. Apply guided waves to the steel plate. When the application of guided waves ends and the steel plate is in free vibration, select M time points during the free vibration process of the steel plate, and use the physical equations based on plate and shell theory to calculate the out-of-plane displacement of the steel plate at all guided wave receiving points corresponding to each of the M time points. Based on plate and shell theory, the out-of-plane displacement of the steel plate at each waveguide receiving point is calculated by the following formula: ； in, It is the out-of-plane displacement of particles on the surface of the steel plate; and These are the coordinates of the point mass; It is time; It is the density of the steel plate; It refers to the bending stiffness of the steel plate; The bending stiffness of the steel plate for: ； in, For elastic modulus, Poisson's ratio, The thickness of the steel plate; S4. Construct a PINNs model and a DNN model. The PINNs model is used to solve the physical equations, and the DNN model is used to train the parameters that characterize the changes in the material properties of the steel plate. The PINNs model and the DNN model are trained simultaneously 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. The PINNs model includes an input layer, a hidden layer, and an output layer. The input layer has 3 neurons, the hidden layer has 3 layers and 100 neurons, and the output layer has 1 neuron. The loss function of the PINNs model is: ； Loss due to physical constraints; For data loss items; The measured true value; This is a predicted value; The total number of particles; These are the weights and biases of the PINNs model; This is the output of the DNN model; As weight; The DNN model includes an input layer, a hidden layer, and an output layer. The input layer has 3 neurons, the hidden layer has 3 layers and 40 neurons, and the output layer has 1 neuron. The loss function of the DNN model is: ； in, These are the weights and biases of the DNN model; S5. Use the trained PINNs model and DNN model to detect the steel plate, obtain the parameters that characterize the changes in the material properties of the steel plate, and locate the location of the damage in the steel plate based on the parameters.

2. The method for detecting internal damage in steel plates based on guided waves and PINNs according to claim 1, characterized in that: In step S3, the guided wave is an ultrasonic wave, which is expressed by the following formula: ； in, The amplitude; The center frequency; The number of peaks; This is the Heaviside function.

3. The method for detecting internal damage in steel plates based on guided waves and PINNs according to claim 2, characterized in that: The Heaviside function It can be expressed by the following formula: 。 4. The method for detecting internal damage in steel plates based on guided waves and PINNs according to claim 1, characterized in that: In step S4, the training methods for the PINNs model and the DNN model are as follows: 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.

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