Method for predicting residual life of mechanical structure based on phase field method and BP neural network

Abstract

This invention proposes a method for predicting the remaining life of mechanical structures based on the phase-field method and a backpropagation (BP) neural network. First, a physical model of the mechanical structure is established. Based on this physical model, a phase-field fracture model of the mechanical structure is constructed using the phase-field method, and crack propagation analysis is performed on the model. Second, easily measurable observation points are selected within the mechanical structure to obtain the strain values ​​and corresponding remaining life values ​​at these observation points during crack propagation, forming a dataset of strain and remaining life. Then, this dataset is input into a BP neural network for training, obtaining a predictive model between strain and remaining life. Finally, by continuously collecting strain values ​​at the observation points of the mechanical structure and inputting these strain values ​​into the trained network prediction model, the remaining life information of the mechanical structure can be predicted. This invention only requires obtaining the corresponding response values ​​at the observation points to predict the remaining life information of the mechanical structure.

Description

Technical Field

[0001] This invention relates to the field of remaining life prediction for mechanical structures, and particularly to a method for predicting the remaining life of mechanical structures that combines neural networks and the phase-field method. Background Technology

[0002] With the rapid development of industrial technology, the quality of engineering materials has a significant impact on the service life of engineering structures. If structural materials contain defects such as cracks and voids, internal strain energy will gradually accumulate during use, exceeding a critical value, causing sudden fracture and resulting in significant economic losses and endangering human life. Therefore, predicting the remaining service life of engineering structures is of great importance. By monitoring the structural operating status in real time and focusing on its remaining service life, we can anticipate and reduce the probability of danger, which is beneficial to ensuring the safe and stable operation of engineering structures.

[0003] In recent years, with the rapid development of computational science, numerical methods based on computational mechanics have been successfully applied to crack analysis in engineering structures. Methods such as the finite element method, boundary element method, and phase field method can all simulate crack propagation. However, when analyzing cracks using the finite element method, a large number of meshes need to be generated at the crack tip. During crack propagation simulation, the mesh needs to be repeatedly generated with each propagation step, leading to reduced computational efficiency and high computational cost. The boundary element method encounters singular and near-singular integral problems. The phase field method, on the other hand, is particularly competitive in crack analysis. Researchers using the phase field method have derived a variational formula for brittle fracture by introducing order parameters, regularizing the crack topology, and characterizing the dispersion of the fracture surface. Its advantage lies in the fact that it does not require explicit tracking of the crack surface; the evolution of the order parameters is controlled through the phase field expression, automatically obtaining the crack location, and the gradient of the order parameters is used to track the crack propagation interface. The main advantages of the phase-field method are: 1. The mesh only needs to be generated once, and the model does not need to be meshed again in subsequent crack propagation simulations; 2. The results are not sensitive to the number of meshes, and the number of meshes has little impact on the results; 3. No special treatment of cracks is required.

[0004] Neural network technology has significant advantages in processing big data and is beginning to be applied to fracture mechanics analysis. There are many types of neural network models for data prediction, such as backpropagation (BP) neural networks, convolutional neural networks, and graph convolutional neural networks. BP neural networks, based on deep learning technology, are particularly well-suited for fitting nonlinear data. By utilizing the error propagation mechanism, the error range is reduced by adjusting weights and thresholds layer by layer, effectively improving the model's fitting accuracy.

[0005] There is a lack of literature on the prediction of mechanical structure lifespan. A patent (CN112784495A) describes a data-driven real-time fatigue life prediction method for mechanical structures. This patent primarily employs the boundary element method (BEM) and backpropagation (BP) neural network technology. The BEM encounters challenges with singular and near-singular integrals, requiring the placement of singular elements at the crack tip and the use of the Pairs formula to simulate crack propagation. During crack simulation, the number of meshes increases with crack tip propagation, leading to a larger overall stiffness matrix and additional computational burden. This invention uses a combination of the phase-field method and neural networks. This eliminates the need for multiple mesh generation during crack propagation; the mesh is generated in a single step, reducing computational load and enabling the prediction of the remaining lifespan of the mechanical structure. Summary of the Invention

[0006] To address the issue that defects in mechanical structures, such as cracks and holes, can affect the safety and stability of structural operation, this invention proposes a method for predicting the remaining life of a structure based on a combination of the phase-field method and deep learning. A phase-field fracture model of the structure based on the phase-field method is established, and a corresponding neural network model structure is built. The functional relationship between strain values ​​at observation points in the structure and the structural life is clarified. A suitable prediction model is trained using a BP neural network, enabling the prediction of the structure's remaining life using only the measured strain values ​​at the observation points.

[0007] The technical solution of this invention is implemented as follows:

[0008] A method for predicting the remaining life of a mechanical structure based on a combination of neural networks and the phase-field method includes the following steps:

[0009] S1: Construct a CAD model of the mechanical structure, including the location and size of the cracks; use ultrasonic detection technology to obtain the location and size of the cracks in the mechanical structure, and use a laser scanner to obtain the shape, geometry and location information of the mechanical structure to create a high-precision CAD model, providing a physical model for constructing a phase-field fracture model;

[0010] S2: Construct a phase-field fracture model of the mechanical structure;

[0011] S2.1: An order parameter φ is introduced to describe the damage evolution of cracks. The crack initiation, propagation, and fracture are represented by an auxiliary damage scalar φ. φ = 0 indicates that the material is intact, and φ = 1 indicates that the material is completely fractured. A continuous smoothness function φ(x) is introduced to approximate the crack propagation.

[0012] S2.2: The total energy functional of the mechanical structure is obtained from the fracture variational principle;

[0013] S2.3: Calculate the elastic strain energy of the mechanical structure;

[0014] S2.4: Calculate the virtual work of external forces and virtual work of internal forces in a mechanical structure using the principle of virtual work;

[0015] S3: Select appropriate observation points on the mechanical structure and obtain corresponding sample data;

[0016] S3.1: By establishing a phase-field fracture model of the mechanical structure, input the physical and material property parameters of the mechanical structure, including Young's modulus E and Poisson's ratio ν;

[0017] S3.2: Set the increment step; where the displacement increment is Δu, the extended time step is Δt, and the number of increment steps is NN;

[0018] S3.3: Grid division; the number of grid divisions is N1, N2, N3, ..., N m Where N1 < N2 < ... < N m ;

[0019] S3.4: Select the observation point; the location of the observation point is used to place the strain gauge.

[0020] S3.5: Extract model data; using the established phase-field fracture model, extract the strain and displacement values ​​at the observation points. The total number of samples obtained is NM. The remaining life value t of the structure can be expressed as:

[0021] t=(x NM -x i ) / Δu*Δt

[0022] In the formula, x represents the displacement, NM is the total number of the original sample set, and i represents the nth sample point. N It is the maximum displacement value when the mechanical structure completely breaks, x i It is the displacement value corresponding to the i-th sample point; the functional relationship between the strain value and life of the mechanical structure is expressed as F(ε,t), where ε is the strain value of the structure and t is the remaining life of the mechanical structure.

[0023] S4: Construct a neural network model to predict the remaining lifespan of mechanical structures;

[0024] S4.1: Construct a neural network model; First, clarify the data of the input layer and the data of the output layer of the model structure. The data of the input layer uses the strain value data of the observation points, and the data of the output layer is the life value of the mechanical structure.

[0025] S4.2: Training the Neural Network; Strain value samples are input from the input layer and processed through the neural network structure to calculate the output value. The output value is compared with the expected value to obtain the error between them. It is then determined whether the termination condition is met. If not, the error is propagated back through the output layer to the intermediate layer and then back to the input layer, and the weights and thresholds between each layer are modified. This process is repeated to obtain a smaller error while still satisfying the iteration termination condition. The iteration termination condition is to meet the set training accuracy. By continuously reducing the training error, the neural network gradually approaches the target function, thus achieving the training objective of improving the accuracy of the network model's predictions.

[0026] S4.3: Combining the phase-field method and BP neural network, the functional relationship between the strain value and the life value of the mechanical structure is realized and its life value is predicted; the phase-field method is used to effectively track the crack propagation of the mechanical structure, and the strain value and displacement value data at the observation points in the mechanical structure that are easy to measure are exported and saved;

[0027] S4.4: Arrange the original dataset in order and group it into sets of 6 data points. Then process the dataset sequentially using this method. Construct a BP neural network model structure suitable for this dataset. Divide the processed data into training and test sets in a 7:3 ratio. Use the data from the training set to continuously optimize and improve the correlation coefficient of the BP neural network to reduce errors and improve prediction accuracy. Use the data from the test set to verify the performance of the trained model and achieve the prediction of the remaining lifespan of mechanical structures.

[0028] Compared to existing technologies, the advantages of this invention are as follows: This invention uses the phase-field method and neural networks to predict the remaining life of a structure. The phase-field method is used to track the crack propagation process, obtaining a sample set of structural response values ​​and remaining life. Combined with the BP neural network algorithm, the remaining life of the structure can be predicted simply by obtaining the corresponding response values ​​at observation points on the mechanical structure. By monitoring the structural operating status in real time and focusing on its remaining life, the probability of danger can be predicted and reduced in advance, which is beneficial to ensuring the safe and stable operation of engineering structures. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a physical model of a mechanical structure.

[0030] Figure 2 A schematic diagram of strain-displacement at the structural observation point.

[0031] Figure 3 Intended structure of BP neural network

[0032] Figure 4 This is a schematic diagram of the first data processing method.

[0033] Figure 5 This is a schematic diagram of the second data processing method.

[0034] Figure 6 A flowchart of the phase-field model and neural network. Detailed Implementation

[0035] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific figures. It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of this application can be combined with each other.

[0036] Example 1:

[0037] This embodiment uses a rectangular steel plate as the mechanical mechanism, wherein there is a crack in the steel plate, such as Figure 1 As shown;

[0038] like Figures 2 to 6 As shown, a method for predicting the remaining life of a mechanical structure based on a combination of neural networks and the phase-field method includes the following steps:

[0039] S1: Construct a CAD model of the steel plate, including the location and size of the cracks; use ultrasonic detection technology to obtain the location and size of the cracks in the steel plate, and use a laser scanner to obtain structural shape, geometry and location information to create a high-precision CAD model, providing a physical model for constructing a phase-field fracture model.

[0040] S2: Construct a phase-field fracture model for the steel plate;

[0041] S2.1: An order parameter φ is introduced to describe the damage evolution of cracks. The crack initiation, propagation, and fracture are represented by an auxiliary damage scalar φ. φ = 0 indicates that the material is intact, and φ = 1 indicates that the material is completely fractured. Crack propagation is a gradual process that occurs gradually with energy accumulation; the propagation process is continuous rather than discontinuous. To better illustrate the propagation process, a continuous smoothness function φ(x) is introduced to approximate crack propagation.

[0042] S2.2: The total energy functional of the steel plate is obtained from the fracture variational principle:

[0043] The total energy functional is shown below:

[0044]

[0045] In the formula, Ψ is the total energy of the mechanical structure, ψ is the elastic energy density function, ε(u) is the strain tensor, Γ is the crack surface energy, and G... c It is the critical energy release rate.

[0046] Based on the order parameter φ introduced above, the crack density function is expressed as:

[0047]

[0048] Where l0 is the width of the crack, It is the derivative of the order parameter, and φ is the order parameter.

[0049] The functional formula for the total energy of a mechanical structure becomes

[0050]

[0051] In equation (2), ψ0 is the elastic strain energy, and g(φ) is the degradation function, which means that as the crack damage continues to evolve, the stored strain energy also continuously decays and degrades. The function g(φ) = (1-φ). 2 +k, where k is as small as possible to ensure that no singularities occur during the calculation. g(φ) needs to satisfy:

[0052] g(0)=1, g(1)=0, g′(1)=1 (4)

[0053] The above equation shows the limitations of energy storage in a mechanical structure under both intact and fractured conditions.

[0054] S2.3: Calculate the elastic strain energy of the steel plate.

[0055] The energy stored in a solid system by elastic deformation under external force; when the mechanical structure remains intact, it exhibits linear elasticity.

[0056] Elastic strain energy can be expressed as:

[0057]

[0058] Where C is the elasticity matrix, strain ε is related to displacement, and the expression for strain under small deformation conditions is:

[0059]

[0060] S2.4: Calculate the virtual work of external forces and internal forces on the steel plate using the principle of virtual work.

[0061] The change in the increment of external work can be expressed in a weak form as:

[0062]

[0063] Where b j and h j Let these represent volume forces and boundary forces, respectively. The incremental change within the force can be expressed in weak form as follows:

[0064]

[0065] From equations (2), (6), and (7), the functional variational formula for the total energy can be expressed as:

[0066]

[0067] Weak form processing is used to obtain the solution of the coupled partial differential equation system.

[0068]

[0069]

[0070] Discretize the displacement field u and the phase field φ as follows:

[0071]

[0072] The shape function matrix is ​​represented as follows:

[0073]

[0074] Where, N i Let u be the shape function of node i, m be the total number of nodes for each element, and u be the shape function of node i. i ={u x ,u y} T φ i Let i be the displacement field and phase field values ​​at node i.

[0075]

[0076] Where ε={ε xx ,ε yy ,ε xy} T The strain-displacement matrix is ​​expressed as follows:

[0077]

[0078] Where N i,x and N i,y These are the derivatives of the corresponding shape functions with respect to x and y, respectively. The increments δu and δφ of the phase field and displacement field, and their derivatives, can also be discretized as...

[0079]

[0080]

[0081] According to the above formula, which holds true for any values ​​of δu and δφ, the residual of the displacement field can be expressed by the discrete equation corresponding to the equilibrium condition.

[0082]

[0083] The residual of the crack phase field evolution can be expressed as follows:

[0084]

[0085] The incremental iterative form of the Newton-Raphson method was adopted.

[0086]

[0087] In the formula, the tangent stiffness matrix is ​​expressed as:

[0088]

[0089] The displacement field u and phase field φ in the coupled equations can be solved simultaneously as a fully coupled global field. However, the above equations do not guarantee the irreversibility of crack phase field evolution.

[0090] φ t+Δt ≥φ t (twenty two)

[0091] When the crack propagation path is unstable, the overall model will experience convergence problems. A stable equilibrium solution cannot be found through implicit solutions. To obtain a stable implicit model, the displacement field u and phase field φ in the coupled system can be solved as n sequentially coupled staggered fields, and a history variable field can be introduced. This involves the strong form of the crack phase field evolution with Neumann-type boundary conditions.

[0092]

[0093]

[0094] The introduction of the history field H strengthens the irreversibility of crack phase field evolution. Therefore, the history field satisfies the Kuhn-Tucker condition.

[0095] ψ0-H≤0,H≥0,H(ψ0-H)=0 (25)

[0096] The residuals of the crack phase field evolution and the residuals corresponding to the displacement field are:

[0097]

[0098]

[0099] The following system of equations can be solved iteratively using the Newton-Raphson method.

[0100]

[0101] In equation (27), the tangent stiffness matrix is ​​calculated as follows:

[0102]

[0103]

[0104] S3: Select appropriate observation points on the steel plate and obtain the corresponding sample data;

[0105] S3.1: By establishing a phase-field fracture model of the steel plate, input the physical and material property parameters of the steel plate, including Young's modulus E and Poisson's ratio ν.

[0106] S3.2: Set the increment step. In this invention, each increment is a fixed value, and a displacement loading method is used during model loading. The displacement increment is Δu, the extended time step is Δt, and the number of increment steps is set to N.

[0107] S3.3: Mesh Generation. The mesh size determines the model's convergence and computational cost. A small mesh size results in poor convergence, while a large mesh size increases computational cost. Therefore, it's crucial to choose an appropriate mesh size. The mesh size can be N1, N2, N3, ..., N. m Where N1 < N2 < ... < N m When calculating the convergence of the model, by comparing and selecting an appropriate number of grids, it can achieve good convergence and a suitable amount of computation.

[0108] S3.4: Selecting Observation Points. After the phase-field fracture model is established, appropriate observation points should be selected to obtain the corresponding sample data. The location of the observation points is used to place strain gauges, so the selection of observation points is very important. Their location should not affect the normal mechanical structure, and should also facilitate the acquisition of measurement data of the structure.

[0109] S3.5: Extract model data. Using the established phase-field fracture model, the strain and displacement values ​​at the observation points are extracted, resulting in a total sample size of NM. The remaining life t of the structure can be expressed as:

[0110] t=(x NM -x i ) / Δu*Δt (31)

[0111] In the formula, x represents the displacement, NM is the total number of the original sample set, and i represents the nth sample point. N It is the maximum displacement value when the structure completely fractures, x i This is the displacement value corresponding to the i-th sample point. The functional relationship between the structural strain value and the lifetime can be expressed as F(ε,t), where ε is the strain value of the structure and t is the remaining lifetime of the structure.

[0112] S4: Construct a neural network model to predict the remaining lifetime of the structure;

[0113] S4.1: Constructing the Neural Network Model. When using a backpropagation (BP) neural network to predict the remaining lifetime of a structure, it is necessary to clearly define the data for the input layer and the output layer of the model. The input layer uses strain values ​​from observation points, while the output layer uses the structure's lifetime values.

[0114] S4.2: Training the Neural Network. Strain value samples are input from the input layer and processed through the neural network structure to calculate the output value. This output value is compared with the expected value to obtain the error. The system then determines if the termination condition is met. If not, the error propagates back through the output layer to the intermediate layers and then back to the input layer, modifying the weights and thresholds of each layer. This process is repeated until the error is minimized while still satisfying the iteration termination condition. The iteration termination condition includes meeting a set training accuracy and meeting a set number of iterations. In this invention, the set training accuracy is used. By continuously reducing the training error, the neural network gradually approaches the target function, achieving the training objective of improving the accuracy of the network model's predictions.

[0115] S4.3: Combining the phase-field method and BP neural network, the functional relationship between strain and life of mechanical structures is realized, and the life is predicted. The phase-field method is used to effectively track crack propagation in the structure, and strain and displacement data at easily measurable observation points in the structure are exported and saved.

[0116] S4.4: Arrange the original dataset in order and group it into sets of 6 data points, then process them sequentially using this method, such as... Figure 5 As shown, this method allows for the continuous acquisition of six sets of corresponding strain values ​​at the observation point. These measured strain values ​​are then input into a pre-trained network model to predict the remaining lifespan of the structure. Next, a BP neural network model structure suitable for this dataset is constructed. The processed data is divided into training and test sets in a 7:3 ratio. The correlation coefficient of the BP neural network is continuously optimized and improved using the training set data to reduce errors and increase prediction accuracy. The test set data is used to verify the performance of the trained model, thus achieving the prediction of the remaining lifespan of the mechanical structure.

[0117] Example 2:

[0118] The original sample dataset has a total size of NM, and its strain-displacement function is convex. Using this data for network training will cause significant data errors for the following reasons: when the measured strain value is below the maximum strain value of the structure, errors will occur. Figure 2In the scenario described, the strain values ​​at points a and b are equal, but the corresponding structural lifetime values ​​are different. This is because at point a, the crack has not yet begun to fracture and is in the initiation stage. When it reaches point c, the energy accumulation inside the structure reaches a certain level, causing the crack to begin to fracture and propagate. At point b, the crack is in the propagation stage. Since point a is in the initiation stage and point b is in the propagation stage, although the strain values ​​are the same at both points, the structural lifetime values ​​differ at different stages. If this distinction is not made and such raw data is used directly for training, the trained model will have significant errors, resulting in inaccurate predictions.

[0119] Data processing methods: There are two ways to process the raw data. One is to divide the raw data into two parts, with the maximum strain value of the structure as the dividing line. That is, one part is the crack initiation stage of the structure, and the other part is the crack propagation stage of the structure. These two parts of data are used for network training. The other method is to process the raw dataset into groups of 6 data points. This method can directly predict the life value of the structure by continuously measuring 6 strain values ​​at the observation points of the structure, without having to determine the location of the strain value before making a prediction.

[0120] This embodiment uses the first data processing method.

[0121] Everything else is the same as in Example 1, except that...

[0122] Step 4.4

[0123] S4.4: The first processing method is used to process the original dataset. The grouped datasets are then used to train the network model. This method is operationally complex. First, the data measured from the observation points must be distinguished to determine which side of the boundary line it belongs to. Then, the data is input into the corresponding network model to predict the remaining lifetime of the structure. Although this data processing method yields a smaller error between the predicted and actual results compared to the original data, data classification is more complicated. The boundary line for dataset processing is as follows... Figure 4 As shown.

Claims

1. A method for predicting the remaining life of a mechanical structure based on a combination of neural networks and the phase-field method, characterized in that, Includes the following steps: S1: Construct a CAD model of the mechanical structure, including the location and size of the cracks; use ultrasonic detection technology to obtain the location and size of the cracks in the mechanical structure, and use a laser scanner to obtain the shape, geometry and location information of the mechanical structure to create a high-precision CAD model, providing a physical model for constructing a phase-field fracture model; S2: Construct a phase-field fracture model of the mechanical structure; S3: Select appropriate observation points on the mechanical structure and obtain corresponding sample data; S4: Construct a neural network model to predict the remaining lifespan of mechanical structures; Step S2 is as follows: S2.1: Introducing order parameters To describe the damage evolution of a crack, from crack initiation to fracture, an auxiliary damage scalar is used. To indicate, This indicates that the materials are intact. To represent complete material fracture, a continuous smoothness function is introduced. To approximate the propagation of a crack; S2.2: The total energy functional of the mechanical structure is obtained from the fracture variational principle; S2.3: Calculate the elastic strain energy of the mechanical structure; S2.4: Calculate the virtual work of external forces and virtual work of internal forces in a mechanical structure using the principle of virtual work; Step S4 is as follows: S4.1: Construct a neural network model; First, clarify the data of the input layer and the data of the output layer of the model structure. The data of the input layer uses the strain value data of the observation points, and the data of the output layer is the life value of the mechanical structure. S4.2: Training the neural network; The strain value sample is input from the input layer and passed through the neural network structure to calculate the output value. By comparing it with the expected value and obtaining the error between them, it is determined whether the termination condition is met. If not, the error is propagated back through the output layer to the intermediate layer and then to the input layer, and the weights and thresholds between each layer are modified. This process is repeated to obtain a smaller error while still meeting the iteration termination condition. The termination condition of the iteration is to meet the set training accuracy. By continuously reducing the training error, the neural network gradually approaches the target function, thereby achieving the training objective and improving the accuracy of the network model's prediction. S4.3: Combining the phase-field method and BP neural network, the functional relationship between the strain value and life value of a mechanical structure is realized and its life value is predicted; The phase-field method is used to effectively track the crack propagation of mechanical structures, and the strain and displacement values ​​at easily measurable observation points in the mechanical structure are exported and saved. S4.4: Arrange the original dataset in order and group it into sets of 6 data points. Then process the dataset sequentially using this method. Construct a BP neural network model structure suitable for this dataset. Divide the processed data into training and test sets in a 7:3 ratio. Use the data from the training set to continuously optimize and improve the correlation coefficient of the BP neural network to reduce errors and improve prediction accuracy. Use the data from the test set to verify the performance of the trained model and achieve the prediction of the remaining lifespan of mechanical structures.

2. The method for predicting the remaining life of a mechanical structure based on a combination of neural networks and phase-field methods as described in claim 1, characterized in that, Step S3 is as follows: S3.1: By establishing a phase-field fracture model of the mechanical structure, the physical and material property parameters of the mechanical structure, including Young's modulus, are input. Poisson's ratio ; S3.2: Set the incremental step; where the displacement increment is The extended time step is The increment step number is set to ; S3.3: Grid division; the number of grid divisions is... , , , , in ; S3.4: Select the observation point; the location of the observation point is used to place the strain gauge. S3.5: Extract model data; using the established phase-field fracture model, extract the strain and displacement values ​​at the observation points, resulting in a total sample size of [number missing]. The remaining life value of the structure It can be represented as: ； in the formula The displacement is represented. It is the total number of the original sample set. This indicates which sample point is being referred to. It is the maximum displacement value when the mechanical structure completely breaks. It is the first The displacement values ​​corresponding to each sample point; the functional relationship between the strain value and life of the mechanical structure is expressed as follows: ,in It is the strain value of the structure. It refers to the remaining lifespan of the mechanical structure.

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