Method for reconstructing initial geometric appearance defects of cylindrical shell based on BP neural network
By reconstructing the initial geometric morphology defects of the cylindrical shell using a BP neural network, the problem of inaccurate prediction of the critical instability pressure of the external pressure shell in the prior art is solved, and higher accuracy prediction and safety analysis are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV OF TECH
- Filing Date
- 2022-07-14
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies struggle to accurately predict the critical buckling pressure of external pressure shells, primarily because buckling instability is a complex geometric and material nonlinear problem, and initial geometric defects generated during manufacturing have a significant impact.
A backpropagation (BP) neural network was used to reconstruct the initial geometric morphology defects of a cylindrical shell. By creating an input parameter database, a neural network model was built and trained to predict shell defects and perform buckling analysis, thus establishing a high-fidelity finite element model.
It improves the accuracy of predicting the critical instability pressure of the external pressure shell, which can better avoid sudden instability of the shell and reduce economic losses and safety risks.
Smart Images
Figure CN115270325B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of machine learning technology, specifically relating to a method for reconstructing the initial geometric shape defects of a cylindrical shell based on a BP neural network. Background Technology
[0002] Pressure vessels are typically welded structures composed of plates and shells. Commonly used shell types include cylindrical shells, spherical shells, ellipsoidal shells, conical shells, and combinations thereof. External pressure vessels are generally used in critical industrial sectors such as energy, power, city gas, petroleum, and chemicals. Failure in these vessels can have catastrophic consequences; therefore, the reliability of the equipment structure plays a vital role in workplace safety.
[0003] The primary failure mode of a shell is buckling instability. When the external pressure on the shell gradually increases to a certain critical value, it suddenly changes shape and fails due to instability. This instability occurs suddenly and reacts violently, potentially causing incalculable economic losses and loss of life. Accurately predicting the critical buckling pressure during the design process can effectively prevent buckling instability.
[0004] In previous studies on external pressure vessels, scholars have found a significant discrepancy between the critical buckling pressure obtained from theoretical formulas and actual results. This discrepancy is mainly caused by two factors: firstly, buckling instability is complex, exhibiting both geometric and material nonlinearities, making it difficult to accurately describe using theoretical formulas; secondly, initial geometric defects generated during the manufacturing process can also reduce the critical buckling pressure.
[0005] It wasn't until the 1960s that scholars gradually began to pay attention to the impact of morphological defects on shell instability. With the development of methods for describing morphological defects, the current methods for describing morphological defects mainly involve actual measurement of the shell's morphological defects, the uniform defect mode method using finite element software, and the method using double Fourier functions for fitting.
[0006] For a long time, people have sought to find a system that can simulate the activity mechanisms of neurons in the brain, a dynamic system that possesses both computational power and human reasoning and recognition abilities. Driven by this idea, research into neural networks has emerged. Artificial neural networks are well-structured mathematical models that can mimic the activity mechanisms of neurons in the biological brain.
[0007] Neural networks typically consist of interconnected systems of neurons that exchange information with each other. The weights of these connections can be adjusted based on the accuracy of predictions, giving the network adaptability and learning capabilities. By adjusting the connection weights between neurons, a neural network can be trained to perform specific functions. Neural networks are usually tuned so that a specific input yields a specific target (actual output). Training the network is based on comparing the output and the target until the network output matches the target (actual output). These connections (inputs) have synaptic weights associated with them, which are multiplied by the connection along each signal propagation. Trained neural networks can perform complex functions such as function approximation, pattern recognition, regression analysis, vision and speech recognition, and control systems.
[0008] Training a Back Propagation Neural Network (BPNN) mainly involves two steps. The first step is forward propagation, where each input variable undergoes two processes (input layer – hidden layer, hidden layer – output layer): weighted by the corresponding elements in the weight matrix, adjusted by the corresponding elements in the bias matrix, and activated by the activation function to obtain the predicted output. The error is calculated by comparing the predicted output with the target output, and then the weights are modified layer by layer according to a certain criterion to reduce the error. This process is repeated until the error no longer decreases, at which point the network training is complete. There are different rules for modifying the weights. A standard BPNN modifies the weights along the gradient of the error performance function, similar in principle to the LMS algorithm, belonging to the steepest descent method. In addition, there are some improved algorithms, such as the momentum steepest descent method. Summary of the Invention
[0009] To address the aforementioned problems in the existing technology, the present invention aims to provide a method for reconstructing the initial geometric morphology defects of a cylindrical shell based on a BP neural network. This method uses an artificial neural network to obtain a geometric model containing the initial geometric morphology defects, thereby obtaining another method for further predicting the buckling load of the external pressure shell.
[0010] This invention provides the following technical solution:
[0011] The method for reconstructing the initial geometric shape defects of a cylindrical shell based on a backpropagation neural network includes the following steps:
[0012] Step 1: Obtain the shell input parameters and create input parameter databases for shell out-of-roundness, weld defects, and surface geometric amplitude defects respectively;
[0013] Step 2, Neural Network Construction and Operation: Use MATLAB to create the feedforwardnet function, and use the default transfer function to build the first, second, and third neural network models for shell out-of-roundness, weld defects, and surface geometric amplitude defects.
[0014] Step 3: Train and test the three neural network models built in Step 2;
[0015] Step 4: Predict shell defects and apply them to obtain an initial geometric shape that reflects the actual morphological defects of the shell by superimposing multiple defects.
[0016] Step 5: Perform material and geometric bi-nonlinear buckling analysis on the shell containing initial geometric defects, and verify its applicability based on the buckling analysis results.
[0017] Furthermore, in step 1, the default transfer functions include the hyperbolic tangent tansig function between the input layer and the hidden layer and the linear transfer function purelin between the hidden layer and the output layer.
[0018] Furthermore, in step 3, the Bayesian regularization algorithm trainbr is used to perform multiple training on the first neural network model and the second neural network model; the Levenberg-Marquardt trainlm algorithm is used to perform multiple training on the third neural network model.
[0019] Furthermore, in the training of the first and second neural network models, the number of neurons n is determined using the formula: N hid =2N in +1 confirms, N hid N represents the number of neurons in the hidden layer. in Let n be the number of neurons in the input layer. During the training of the third neural network model, the ranges of two hyperparameters, namely the Marquardt tuning parameter mu and the number of neurons n, are given. Grid search and ten-fold cross-validation are used to search for a suitable combination of hyperparameters (n, mu).
[0020] Furthermore, in step 3, the mean squared error (MSE), correlation coefficient (R), and error histogram are used to evaluate the trained neural network model. Figure 3 Each parameter is tested and evaluated.
[0021] Furthermore, the specific process of step 4 is as follows:
[0022] 4.1 First, create a shell in ABAQUS with the same nominal dimensions as the predicted shell;
[0023] 4.2 Then, the out-of-roundness and weld defects predicted by the pre-trained first neural network model and second neural network model are sequentially applied to the self-built shell using a Python script;
[0024] 4.3. The node data of the predicted shell is used as the test set of the third neural network for prediction, and the predicted surface defect amplitude is obtained. The surface defect amplitude is then imported into the ABAQUS input file inp to obtain the initial geometric shape of multiple defects superimposed, which can truly reflect the actual shape and defects of the shell.
[0025] By employing the above-described technology, the beneficial effects of the present invention compared to the prior art are as follows:
[0026] This invention employs a BP neural network to establish a more accurate and effective method for reconstructing the geometry of thin-walled cylindrical shells, making the distribution of geometric defects closer to the actual situation. This provides technical support for establishing a high-fidelity finite element model of thin-walled cylindrical shells containing initial geometric defects. Through geometric and material dual nonlinear buckling instability analysis, it can more accurately reflect the critical buckling pressure. Attached Figure Description
[0027] Figure 1 This is a flowchart illustrating an embodiment of the present invention;
[0028] Figure 2 This is a schematic diagram of the structure of the first neural network in an embodiment of the present invention;
[0029] Figure 3 This is a schematic diagram of the structure of the second neural network in an embodiment of the present invention;
[0030] Figure 4 This is a schematic diagram of the structure of the third neural network in an embodiment of the present invention;
[0031] Figure 5 A schematic diagram of a mesh model containing out-of-roundness and longitudinal weld defects;
[0032] Figure 6 A schematic diagram of a mesh model containing defects in roundness, weld seams, and surface geometric amplitude.
[0033] Figure 7 This is a diagram illustrating the 10-fold cross-validation. Detailed Implementation
[0034] 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 embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0035] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.
[0036] Please see Figure 1-7 A method for reconstructing the initial geometric morphology defects of a cylindrical shell based on a BP neural network includes the following steps:
[0037] First, obtain the input data needed for training the neural network.
[0038] For the first neural network, select the shell thickness t, radius R, and aspect ratio L / D. o Use the roundness Δ as the input parameter and the non-roundness as the output parameter, such as... Figure 2 As shown, the first neural network model consists of 3 input layer neurons, 7 hidden layer neurons, 1 output layer neuron, and the transfer functions tansig (transfer function between the input layer and the hidden layer) and purelin (transfer function between the hidden layer and the output layer). The feedforwardnet function is used, and the input and output data will pass through the default preprocessing module for normalization and denormalization.
[0039] For the second neural network, the radius-to-thickness ratio R / t and the shell wall thickness t are selected as input parameters, and the edge angle E and the misalignment amount b are selected as output parameters. Figure 3 As shown, the first neural network model consists of 2 input layer neurons, 5 hidden layer neurons, 2 output layer neurons, and the transfer function tansig between the input layer and the hidden layer, and the transfer function purelin between the hidden layer and the output layer.
[0040] For the third neural network, the circumferential radius θ and axial height h are selected as input parameters, and the geometric defect size w is selected as the output parameter. Figure 4 As shown, the first neural network model consists of two input layer neurons, several hidden layer neurons, one output layer neuron, and the transfer function tansig between the input layer and the hidden layer, and the transfer function purelin between the hidden layer and the output layer.
[0041] Here, defects in four cylindrical shells of the same nominal size are used to predict defects in another cylindrical shell of the same nominal size using a BP neural network. The nominal height, thickness, and radius of the five cylindrical shells are 140 mm, 1 mm, and 50 mm, respectively.
[0042] The three neural network databases were divided into training, validation, and test sets at ratios of 70%, 15%, and 15%, respectively. The `trainbr` algorithm was selected as the training algorithm for the first neural network model, and the result was calculated using formula N. hid =2N in +1 determines the number of neurons. The network is trained 10 times to generate 10 neural networks, and simulations are performed sequentially on the test set. The average MSE and R-value of the 10 training results are used as the overall performance evaluation to obtain the predicted shell out-of-roundness defect. Here, MSE is the mean sum of squared errors of the network.
[0043]
[0044] The above formula t i It is the target output, α i It is the predicted output, e i It is the error. The R-value is the correlation coefficient between the output and the target. It is used to measure the degree to which the target explains the variation in the output. If this value is equal to 1.0, there is a perfect correlation between the target and the output.
[0045] The training algorithm in the second neural network model obtains the number of hidden layer neurons in the same way as the first neural network model, and obtains the predicted weld defects of the cylindrical shell under the same steps.
[0046] The predicted out-of-roundness and weld defects are imported into ABAQUS using a Python script. A cylindrical shell containing these defects and with the same measured dimensions as the predicted shell is then created. Figure 5 As shown, the 3D coordinates of the predicted shell mesh nodes are exported, and the Cartesian coordinates of the nodes are converted to cylindrical coordinates in MATLAB. The relevant parameters of the obtained third neural network model are used as the test set.
[0047] In the third neural network model, trainlm is selected as the training algorithm. The combination of hyperparameters, including the number of neurons, is determined through grid search and ten-fold cross-validation. Figure 7As shown. First, a large range of hyperparameters is selected within n∈[1, 150], mu∈[0.001, 001, 0.1, 1], and then the optimal hyperparameter combination is selected within a defined small range. Each hyperparameter combination network is trained 10 times to generate 10 neural networks, and simulations are performed on the test set sequentially. The average MSE and R values of the 10 training results are used as the overall performance evaluation. The third neural network model with the optimal hyperparameter combination is selected for training and prediction to obtain the predicted surface geometric amplitude defects of the cylindrical shell. By modifying the ABAQUS input file inp, the predicted surface geometric amplitude defects are applied to the previously created self-built shell containing out-of-roundness and weld defects. This yields an initial geometric morphology defect that realistically reflects the actual morphological defects of the shell, such as... Figure 6 As shown.
[0048] Finally, the .inp file containing isolated meshes was imported into ABAQUS for geometric and material bilinear buckling analysis. The applicability of the BP neural network method for predicting initial geometric morphology defects in the shell was evaluated by analyzing the buckling results.
[0049] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for reconstructing the initial geometric morphology defects of a cylindrical shell based on a BP neural network, characterized in that, Includes the following steps: Step 1: Obtain the shell input parameters and create input parameter databases for shell out-of-roundness, weld defects, and surface geometric amplitude defects respectively; Step 2, Neural Network Setup and Execution: Using MATLAB, create the `feedforwardnet` function and, using the default transfer function, build the first, second, and third neural network models targeting shell out-of-roundness, weld defects, and surface geometric amplitude defects, as detailed below: The first neural network selects the shell thickness t, radius R, and aspect ratio. Input parameters, non-roundness Output parameters; The second neural network selects the radius-to-thickness ratio. The shell wall thickness t is used as the input parameter, and the edge angle E and the misalignment amount b are used as the output parameters. The third neural network selects the circumferential radian. And the axial height h as input parameters, geometric defect size w As an output parameter; Step 3: Train and test the three neural network models built in Step 2; Step 4: Predict shell defects and apply them to obtain an initial geometric morphology that accurately reflects the actual shell morphology. The specific process is as follows: 4.1 First, create a shell in ABAQUS with the same nominal dimensions as the predicted shell; 4.2 Then, the out-of-roundness and weld defects predicted by the pre-trained first neural network model and second neural network model are sequentially applied to the self-built shell using a Python script; 4.
3. The node data of the predicted shell is used as the test set of the third neural network for prediction, and the predicted surface defect amplitude is obtained. The surface defect amplitude is then imported into the ABAQUS input file inp to finally obtain the initial geometric shape of multiple defects superimposed that can truly reflect the actual shape defects of the shell. Step 5: Perform material and geometric bi-nonlinear buckling analysis on the shell containing initial geometric defects, and verify its applicability based on the buckling analysis results.
2. The method for reconstructing the initial geometric shape defects of a cylindrical shell based on a BP neural network according to claim 1, characterized in that... In step 1, the default transfer functions include the hyperbolic tangent tansig function between the input layer and the hidden layer, and the linear transfer function purelin between the hidden layer and the output layer.
3. The method for reconstructing the initial geometric shape defects of a cylindrical shell based on a BP neural network according to claim 1, characterized in that... In step 3, the Bayesian regularization algorithm trainbr is used to perform multiple training on the first neural network model and the second neural network model; the Levenberg-Marquardt trainlm algorithm is used to perform multiple training on the third neural network model.
4. The method for reconstructing the initial geometric morphology defects of a cylindrical shell based on a BP neural network according to claim 3, characterized in that... In step 3, the trained neural network model is tested and evaluated using three parameters: mean squared error (MSE), correlation coefficient (R), and error histogram.