A method for predicting cross-section deformation of a bend pipe by using a reinforcement QPSO-BPNN with informed initialization

Abstract

The application discloses a method for predicting elbow section deformation by using reinforced QPSO-BPNN with informed initialization. Latin hypercube uniform sampling technology is used to sample the determined elbow process parameter variables, a finite element numerical simulation test is established, the elbow section deformation indexes corresponding to each group of sample inputs are calculated, and a sample data set is constructed; a BPNN prediction model is established, the initial weights and thresholds of the BPNN are optimized by using informed reinforcement QPSO, a Gaussian random vector and an adaptive parameter adjustment strategy are introduced to strengthen the optimization performance of the QPSO, the population is informed and initialized based on the prior knowledge of the elbow, and the optimization process of the algorithm is accelerated; the optimized BPNN prediction model is trained, and the trained model is used to predict the elbow section deformation. The application realizes flexible, reliable, accurate and efficient prediction of the elbow section deformation.

Description

Technical Field

[0001] This invention relates to the field of pipe bending quality prediction, and in particular to the direction of pipe bending cross-sectional deformation prediction. Specifically, it relates to a method for predicting pipe bending cross-sectional deformation using an enhanced QPSO-BPNN with informed initialization. Background Technology

[0002] Metal bends, used as transport carriers for various liquids and gaseous fuels, are widely applied in aviation, aerospace, automotive, and shipbuilding industries, and are often referred to as the "blood vessels" of industry. The forming conditions for bends are extremely complex, leading to a variety of forming defects, such as cross-sectional deformation, unloading springback, wall thickening and wrinkling, and wall thinning and cracking. These defects affect the product quality and performance of bend components to varying degrees, causing unavoidable engineering losses, and in severe cases, even safety accidents.

[0003] Cross-sectional deformation in pipe bends is a serious defect that occurs during the pipe bending process. When transporting fluids, the twisting deformation of the cross-section leads to increased head loss and pressure drop inside the bend, reducing the flow rate and velocity of the fluid and affecting its performance. Therefore, accurate prediction of cross-sectional deformation is a crucial problem that urgently needs to be solved in order to improve the production quality of bends and ensure the safe and reliable use of bend components.

[0004] Currently, there are three main methods for predicting the cross-sectional deformation of bent pipes: theoretical analysis, experimental analysis, and finite element numerical analysis. Because the pipe bending process involves multiple complex factors, theoretical analysis requires numerous assumptions and simplifications, leading to significant discrepancies between theoretical and actual results. Experimental analysis can provide relatively accurate predictions, but it often comes with high costs and material waste. Finite element numerical analysis can simulate the actual bending process of pipes and provide accurate predictions of forming defects, but high-precision finite element simulation imposes a huge computational burden. Therefore, there is an urgent need to develop a flexible and reliable prediction method to achieve rapid and accurate prediction of the cross-sectional deformation of bent pipes. Summary of the Invention

[0005] To address the shortcomings of the aforementioned technologies, this invention provides an enhanced informed QPSO-BPNN method for predicting the deformation of bent pipe sections, enabling flexible, rapid, and accurate prediction of bent pipe section deformation.

[0006] The technical solution adopted in this invention includes the following steps:

[0007] Step 1: Perform Latin hypercube sampling on the process parameter variables in the metal tube bending and forming process, taking the value range of each process parameter variable as input, and outputting multiple sets of sampled process parameters.

[0008] Step 2: Based on the sampling of process parameters, establish multiple sets of finite element numerical simulation tests, calculate the deformation index of the pipe section corresponding to each set of inputs, construct a sample dataset and normalize it;

[0009] Step 3: Construct a BPNN prediction model, using the process parameter variables in Step 1 as input variables and the corresponding bending pipe cross-section deformation index as output variables. Determine the hidden layer structure of the BPNN by setting the number of hidden layer nodes and the number of layers.

[0010] Step 4: Since the small number of samples in physical engineering problems can easily lead to low model prediction accuracy, we use enhanced QPSO with informed initialization to optimize the initial weights and thresholds of the BPNN prediction model. To address the problems of poor diversity and premature convergence that QPSO is prone to, we introduce Gaussian random vectors and adaptive parameter adjustment strategies to enhance the optimization performance of QPSO. We also perform informed initialization of the population based on prior knowledge of the bent pipe to accelerate the algorithm optimization process.

[0011] Step 5: Use the normalized sample dataset from Step 2 to train the optimized BPNN prediction model to generate a bending pipe cross-section deformation prediction model. Input the process parameter samples of each group of the bending pipe to be tested into the trained bending pipe cross-section deformation prediction model to complete the deformation prediction of the bending pipe cross-section.

[0012] In step 1, the process parameter variables include pipe diameter d0, thickness ratio t0 / d0, and the ratio of pressure block push distance to bending arc length L. p / L b Bending angle θ0, relative pipe bending radius R0 / d0, pressure block friction coefficient f p The coefficient of friction f of the anti-wrinkle block w The coefficient of friction f of the rotary bending die b Pressure block gap ratio c p / d0, Rotary bending die clearance ratio c b / d0.

[0013] Step 2 specifically involves:

[0014] 2.1) Based on the process parameter samples in step 1, establish the finite element numerical model corresponding to each set of samples;

[0015] 2.2) Based on multiple sets of finite element numerical models, calculate the bending section deformation index corresponding to each set of process parameter samples, thereby constructing a sample dataset and normalizing it; the input data in the sample dataset are multiple sets of process parameter samples, and the output data is the magnitude of the corresponding bending section deformation index.

[0016] In step 2.2), the specific steps for calculating the deformation index of the bent pipe section are as follows:

[0017] 1) Starting from the starting face of the pipe bend, cut the pipe bend uniformly at intervals of the same bending angle β to obtain N bend cross sections; where β=θ0 / N, N is the set number of sections, and θ0 is the pipe bending angle;

[0018] 2) Calculate the rate of change of the minor axis of each bend cross section.

[0019]

[0020] Where d0 is the original diameter of the pipe before bending, d min It is the length of the minor axis of the cross-section of the pipe after it is bent;

[0021] 3) For all the cut cross sections, calculate the bending angle θ of each cross section. i The independent variable is the rate of change of the minor axis of the corresponding cross section. As the dependent variable, cubic spline interpolation is used for all points. By fitting the data, the cross-sectional deformation curve of the bent section of the pipe is obtained; where θ i =β×i;

[0022] 4) Calculate the average value of the minor axis change rate on the cross-sectional deformation curve, which gives the magnitude of the bending pipe cross-sectional deformation index.

[0023] The specific steps of step 4 include:

[0024] 4.1) Use the initial weights and threshold of the BPNN as the search dimension d of the particles, and set the number of particles in the population.

[0025] 4.2) Perform informed initialization of the particle population;

[0026] 4.3) The mean square error of BPNN is used as the fitness function of QPSO, and the fitness value of each particle is calculated according to the fitness function f(x).

[0027] 4.4) Update the individual optimal position pbest of the particles. i And the global optimal position of the population, gbest, pbest i The formula for calculating gbest is:

[0028]

[0029] gbest(t) = argminf(pbest) i (t))

[0030] Wherein, argmin refers to making f(pbest) i pbest when (t) takes the minimum valuei (t), where t is the iteration number, x i (t) represents the position of the i-th particle in the t-th iteration;

[0031] Initial individual optimal position pbest i (0) is the first-generation particle x i (0);

[0032] 4.5) Update the current position of the particle;

[0033] 4.6) Determine if the iteration count t has reached the set maximum iteration count T:

[0034] If so, the iteration ends and the global optimal position of the population is output. The global optimal position of the population is used as the initial weights and thresholds of the optimized BPNN prediction model.

[0035] Otherwise, return to step 4.3).

[0036] Step 4.2) specifically refers to:

[0037] Informed initialization refers to applying a Gaussian distribution N(C(d),(S(d))) to the d-th dimension of the initial population. 2 Initialize the particle by 1 ≤ d ≤ D, where D is the total search dimension of the particle, and C(d) and S(d) are manually set parameters.

[0038] C(d) is the center of the Gaussian distribution initialization. Based on the Sobol' sensitivity analysis method, the sensitivity of the bending process parameters to the bending section deformation index is analyzed. Parameters with a sensitivity value greater than 0.3 are regarded as parameters with a greater influence on the bending section deformation. C(d) on the dimensions related to these parameters is set to 0.1, and C(d) on the other dimensions is set to 0.

[0039] S(d) controls the magnitude of the diversity in the d-th dimension of the particles during initialization. The higher the value of S(d), the higher the diversity in the d-th dimension of the particles. The value of S(d) can be set manually to control the diversity in the d-th dimension of the population.

[0040] Step 4.5) specifically refers to:

[0041] The formula for updating the particle's current position is:

[0042] x i (t+1)=p i (t)±αR(t)-x i (t)ln(1 / u(t))

[0043] Where, x i (t+1) represents the position of the i-th particle in the (t+1)-th iteration; p i(t) is the local attractor of the i-th particle in the t-th iteration; α is the contraction-expansion coefficient, which is adaptively adjusted using a linear decreasing strategy; R(t) is an introduced Gaussian random vector used to increase the diversity and cooperation of the population; u(t) is a random number uniformly generated between [0,1);

[0044] The formula for calculating the local attractor is as follows:

[0045] in, is a random number generated uniformly between [0,1).

[0046] The d-th dimension of a Gaussian random vector R(t) is calculated as follows:

[0047]

[0048] Where M is the total number of particles in the population, pbest i,d The d-th search dimension represents the optimal position of the i-th particle.

[0049] The adaptive adjustment formula for α is:

[0050]

[0051] Where α(t) represents the value of α when the iteration number is t, α max α min α and α represent the upper and lower limits of the value of α, respectively, and T represents the maximum number of iterations.

[0052] The beneficial effects of this invention are:

[0053] 1) When calculating the deformation index of the bent pipe section, this invention considers the deformation of the bent pipe cross section at different bending angles, thus more comprehensively characterizing the overall cross-sectional deformation of the bent pipe.

[0054] 2) This invention employs an enhanced QPSO algorithm with informed initialization to optimize the initial weights and thresholds of the BPNN, effectively addressing the problem of low model prediction accuracy due to insufficient samples in physical engineering problems. Gaussian random vectors and adaptive parameter adjustment strategies are introduced to enhance the optimization performance of QPSO, resolving the issues of poor diversity and premature convergence that QPSO is prone to. Furthermore, informed initialization of the population is performed based on prior knowledge of the bent pipe, accelerating the algorithm's optimization process.

[0055] 3) This invention uses an enhanced QPSO-BPNN algorithm with informed initialization to predict the cross-sectional deformation generated during pipe bending, avoiding the problems of large deviations in theoretical analysis results, high cost of experimental analysis, and huge computational power of finite element numerical analysis, and realizing flexible, reliable, accurate and efficient prediction of cross-sectional deformation of bent pipes. Attached Figure Description

[0056] Figure 1 A schematic diagram of the overall process for the enhanced QPSO-BPNN method for predicting the cross-sectional deformation of bent pipes with informed initialization.

[0057] Figure 2 This is a schematic diagram for calculating the deformation index of a bent pipe section. In the diagram: 1. Pressure block; 2. Anti-wrinkle block; 3. Rotary bending die; 4. Bending die insert; 5. Pipe blank; 6. Clamping die.

[0058] Figure 3 A flowchart illustrating the enhanced QPSO-BPNN with informed initialization.

[0059] Figure 4 This is a flowchart of the enhanced QPSO algorithm with informed initialization. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0061] Example 1

[0062] This embodiment discloses an enhanced QPSO-BPNN method with informed initialization for predicting the cross-sectional deformation of bent pipes, such as... Figure 1 As shown, it includes the following steps:

[0063] S1: The ratio of pipe diameter d0, thickness ratio t0 / d0, pressure block push distance to bending arc length L p / L b Bending angle θ0, relative pipe bending radius R0 / d0, pressure block friction coefficient f p The coefficient of friction f of the anti-wrinkle block w The coefficient of friction f of the rotary bending die b Pressure block gap ratio c p / d0, Rotary bending die clearance ratio c b / d0 is used as a process parameter variable. Based on the Latin hypercube uniform sampling method, the value range of each process parameter variable is used as input, and multiple sets of sampled process parameters are output.

[0064] S2: Based on the process parameters of each sample group, establish the corresponding finite element numerical model (i.e., obtain the corresponding bend model). Based on multiple finite element numerical models, calculate the bend cross-sectional deformation index corresponding to the input of each sample group, thereby constructing a sample dataset and normalizing it. The input of the sample dataset is multiple sets of process parameter samples, and the output is the magnitude of the corresponding bend cross-sectional deformation index.

[0065] like Figure 2 As shown, the specific steps for calculating the deformation index of the bend section in S2 are as follows:

[0066] 2.1) Starting from the starting face of the pipe bend, N bend cross sections are uniformly cut from the pipe bend at the same bend angle interval β=θ0 / N.

[0067] 2.2) Calculate the rate of change of the minor axis of the cross-section of each bend.

[0068]

[0069] Where d0 is the original diameter of the pipe before bending, d min It is the length of the minor axis of the cross-section of the pipe after it is bent;

[0070] 2.3) For all the cut cross sections, the bending angle θ of each cross section is... i =β×i is the independent variable, corresponding to the rate of change of the minor axis of the cross section. As the dependent variable, cubic spline interpolation is used for all points. By fitting the data, the cross-sectional deformation curve of the bent section of the pipe is obtained;

[0071] 2.4) Calculate the average value of the minor axis change rate on the deformation curve of the bent pipe section, which gives the magnitude of the deformation index of the bent pipe section.

[0072] S3: Construct a BPNN prediction model, using the process parameter variables in S1 as input variables and the corresponding bending pipe cross-section deformation index as output variables. Determine the hidden layer structure of the BPNN by setting the number of hidden layer nodes and the number of layers.

[0073] S4: The initial weights and thresholds of the BPNN are optimized using an enhanced QPSO with informed initialization. To address the issues of poor diversity and premature convergence that QPSO is prone to, Gaussian random vectors and adaptive parameter adjustment strategies are introduced to enhance the optimization performance of QPSO. Informed initialization is also performed based on prior knowledge of the pipe bend to accelerate the algorithm's optimization process.

[0074] like Figure 3 and Figure 4As shown, the initial parameters (weights and thresholds) of the BPNN are optimized using a reinforced QPSO with informed initialization. The specific steps include:

[0075] 4.1) Use the initial weights and threshold of the BPNN as the search dimension d of the particles, and set the number of particles in the population.

[0076] 4.2) Based on prior knowledge existing in the bend, the particle population is initialized with knowledge.

[0077] Informed initialization refers to the fact that different process parameter variables have different degrees of influence on the deformation of the pipe section, which leads to differences in the corresponding connection weights of the BPNN. Therefore, a Gaussian distribution N(C(d),(S(d))) is adopted for the d-th dimension (1≤d≤D) of the population. 2 Initialization is performed, where D is the total search dimension of the population, and C(d) is the center of the Gaussian distribution initialization. Based on the Sobol' sensitivity analysis method, the sensitivity of bending process parameters to bending cross-sectional deformation indices is analyzed. Parameters with a sensitivity value greater than 0.3 are considered to have a significant impact on bending cross-sectional deformation. C(d) in dimensions related to these parameters is set to 0.1, while C(d) in other dimensions is set to 0. S(d) controls the magnitude of the d-th dimension diversity of particles during initialization; the higher the value of S(d), the higher the d-th dimension diversity of particles.

[0078] 4.3) The mean square error of BPNN is used as the fitness function of QPSO, and the fitness value of each particle is calculated according to the fitness function f(x).

[0079] 4.4) Update the individual optimal position pbest of the particles. i And the global optimal position of the population, gbest, pbest i The formula for calculating gbest is:

[0080]

[0081] gbest(t) = argminf(pbest) i (t))

[0082] Wherein, argmin refers to making f(pbest) i pbest when (t) takes the minimum value i (t), the initial optimal position of the individual is the first generation particle x. i (0).

[0083] 4.5) Update the current position of the particle;

[0084] The formula for updating the particle's current position is:

[0085] xi (t+1)=p i (t)±α|R(t)-x i (t)|ln(1 / u(t))

[0086] Where, x i (t+1) represents the position of the i-th particle in the (t+1)-th iteration; p i (t) represents the local attractor of particle i in the t-th iteration; α is the contraction-expansion coefficient, adaptively adjusted using a linear decreasing strategy; R(t) is an introduced Gaussian random vector used to increase population diversity and cooperation; x i u(t) is the position of particle i in the t-th iteration; u(t) is a random number uniformly generated between [0,1).

[0087] The formula for calculating local attractors is:

[0088]

[0089] in, is a random number generated uniformly between [0,1).

[0090] The d-th dimension of R(t) is calculated as follows:

[0091]

[0092] Where M is the total number of particles in the population, pbest i,d The d-th search dimension represents the optimal position of the i-th particle.

[0093] The adaptive adjustment formula for α is:

[0094]

[0095] Where α(t) represents the value of α when the iteration number is t, α max α min α and α represent the upper and lower limits of the value of α, respectively, and T represents the maximum number of iterations.

[0096] 4.6) Determine if the number of iterations has reached the set maximum number of iterations. If so, the algorithm iteration ends and the global optimal position of the population is output. The global optimal position of the population is used as the initial weights and thresholds of the optimized BPNN prediction model. Otherwise, return to step 4.3).

[0097] The global optimal position of the population (search dimension) is used as the initial weight and threshold of the BPNN.

[0098] S5: Use the normalized sample dataset from step 2 to train the optimized BPNN prediction model, generate a bending pipe cross-section deformation prediction model, input the process parameter samples of each group of the bending pipe to be tested into the trained bending pipe cross-section deformation prediction model, thereby completing the deformation prediction of the bending pipe cross-section.

[0099] Example 2

[0100] This second embodiment is a method for predicting the cross-sectional deformation of aluminum bends using an enhanced QPSO-BPNN with informed initialization. The specific implementation process includes the following steps:

[0101] 1. Set the range of process parameter variables for bent pipes as shown in Table 1.

[0102] Table 1 Range of process parameter variables

[0103]

[0104]

[0105] 2. Within the range of values, Latin hypercube uniform sampling was performed on the process parameter variables, resulting in 500 sets of input samples. Based on the sampling of process parameters, a finite element numerical simulation experiment was established. The pipe material was 6061-T6 aluminum alloy, and the material model was set as a power-strength material model. The cross-sectional deformation output index corresponding to each set of finite element experiments was calculated, a sample dataset was constructed and normalized, and 80% of the dataset was used as the training set, with the remaining 20% ​​used as the test set.

[0106] 3. Using the process parameter variables in Table 1 as inputs and the cross-sectional shape variables of the bend as outputs, the number of hidden layer nodes is set to 6 and the number of layers is set to 1 to construct a BPNN prediction model.

[0107] 4. Using the initial weights and threshold of the BPNN as the search dimension for particles, the number of particles M is set to 50, and the maximum number of iterations T is set to 400. Based on Sobol's sensitivity analysis, it is found that θ0 has a significant impact on the deformation of the bent pipe cross-section; therefore, M(d) is set to... θ0 Set M(d) to 0.1, and set M(d) to 0 in other dimensions. Set S(d) to 0.5, and α... max It is 1.7, α min The value is 0.3. The mean squared error of the BPNN training set is used as the fitness function of QPSO, and the initial weights and thresholds of the BPNN are optimized by reinforcement QPSO with informed initialization.

[0108] 5. Train the optimized BPNN model using the training set, and use the trained model to make predictions on the test set, using the decision coefficients R0. 2The differences are explained using the Value at First Fact (VAF), Root Mean Square Error (RMSE), and Evaluation Absolute Error (MAE), which measure the predictive accuracy of the model. The formulas for each indicator are as follows:

[0109]

[0110]

[0111]

[0112]

[0113] Among them, y i and Table 2 shows the actual, predicted, and average values ​​of the cross-sectional deformation of the bent pipe, respectively, where m is the total number of data points. The model's prediction results are shown in Table 2.

[0114] Table 2. Deformation prediction results of the bend cross-section using the enhanced QPSO-BPNN with informed initialization.

[0115]

[0116] This invention considers the deformation of the cross-section of a bent pipe at different bending angles and proposes an index calculation method that can more comprehensively characterize the overall cross-sectional deformation of the bent pipe. It employs an enhanced QPSO algorithm with informed initialization to optimize the initial weights and thresholds of the BPNN, introduces Gaussian random vectors and adaptive parameter adjustment strategies to enhance the optimization performance of QPSO, and performs informed initialization of the population based on prior knowledge of the bent pipe, accelerating the algorithm's optimization process. Using the enhanced QPSO-BPNN with informed initialization to predict the cross-sectional deformation of the bent pipe, the prediction accuracy on the training set is found to be above 95%, and the accuracy on the test set is above 92%, achieving flexible, reliable, accurate, and efficient prediction of the cross-sectional deformation of the bent pipe.

[0117] The examples described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the cross-sectional deformation of a bend pipe using an enhanced QPSO-BPNN with informed initialization, characterized in that, Includes the following steps: Step 1: Perform Latin hypercube sampling on the process parameter variables in the metal tube bending and forming process, taking the value range of each process parameter variable as input, and outputting multiple sets of sampled process parameters. Step 2: Based on the sampling of process parameters, establish multiple sets of finite element numerical simulation tests, calculate the deformation index of the pipe section corresponding to each set of inputs, construct a sample dataset and normalize it; Step 3: Construct a BPNN prediction model, using the process parameter variables in Step 1 as input variables and the corresponding bending pipe cross-section deformation index as output variables. Determine the hidden layer structure of the BPNN by setting the number of hidden layer nodes and the number of layers. Step 4: The initial weights and thresholds of the BPNN prediction model are optimized using reinforced QPSO with informed initialization; Gaussian random vectors and adaptive parameter adjustment strategies are introduced to enhance the optimization performance of QPSO, and informed initialization of the population is performed based on prior knowledge of the pipe bend to accelerate the algorithm optimization process. Step 5: Use the normalized sample dataset from Step 2 to train the optimized BPNN prediction model to generate a bending pipe cross-section deformation prediction model. Input the process parameter samples of each group of the bending pipe to be tested into the trained bending pipe cross-section deformation prediction model to complete the deformation prediction of the bending pipe cross-section. In step 1, the process parameter variables include the pipe diameter. Thickness ratio The ratio of the pressure block's boosting distance to the bending arc length Bending angle Relative pipe bending radius Coefficient of friction of pressure block Coefficient of friction of anti-wrinkle block Coefficient of friction of rotary bending die Pressure block gap ratio Rotary bending die clearance ratio ; Step 2 specifically involves: 2.1) Based on the process parameter samples in step 1, establish the finite element numerical model corresponding to each set of samples; 2.2) Based on multiple sets of finite element numerical models, calculate the deformation index of the bent pipe section corresponding to each set of process parameter samples, thereby constructing a sample dataset and normalizing it; The input data in the sample dataset consists of multiple sets of process parameter samples, and the output data is the magnitude of the corresponding bending pipe cross-section deformation index. In step 2.2), the specific steps for calculating the deformation index of the bent pipe section are as follows: 1) Starting from the beginning of the bend in the pipe section, bend at the same angle. As intervals, the bent section of the pipe is cut evenly to obtain N cross-sections of the bend; among them... = / N, where N is the set number of segments to extract. For the pipe bending angle; 2) Calculate the rate of change of the minor axis of each bend cross section. : in, The original diameter of the pipe before bending. It is the length of the minor axis of the cross-section of the pipe after it is bent; 3) For all the cut cross sections, calculate the bending angle of each cross section. The independent variable is the rate of change of the minor axis of the corresponding cross section. As the dependent variable, cubic spline interpolation is used for all points ( , By fitting the data, the cross-sectional deformation curve of the bent section of the pipe is obtained; where, ; 4) Calculate the average value of the minor axis change rate on the cross-sectional deformation curve, which gives the magnitude of the cross-sectional deformation index of the bent pipe.

2. The method for predicting the cross-sectional deformation of a bend pipe with enhanced QPSO-BPNN and informed initialization as described in claim 1, characterized in that, The specific steps of step 4 include: 4.1) Use the initial weights and threshold of the BPNN as the search dimension d of the particles, and set the number of particles in the population. 4.2) Perform informed initialization of the particle population; 4.3) The mean square error of BPNN is used as the fitness function of QPSO, and the fitness value of each particle is calculated according to the fitness function f(x). 4.4) Update the individual optimal position of the particle and the global optimal position of the population , and The calculation formula is: in, It means to make When taking the minimum value t is the number of iterations. Let be the position of the i-th particle at the t-th iteration; Initial optimal position of the individual These are the first generation particles. ; 4.5) Update the current position of the particle; 4.6) Determine if the number of iterations t has reached the set maximum number of iterations. : If so, the iteration ends and the global optimal position of the population is output. The global optimal position of the population is used as the initial weights and thresholds of the optimized BPNN prediction model. Otherwise, return to step 4.

3.

3. The method for predicting the cross-sectional deformation of a bend pipe with enhanced QPSO-BPNN and informed initialization according to claim 2, characterized in that, Step 4.2) specifically refers to: Informed initialization refers to applying a Gaussian distribution to the d-th dimension of the initial population. Initialize the data, where 1≤d≤D, D is the total search dimension of the particles, and C(d) and S(d) are manually set parameters; C(d) is the center of the Gaussian distribution initialization. Based on the Sobol' sensitivity analysis method, the sensitivity of the bending process parameters to the bending section deformation index is analyzed. Parameters with a sensitivity value greater than 0.3 are regarded as parameters with a greater influence on the bending section deformation. C(d) on the dimensions related to these parameters is set to 0.1, and C(d) on the other dimensions is set to 0.

4. The method for predicting the cross-sectional deformation of a bend pipe with enhanced QPSO-BPNN and informed initialization according to claim 3, characterized in that, Step 4.5) specifically refers to: The formula for updating the particle's current position is: in, Let be the position of the i-th particle in the (t+1)-th iteration; Let be the local attractor of the i-th particle in the t-th iteration; To adjust the shrinkage expansion coefficient, a linear decreasing strategy is adopted for adaptive adjustment; This is an introduced Gaussian random vector; is a random number uniformly generated between [0, 1); The formula for calculating the local attractor is as follows: in, is a random number uniformly generated between [0, 1).

5. The method for predicting the cross-sectional deformation of a bend pipe with enhanced QPSO-BPNN and informed initialization according to claim 4, characterized in that, Gaussian random vectors The d-th dimension is calculated as follows: Where M is the total number of particles in the population. The d-th search dimension represents the optimal position of the i-th particle.

6. The method for predicting the cross-sectional deformation of a bend pipe with enhanced QPSO-BPNN and informed initialization according to claim 5, characterized in that, The adaptive adjustment formula is: in, When the number of iterations is t The value, , Represent The upper and lower limits of the value, This indicates the maximum number of iterations.

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