A method for predicting mechanical properties of dual-phase high-strength steel welds containing Ce and Nb

Abstract

The present invention discloses a method for predicting the mechanical properties of a dual-phase high-strength steel weld containing Ce and Nb. The method comprises the following steps: a differential evolution (DE) algorithm is used to optimize a support vector machine (SVM) DE-SVM prediction model, wherein the Ce and Nb contents are used as input variables, and the weld tensile strength, yield strength, elongation and impact energy are used as output variables. The DE-SVM prediction model is used to predict the mechanical properties of the dual-phase high-strength steel; the DE-SVM prediction model adopts an adaptive selection strategy to obtain higher prediction accuracy; and, by continuously adjusting the distribution range of control parameters according to evolutionary experience and searching for more optimal penalty function c and kernel function g parameters for the SVM through adaptive control parameters, the model's evolutionary generations can be significantly reduced. The method has excellent adaptability and stability, and can provide data support for optimizing the influence of Ce / Nb addition on the mechanical properties of the dual-phase high-strength steel weld.

Description

Technical Field

[0001] The present invention relates to a method for predicting the mechanical properties of a duplex high-strength steel weld, in particular to a method for predicting the mechanical properties of a duplex high-strength steel weld containing Ce and Nb based on DE optimized SVM, and belongs to the technical field of duplex high-strength steel welding. Background Art

[0002] Dual-phase high-strength steel (DP steel), also known as complex-phase steel, consists of a two-phase structure consisting of martensite, austenite, or bainite in a ferrite matrix. It is obtained by intercritical heat treatment or controlled rolling of low-carbon or low-alloy high-strength steel. DP steel features light weight, high strength, and excellent formability. Data indicates that a 10% reduction in vehicle weight results in a 5% reduction in fuel consumption per 100 kilometers. Therefore, DP steel has been successfully adopted in the automotive industry as a preferred alternative to traditional steel in lightweight vehicle designs.

[0003] In the automotive industry today, the most common steel used in vehicle bodies is duplex high-strength steel with a tensile strength range of 700-1100 MPa. DP780 duplex high-strength steel, with a tensile strength of 700 MPa, is widely used in lightweight automotive designs due to its excellent strength and formability. Due to the difficulty of integrally forming a vehicle body, welding is a necessary step in vehicle body production. However, due to the disparity in properties between the ferrite and martensite phases in duplex high-strength steel, welding can lead to failure due to softening of the weld joint during tensile testing. Furthermore, the reduced impact energy at lower operating temperatures can cause the material to transition from a ductile to a brittle state, leading to low-temperature brittle fracture. To address this issue, industry researchers have demonstrated that Ce-based compounds can modify the interaction between inclusions and the matrix in welded joints, improving impact performance and toughness. Furthermore, they have found that Nb, as a microalloying element, combines with C, N, and S in the steel to promote the resolubility of carbonitrides and the nucleation of ferrite, mitigating the adverse effects of dispersed precipitation on weaker areas of the weld joint. Therefore, the key to resolving the issues of weld softening and low-temperature brittleness lies in optimizing the effect of Ce / Nb additions on the mechanical properties of duplex high-strength steel welds. However, due to the limited sample data used in existing tests, the time-consuming process, and the lack of a definitive functional relationship affecting the mechanical properties of duplex high-strength steel welds, mechanical property tests on duplex high-strength steel welds containing Ce and Nb often cannot accurately determine the exact Ce / Nb addition level.

[0004] To address these issues, the relationship model between the independent variables of process parameters and the response variables can be established through RSM response surface models, Kriging models, artificial neural networks, and support vector machine models, and predictions can be made using mathematical models. Among them, support vector machines (SVMs) require fewer training samples, and the final decision function is determined by only a small number of support vectors (SVs). They can quickly classify high-dimensional data through kernel calculations, and therefore have a wide range of applications in the field of classification prediction. However, the classic support vector machine algorithm only provides a binary classification algorithm and has inherent limitations. Summary of the Invention

[0005] In response to the above problems, the present invention provides a method for predicting the mechanical properties of dual-phase high-strength steel welds containing Ce and Nb. It aims to predict the effect of Ce / Nb on the softening and low-temperature brittleness of dual-phase high-strength steel weld joints. It can predict the mechanical properties of dual-phase high-strength steel welds with different Ce and Nb contents with high accuracy and high stability, and provide data support for optimizing the influence of Ce / Nb addition on the mechanical properties of dual-phase high-strength steel welds.

[0006] To achieve the above objectives, the mechanical properties prediction method of dual-phase high-strength steel welds containing Ce and Nb is based on the DE-SVM prediction model of the support vector machine (SVM) optimized by the differential evolution algorithm DE, which specifically includes the following steps:

[0007] The specific steps include:

[0008] Step 1: Uniform test design: Use homogenization test design to determine the specific addition amount and grouping of Ce and Nb elements during welding;

[0009] Step 2: Establish an SVM classification model: Take the Ce content wt1 and Nb content wt2 as input variables, and the tensile strength R m , lower yield strength R el , elongation after fracture A 5.65 And the impact energy KV is used as the output variable, the uniform test data is divided into training data and test data, and a SVM classification model with multi-variable input and multi-variable output is established;

[0010] The specific process of establishing an SVM classification model with multi-variable input and multi-variable output is as follows:

[0011] I. Design support vector machine training set input N={(B1,N1)(B2,N2)(B3,N3)…(B n ,N n )}, n is the number of training samples, and the relationship between input variables and output variables is established:

[0012] N i =ωΤ Φ(Β i )+b

[0013] Where: ω represents the normal vector, b represents the displacement, Φ(B i ) represents the mapping function, B i is the training sample size;

[0014] II. Definition of the hyperplane ω for the output of mechanical properties of dual-phase high-strength steel welds Τ x+b=0, after classifying the hyperplane, the mathematical model formula is established as follows:

[0015]

[0016] III. Use hinge loss to transform the optimization problem and list the basic model formula of SVM classification model:

[0017]

[0018] where ξ i is the slack variable, c is the penalty function, and the penalty parameter c>0 is selected, and n is the number of training samples;

[0019] IV. With kernel function g(B i ,B j ) Construct and solve the convex quadratic programming problem, introduce the Lagrange multiplier, and establish the Lagrange function as follows:

[0020]

[0021] Where α i , α j is the Lagrange multiplier, and the optimal solution is:

[0022] Ⅴ. * Perform calculations, is α * Quantity, satisfying It can be calculated

[0023]

[0024] Where ω * is the normal vector of the decision function, b * is the displacement component;

[0025] VI. Using the hyperplane classification decision function f(x)=sign(ω * ×B)+b * Find the hyperplane;

[0026] Step 3: Establish an adaptive DE algorithm based on the DE algorithm: Change the precise strategy assignment of the DE algorithm to an approximate strategy assignment, select individuals participating in the operation based on the difference in convergence, and adaptively select the differential strategy and algorithm control parameters that best suit the current population based on the population's evolutionary experience. By calculating the objective function value of each individual in the population, the best individual is randomly selected from each time, and a strategy is selected for each target vector.

[0027] The specific process of establishing the adaptive DE algorithm is as follows:

[0028] I. Initialize a population B of size NP i (i=1,2,…,N), and B i is a D-dimensional vector;

[0029] Ⅱ. Using the DE / rand / 1 / bin differential strategy in the basic differential evolution algorithm, the basic mutation vector is the Gth (G=1,2,…,D)th generation of the i-th individual, which can generate mutant individuals V i,G for:

[0030]

[0031] Where G is the current evolutionary generation, V i,G is the G-th generation population, F is the mutation operator, and subscripts r1, r2, and r3 are integers randomly selected between 1 and NP that are different from i;

[0032] III. Through mutation of individual V i,G and individual B i,G Crossover operation can obtain experimental individuals

[0033]

[0034] Where C r is the cross factor, j rand is a random integer in the vector set [1,2,…,D];

[0035] IV. Cross-operate all populations and optimize the next iteration based on the fitness of the corresponding individuals

[0036]

[0037] where X i,G For other individuals in the previous iteration;

[0038] Step 4: Use the adaptive DE algorithm to optimize the SVM classification model: Use the adaptive DE algorithm to randomly optimize the parameters of the penalty function c and kernel function g of the SVM classification model. The design mutation rate is: Where e is the base of natural logarithm, G mis the maximum number of iterations, G is the current number of iterations, 1 is the adaptive adjustment coefficient, and the scaling factor F is the exponential function of the mutation rate, then F=F0×2 λ , where F0 is the initial value of the scaling factor, the DE-SVM model is generated to obtain the prediction results of the output variables.

[0039] Furthermore, when the adaptive DE algorithm is used to randomly optimize the parameters of the penalty function c and kernel function g of the SVM classification model, a random crossover operator C is designed. r , take C r The lower limit is 0.2 and the upper limit is 0.9.

[0040] Furthermore, in step 2, MATLAB is used to perform SVM grid training and testing, and the data is normalized to [-1, 1]. Then, inputps is used to perform the same normalization process again.

[0041] Compared with the existing technology, this method for predicting the mechanical properties of dual-phase high-strength steel welds containing Ce and Nb aims to solve the problems of large prediction errors and poor fitness caused by the fixed c and g parameters of the support vector machine (SVM). A DE-SVM prediction model based on the differential evolution algorithm (DE) to optimize the support vector machine (SVM) is proposed to avoid the inherent limitations of the prediction model. The effective evolution direction and step size of the iteration can be determined more simply and efficiently. The Ce and Nb contents are used as input variables, and the weld tensile strength, yield strength, elongation and impact energy are used as output variables. The mechanical properties of the dual-phase high-strength steel are predicted through the DE-SVM prediction model. The DE-SVM prediction model adopts an adaptive selection strategy, which changes the precise strategy assignment that is difficult to determine by DE to an approximate strategy assignment, and selects individuals participating in the operation based on the difference in convergence. While improving the performance of the DE algorithm, the use of an adaptive operator allows the evolutionary experience of the population to adaptively select the differential strategy and algorithm control parameters that are most suitable for the current population. By calculating the objective function value of each individual in the population, randomly selecting the best individual from each time, and selecting a strategy for each target vector, higher prediction accuracy can be achieved. At the same time, by continuously adjusting the distribution range of the control parameters based on the evolutionary experience and finding better parameters for the penalty function c and kernel function g for the SVM through adaptive control parameters, the model's evolutionary generations can be greatly reduced. It has excellent adaptability and stability in predicting the mechanical properties of duplex high-strength steel welds. It can provide data support for optimizing the effect of Ce / Nb addition on the mechanical properties of duplex high-strength steel welds by improving the softening and low-temperature brittleness of duplex high-strength steel welds. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1Figure 1 shows the V-shaped impact and tensile specimens of the DP780 dual-phase high-strength steel test sample, where (a) is the impact specimen and (b) is the tensile specimen.

[0043] Figure 2 It is a graph of mechanical properties of DP780 duplex high-strength steel test sample;

[0044] Figure 3 This is the numerical graph of the DE-SVM model kernel function g and penalty function c obtained after 50 iterations of the adaptive random algorithm;

[0045] Figure 4 It is the adaptive curve diagram of the mechanical properties of the weld of DP780 specimen;

[0046] Figure 5 This is the predicted result diagram of the mechanical properties of the DP780 sample weld. DETAILED DESCRIPTION

[0047] Differential evolution (DE) is a heuristic random search algorithm based on population differences. It is often used to solve practical value optimization problems, including multi-peak and highly nonlinear problems. DE can seek the optimal solution to nonlinear problems through a limited number of patterns. Due to its high optimization efficiency and robustness, it is applied in materials. However, the success of the DE algorithm in prediction depends on the crossover and mutation strategies currently used. Therefore, in order to solve the defects of using support vector machine prediction, it is necessary to improve the algorithm crossover and mutation strategies.

[0048] This method for predicting the mechanical properties of dual-phase high-strength steel welds containing Ce and Nb is based on a prediction model (DE-SVM) optimized with a support vector machine (SVM) using a differential evolution algorithm (DE). This model avoids the inherent limitations of prediction models and more simply and efficiently determines the effective evolutionary direction and step size for iteration. Using Ce and Nb contents as input variables and weld tensile strength, yield strength, elongation, and impact energy as output variables, the DE-SVM prediction model's convergence and predictive capabilities are analyzed. The mechanical properties of the dual-phase high-strength steel are then predicted using the DE-SVM prediction model.

[0049] The present invention is described in detail below by taking DP780 dual-phase high-strength steel as a welding base material.

[0050] 1. Sample test process and results

[0051] The DP780 duplex high-strength steel used in the welding test is the cold-rolled DP780 duplex high-strength steel produced by China Baosteel. The base material specification is 160mm×65mm×2mm. The welding equipment model is TIG-200A inverter argon arc welding machine, double-sided welding, and the welding wire is ER304 solid welding wire with a diameter of 1.6mm. The chemical composition of the DP780 duplex high-strength steel welding base material and welding wire used in the welding test is shown in Table 1. During welding, different contents of CeO2 and Nb elements were added to the welding wire. The homogenization test design was used to determine the specific addition amount and grouping of each element during welding as shown in Table 2. Sample No. 1 is a control group without any additives. In order to increase the penetration depth and remove oxides, an activator composed of stearic acid and palm oil was added during welding. The welding current is 135A, the voltage is 16V, and the welding speed is 2.32mm / s. The welded sample is processed into the following Figure 1 The "V"-shaped impact specimen and tensile specimen shown are subjected to annealing heat treatment process, and the black framed area is the location of the weld.

[0052] Table 1 Chemical composition of base metal and welding wire (wt%)

[0053]

[0054] Table 2 Mass of CeO2 and Nb and their percentage in deposited metal

[0055]

[0056] The weld tensile and impact tests were carried out on a universal testing machine and a low-temperature impact device respectively, and the tensile strength, lower yield strength, elongation after fracture and weld impact energy of the deposited metal were measured. The mechanical properties are as follows: Figure 2 The specific values ​​are shown in Table 3.

[0057] Table 3 Mechanical properties of samples with different Ce / Nb addition amounts

[0058]

[0059] Among them, the mechanical properties of DP780 dual-phase high-strength steel showed a continuous wave peak state with slight fluctuations in the middle. The elongation after fracture increased, with sample No. 4 showing the highest value. The lower yield strength of samples No. 3, 4, 5, and 6 decreased, while the remaining samples increased. Sample No. 7 showed the highest value of 469.5 MPa. The increase in impact energy due to the addition of Ce and Nb was nonlinearly related. When the addition of CeO2 and Nb accounted for 0.35% and 0.15% of the mass of the deposited metal, respectively (sample No. 8), the absorbed impact energy and tensile strength reached their highest points, at 3.9 J and 685.3 MPa, respectively. Compared with sample No. 1 without the addition of Ce / Nb, the impact energy of sample No. 8 increased by 3.435 J and the tensile strength increased by 344.8 MPa. Its elongation after fracture and lower yield strength were also not low. The above shows that sample No. 8 exhibited good mechanical properties.

[0060] 2. Establishment and prediction of support vector machine model

[0061] Support vector machines (SVMs) are models for binary classification problems. They use nonlinear mapping relationships to map the sample space to a high-dimensional feature space, define a classification hyperplane as the decision surface, and determine the final global optimal solution by solving the corresponding quadratic convex programming problem. They are often used for pattern recognition and regression analysis involving small sample sizes, nonlinearity, and high dimensionality.

[0062] The difference in additives and welding process will affect the mechanical properties of DP780 dual-phase high-strength steel welds. The content of CeO2 in the weld, wt1, and the content of Nb, wt2, are the main factors affecting the improvement of the mechanical properties of DP780 dual-phase high-strength steel welds. The main indicator for judging the mechanical properties is the mechanical properties of the weld, so wt1 and wt2 are used as input variables, and the tensile strength R of the weld is used as the input variable. m , lower yield strength R el , elongation after fracture A 5.65 With the impact energy KV as the output of the prediction model, a multi-variable input and multi-variable output SVM classification model is established. The sample space and the specific establishment process are as follows:

[0063] Design the support vector machine training set input as N={(B1,N1)(B2,N2)(B3,N3)…(B n ,N n )}, n is the number of training samples. The relationship between input variables and output variables is established using 13 groups of DP780 samples:

[0064] N i =ω Τ Φ(Β i )+b (1)

[0065] Where: ω represents the normal vector, b represents the displacement, Φ(B i ) represents the mapping function, B i is the training sample size.

[0066] Define the DP780 mechanical performance output hyperplane ω Τ x+b=0, after classifying the hyperplane, the mathematical model formula is established as follows:

[0067]

[0068] Hinge loss is used to transform the optimization problem into the following formula, and the basic model formula of the support vector machine is listed:

[0069]

[0070] where ξ i is the slack variable, c is the penalty function, and the penalty parameter c>0 is selected, and n is the number of training samples. i ,B j ) Construct and solve the convex quadratic programming problem, introduce the Lagrange multiplier, and establish the Lagrange function as follows:

[0071]

[0072] Where α i , α j is the Lagrange multiplier, and the optimal solution is: Right * Perform calculations, is α * Quantity, satisfying It can be calculated

[0073]

[0074] Where ω * is the normal vector of the decision function, b * is the displacement component, then the hyperplane can be obtained, and the hyperplane classification decision function

[0075] f(x)=sign(ω * ×B)+b * (6)

[0076] The kernel function g = K(B i ,B jThe choice of the c and g parameters has a significant impact on classification performance, so optimizing them is crucial for optimizing the support vector machine. MATLAB was used for grid training and testing of the SVM. The data was normalized to the range [-1, 1] and the same normalization was repeated using inputps. Eight of the 13 data sets were randomly selected as the training set for testing, and the remaining five sets were randomly numbered as the test set.

[0077] 3. Differential Evolution Algorithm Optimization Support Vector Machine Model

[0078] (1) Differential Evolution Algorithm (DE)

[0079] The basic DE algorithm first initializes a population B of size NP (population size) i (i=1,2,…,N), and B i is a D-dimensional vector, and then each individual in the population is subjected to continuous mutation, crossover, and selection operations. This algorithm adopts the DE / rand / 1 / bin differential strategy in the basic differential evolution algorithm. The basic mutation vector is the G (G=1,2,…,D) generation of the i-th individual, which can generate mutant individuals V i,G for:

[0080]

[0081] Where G is the current evolutionary generation, V i,G is the G generation population, that is, the optimal solution, and F is the mutation operator, which controls the amplification of the deviation vector. In the formula, the subscripts r1, r2, and r3 are randomly selected integers different from i between 1 and NP. The role of the crossover operation is to exchange the objective function and the crossover individual information, and increase the number of interference vectors. By mutating individual V i,G and individual B i,G Crossover operation can obtain experimental individuals

[0082]

[0083] C r is the cross factor, j rand is a random integer in the vector set [1,2,…,D]. Crossover is performed on all populations, and the next iteration is optimized based on the fitness of the corresponding individuals.

[0084]

[0085] where X i,G For other individuals in the previous iteration.

[0086] (2) DE algorithm optimization support vector machine

[0087] Predicting the mechanical properties of DP780 dual-phase high-strength steel welds containing Ce / Nb requires a model. The goal is to ensure that the predicted values ​​are as close as possible to the optimal mechanical property data within a certain range. The selection of the kernel function g and penalty function c for support vector machines remains an unresolved issue. Empirical selection methods are often used, which can lead to excessively fast convergence or large errors.

[0088] In the basic DE algorithm, the mutation rate F is a fixed constant. Excessive constants in the selection range make it difficult to determine, resulting in either an excessively large mutation rate, reducing optimization accuracy, or a reduced mutation rate, reducing population diversity. To accelerate iterative convergence and improve optimization, an adaptive selection strategy is proposed. This strategy replaces the difficult-to-determine exact strategy assignment with an approximate one. Individuals participating in the operation are selected based on differences in convergence, thereby improving the performance of the differential algorithm. Using this adaptive operator, the population's evolutionary experience can adaptively select the optimal differential strategy and algorithm control parameters for the current population. By calculating the objective function value for each individual in the population and randomly selecting the best individual from each iteration, a strategy is selected for each objective vector. The adaptive DE algorithm randomly optimizes the c and g parameters, depending on the number of individual solutions generated by a particular adaptive strategy that advances to the next generation. A higher number indicates that the strategy has been adapted and used in the current generation with high predictive accuracy, increasing the probability of generating promising solutions.

[0089] Therefore, the mutation rate can be designed as: Where e is the base of natural logarithm, G m is the maximum number of iterations, G is the current number of iterations, 1 is the adaptive adjustment coefficient, and the scaling factor F is the exponential function of the mutation rate, then F=F0×2 λ , where F0 is the initial value of the scaling factor, the random crossover operator C can be designed r , C r Usually the value is between 0 and 1. In order to ensure that the population has a good search ability, C r The lower limit is 0.2 and the upper limit is C r =0.9, which can ensure that its mean is around 0.55 and will not be affected by C r If the size is too small, the population iteration speed will be too fast and the accuracy will be reduced, or if the size is too large, the crossover rate will be increased. The adaptive random algorithm is iterated 50 times to obtain the values ​​of c and g in DE-SVM. Figure 3 shown.

[0090] 4. DE-SVM model prediction results and analysis

[0091] (1) Optimal fitness curve analysis

[0092] According to the principle of DE optimization SVM model, after generating the initial population and n D-dimensional vectors, different position indexes are used during mutation, and 4 individuals in the DP780 data are randomly selected. The mutated individuals come from three random parent generations. The vector scaling and the individuals to be mutated are synthesized, and out-of-bounds processing is performed. Random points are used to determine whether there is crossover, and the minimum value of the objective function in the G generation is selected to save the optimal individual. The prediction uses the mean square error (MSE) as the fitness. The smaller the error fitness, the better the performance, so the adaptive curve shows a downward trend. The adaptive curve of the mechanical properties of the DP780 dual-phase high-strength steel weld is as follows: Figure 4 As shown in the figure, Bestfitness is the best fitness curve of DE-SVM. Compared with the average fitness, the error of the predicted best fitness curve is smaller because c and g can be adaptively changed, and the error fluctuation is not obvious or the error decreases rapidly with the increase of the number of iterations.

[0093] A support vector machine was used to perform similar parameter predictions for each data point with varying Ce / Nb additions. However, the predictions for c and g remained constant across iterations, resulting in poor error adaptation. In the impact energy adaptation curve, the DE-SVM prediction error rapidly dropped to 0.4 J at the eighth iteration, while the SVM prediction MSE value was reduced below 0.4 J by the 35th iteration. The elongation exhibited a step-like downward trend and began to converge at the third iteration. In the tensile strength curve, the initial DE-SVM mean square error was 0.56×10-10 lower than the SVM prediction error. 4 MPa, convergence begins around the 11th generation. The optimal parameter combinations for different operating points on the lower yield strength curve are not exactly the same, and the optimal fitness after DE optimization shows a downward trend. A smaller value indicates increased prediction accuracy, and a reduced number of iterations indicates greater prediction stability. The DE-optimized support vector machine can stably predict the mechanical properties of DP780 dual-phase high-strength steel for most parameter combinations up to 30 generations. By adaptively controlling the support vector machine parameters, finding optimal c and g parameters demonstrates excellent adaptability and stability in predicting the mechanical properties of DP780 dual-phase high-strength steel.

[0094] (2) Analysis of predicted values ​​and actual values

[0095] After the DE algorithm mutates and crosses, it continuously adjusts the distribution range of the control parameters based on the evolutionary experience. By adaptively controlling the control parameters, it searches for better penalty functions and kernel function parameters for the support vector machine, and establishes a more ideal and accurate prediction model for the mechanical properties of DP780 dual-phase high-strength steel welds. The prediction results of the SVM and DE-SVM models are compared with the actual results of the randomly selected test set, and the prediction results of the impact energy, elongation, tensile strength and lower yield strength of the DP780 dual-phase high-strength steel welds are obtained as follows: Figure 5As shown. Actual Value is the actual test result, which indicates the expected value of the prediction result. The closer the prediction is to the expected value, the higher the prediction accuracy. Overall, after the DE algorithm optimizes SVM, its predicted value is closer to the expected value. The DE-SVM prediction of impact energy changes less with the expected value, and the result is relatively stable. The SVM prediction shows a large jump. In the lower yield strength, two predictions appear to be basically coincident with the expected value, indicating that the error is approaching 0. After DE optimization, the predicted values ​​of elongation and tensile strength fluctuate with the expected value. The predicted values ​​are closer to the expected value, and the error is lower than that of the support vector machine.

[0096] (3) Error analysis

[0097] Table 4 lists the mechanical properties of the DP780 weld predicted by the support vector machine model and the differential evolution algorithm-optimized support vector machine model after 100 iterations. The average relative errors of the SVM predictions for the weld outputs of impact energy, elongation, tensile strength, and lower yield strength, as determined by Matlab, were 46.41%, 21.35%, 16.41%, and 24.76%, respectively. The average relative errors of the DE-SVM predictions for these four output variables were 2.29%, 2.51%, 3.56%, and 2.93%, respectively. The average relative error of the DE-SVM predictions was below 5%, with the relative errors for impact energy, elongation, and lower yield strength not exceeding 3%, indicating high prediction accuracy.

[0098] Table 4 Relative error of predicted data

[0099]

[0100]

[0101] Through error analysis, it can be seen that after the differential evolution algorithm optimizes the support vector machine, the evolutionary generations of the model are greatly reduced, and the prediction error is reduced by adaptively controlling the parameter distribution.

[0102] In summary, for the problem of improving the softening and low-temperature brittleness of DP780 welded joints by Ce / Nb, the support vector machine prediction model optimized by the differential evolution algorithm has high prediction accuracy. The distribution range of the control parameters can be continuously adjusted according to the evolutionary experience. The support vector machine can find better c and g parameters through adaptive control parameters. It has excellent adaptability and stability in predicting the mechanical properties of DP780 dual-phase high-strength steel.

Claims

1. A method for predicting the mechanical properties of dual-phase high-strength steel welds containing Ce and Nb, characterized in that: The DE-SVM prediction model based on the differential evolution algorithm DE optimized support vector machine SVM specifically includes the following steps: Step 1: Uniform test design: Use homogenization test design to determine the specific addition amount and grouping of Ce and Nb elements during welding; Step 2: Establish an SVM classification model: Take the Ce content wt1 and Nb content wt2 as input variables, and the tensile strength R m , lower yield strength R el , elongation after fracture A 5.65 And the impact energy KV is used as the output variable, the uniform test data is divided into training data and test data, and a SVM classification model with multi-variable input and multi-variable output is established; The specific process of establishing an SVM classification model with multi-variable input and multi-variable output is as follows: I. Design support vector machine training set input N={(B1,N1)(B2,N2)(B3,N3)…(B n ,N n )}, n is the number of training samples, and the relationship between input variables and output variables is established: N i =ω Τ F(B i )+b Where: ω represents the normal vector, b represents the displacement, Φ(B i ) represents the mapping function, B i is the training sample size; II. Definition of the hyperplane ω for the output of mechanical properties of dual-phase high-strength steel welds Τ x+b=0, after classifying the hyperplane, the mathematical model formula is established as follows: III. Use hinge loss to transform the optimization problem and list the basic model formula of SVM classification model: where ξ i is the slack variable, c is the penalty function, and the penalty parameter c>0 is selected, and n is the number of training samples; IV. With kernel function g(B i ,B j ) Construct and solve the convex quadratic programming problem, introduce the Lagrange multiplier, and establish the Lagrange function as follows: Where α i , α j is the Lagrange multiplier, and the optimal solution is: Ⅴ. * Perform calculations, is α * Quantity, satisfying It can be calculated Where ω * is the normal vector of the decision function, b * is the displacement component; VI. Using the hyperplane classification decision function f(x)=sign(ω * ×B)+b * Find the hyperplane; Step 3: Establish an adaptive DE algorithm based on the DE algorithm: Change the precise strategy assignment of the DE algorithm to an approximate strategy assignment, select individuals participating in the operation based on the difference in convergence, and adaptively select the differential strategy and algorithm control parameters that best suit the current population based on the population's evolutionary experience. By calculating the objective function value of each individual in the population, the best individual is randomly selected from each time, and a strategy is selected for each target vector. The specific process of establishing the adaptive DE algorithm is as follows: I. Initialize a population B of size NP i , and B i is a D-dimensional vector; Ⅱ. Using the DE / rand / 1 / bin differential strategy in the basic differential evolution algorithm, the basic mutation vector is the Gth generation of the i-th individual, which can generate mutant individuals V i,G for: Where G is the current evolutionary generation, V i,G is the G-th generation population, F is the mutation operator, and subscripts r1, r2, and r3 are integers randomly selected between 1 and NP that are different from i; III. Through mutation of individual V i,G and individual B i,G Crossover operation can obtain experimental individuals Where C r is the cross factor, j rand is a random integer in the vector set [1,2,…,D]; IV. Cross-operate all populations and optimize the next iteration based on the fitness of the corresponding individuals where X i,G For other individuals in the previous iteration; Step 4: Use the adaptive DE algorithm to optimize the SVM classification model: Use the adaptive DE algorithm to randomly optimize the parameters of the penalty function c and kernel function g of the SVM classification model. The design mutation rate is: Where e is the base of natural logarithm, G m is the maximum number of iterations, G is the current number of iterations, 1 is the adaptive adjustment coefficient, and the scaling factor F is the exponential function of the mutation rate, then F=F0×2 λ , where F0 is the initial value of the scaling factor, the DE-SVM model is generated to obtain the prediction results of the output variables.

2. The method for predicting mechanical properties of dual-phase high-strength steel welds containing Ce and Nb according to claim 1, characterized in that: When using the adaptive DE algorithm to randomly optimize the parameters of the penalty function c and kernel function g of the SVM classification model, the random crossover operator C is designed. r , take C r The lower limit is 0.2 and the upper limit is 0.

9.

3. The method for predicting mechanical properties of dual-phase high-strength steel welds containing Ce and Nb according to claim 1, characterized in that: In step 2, MATLAB is used to perform SVM grid training and testing, and the data is normalized to between [-1, 1]. Then, inputps is used to perform the same normalization process again.

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