Method, equipment and medium for fast determination of integer-order viscoelastic model of viscoelastic materials

Abstract

The present invention relates to a method, device and medium for quickly determining an integer-order viscoelastic model of a viscoelastic material. The method comprises fitting and solving a master curve of a dynamic modulus of a viscoelastic material; initializing a search space including multiple dynamic modulus master curves based on a dynamic modulus master curve obtained from an experiment; minimizing the objective function value of a dynamic modulus master curve corresponding to a combination of the dynamic modulus curves and a target dynamic modulus master curve as an optimization target, and generating a new combination of dynamic modulus master curves based on an evolutionary strategy to form a new search space and complete an iteration; repeating the iteration multiple times, and finally obtaining a dynamic modulus master curve with the highest similarity to the target dynamic modulus master curve. The present invention utilizes an evolutionary strategy and a mutation method in a genetic algorithm, and by introducing randomness, can avoid local optimal solutions, thereby increasing the possibility of finding a global optimal solution.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and in particular to a method, a device and a medium for quickly determining an integer-order viscoelastic model of a viscoelastic material. Background Art

[0002] Among the methods for calculating the dynamic modulus of viscoelastic materials, the commonly used method is the experimental calculation method, which uses specific test equipment to perform dynamic modulus tests. By applying a half-sine wave pressure load to the specimen, the dynamic modulus and phase angle of the viscoelastic material under different temperatures and load frequencies can be obtained. At present, there are certain errors in the method of determining the integer-order viscoelastic model through experimental data. Due to the limitations of experimental equipment, it is impossible to obtain the dynamic modulus master curve of the viscoelastic material in the full frequency domain through experimental testing. The Sigmoidal model based on the time-temperature equivalence principle can convert the dynamic modulus at different temperatures into dynamic modulus values ​​at different frequencies at a certain temperature, and has been widely cited. However, the Sigmoidal model contains a large number of undetermined parameters, and traditional solution methods are often time-consuming and laborious in obtaining the values ​​of the undetermined parameters.

[0003] Traditional methods for calculating the dynamic modulus of viscoelastic materials have some significant disadvantages, including long experimental cycles, complex sample preparation, sensitivity to experimental conditions, low efficiency, and other changes that are difficult to cope with. Therefore, many engineering projects have gradually turned to more modern methods, such as model-based and computer simulation methods, to improve the accuracy, efficiency, and repeatability of calculations. These methods can better meet different performance and mathematical continuity requirements and reduce computational costs. However, most of the existing related methods have unsatisfactory accuracy and are prone to local optimality.

[0004] In summary, there is currently a lack of a method for quickly determining the viscoelastic model to solve or partially solve the aforementioned problems. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method, device and medium for quickly determining the integer-order viscoelastic model of viscoelastic materials, so as to solve or partially solve the problem of complex calculation of dynamic modulus of viscoelastic materials and unsatisfactory accuracy.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] One aspect of the present invention provides a method for quickly determining an integer-order viscoelastic model of a viscoelastic material, comprising the following steps:

[0008] Step S0, obtaining a target dynamic modulus master curve of the viscoelastic material, constructing an optimization problem of the dynamic modulus master curve of the viscoelastic material based on a genetic algorithm, obtaining experimental condition data of the dynamic modulus of the viscoelastic material, and initializing a proportional matrix of unknown numbers for fitting the dynamic modulus of the viscoelastic material;

[0009] Step S1, constructing multiple dynamic modulus master curves based on the ratio matrix as the search space of the optimization problem, with the goal of minimizing the error between the dynamic modulus master curve and the target curve obtained in advance through experiments, and calculating the fitness value of a single solution;

[0010] Step S2, by calculating the fitness value and selecting by probability, a single solution of the next generation is screened and a new search space is constructed;

[0011] Step S3, performing crossover processing and mutation processing on a single solution in the current search space;

[0012] Step S4, repeating steps S1-S3 until the search space converges to the global optimal solution, thus achieving the determination of the viscoelastic model.

[0013] As a preferred technical solution, in step S1, the dynamic modulus master curve in the search space is modeled as:

[0014]

[0015] Among them, E j is the jth dynamic modulus master curve in the search space, P i is the i-th row element of the ratio matrix P, i = 1, 2, 3…m, P j =[P j1 ,P j2 ,P j3 ,…P jn ],f=[f1,f2,f3,…f k ] is the frequency vector serving as experimental condition data.

[0016] As a preferred technical solution, in step S1, the error between the dynamic modulus master curve and the target curve obtained in advance through experiments is minimized as follows:

[0017]

[0018] Among them, SSE j is the jth dynamic modulus master curve E j The error value, is the target dynamic modulus master curve obtained experimentally.

[0019] As a preferred technical solution, in step S2, the process of calculating the fitness value and selecting by probability to screen out a single solution of the next generation includes:

[0020] Step S201, calculating the proportion of the fitness value in the total fitness of the search space as the probability of being selected;

[0021] Step S202, based on the calculated probability of being selected, by comparing the probability with the regional boundary on the preset evolutionary strategy, it is determined whether the solution is selected, and all selected single solutions are used as single solutions of the next generation, wherein the probability of a solution being selected is inversely proportional to the fitness.

[0022] As a preferred technical solution, the crossover processing includes exchanging the positions of variables in a single solution with a preset probability.

[0023] As a preferred technical solution, the variation processing includes exchanging two solutions with a preset probability.

[0024] As a preferred technical solution, in the step S1, based on the proportion matrix, a plurality of dynamic modulus master curves are constructed using the Sigmoidal model.

[0025] As a preferred technical solution, the experimental condition data includes multiple temperature and frequency coupling combinations.

[0026] Another aspect of the present invention provides an electronic device, comprising: one or more processors and a memory, wherein the memory stores one or more programs, and the one or more programs include instructions for executing the aforementioned method for quickly determining an integer-order viscoelastic model of a viscoelastic material.

[0027] Another aspect of the present invention provides a computer-readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the aforementioned method for quickly determining an integer-order viscoelastic model of a viscoelastic material.

[0028] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0029] (1) Realizing rapid calculation of dynamic modulus: The present invention randomly generates a plurality of dynamic modulus master curve combinations, and performs multiple iterations with the goal of minimizing the error between the dynamic modulus master curve and a target curve obtained in advance through experiments. Finally, a fitted dynamic modulus master curve close to the target dynamic modulus master curve is obtained. The dynamic modulus of the final designed viscoelastic material can be accurately predicted through parameter design, which is beneficial to rapidly optimize the dynamic modulus calculation of the viscoelastic material and obtain the expected effect. It has a positive significance for improving the accuracy and speed of the dynamic modulus calculation of the mixture.

[0030] (2) Avoiding falling into local optimum: The present invention introduces evolutionary strategies, interleaving and mutation methods in the iterative process. By introducing randomness, local optimal solutions can be avoided, thereby increasing the possibility of finding a global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of a method for quickly determining an integer-order viscoelastic model of a viscoelastic material in an embodiment;

[0032] Figure 2 It is the best random number value diagram of the Sigmoidal model in the embodiment;

[0033] Figure 3 The figure is a comparison diagram of the optimal dynamic modulus data and the target dynamic modulus data in the embodiment;

[0034] Figure 4 This is a schematic diagram of the dynamic modulus data of the first generation of iterative evolution in the embodiment;

[0035] Figure 5 It is the initial generation iterative evolution error value curve in the embodiment;

[0036] Figure 6 The fifth generation iterative evolution dynamic modulus data in the embodiment;

[0037] Figure 7 The fifth generation iterative evolution error value curve in the embodiment;

[0038] Figure 8 The 30th generation iterative evolution dynamic modulus data in the embodiment;

[0039] Fig. 9 is the 30th generation iterative evolution error value curve in the embodiment;

[0040] Fig.10 The dynamic modulus data of the sixtieth generation of iterative evolution in the embodiment;

[0041] Fig.11 This is the sixtieth generation iterative evolution error value curve in the embodiment;

[0042] Fig.12 The dynamic modulus data of the 100th generation of iterative evolution in the embodiment;

[0043] Fig.13 is the 100th generation iterative evolution error value curve in the embodiment;

[0044] Fig.14 This is the fitness value evolution curve of the 100th generation in the embodiment;

[0045] Fig.15The final optimized data and target dynamic modulus data in the embodiment;

[0046] Fig.16 It is the dynamic modulus master curve finally optimized in the embodiment. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0048] Example 1

[0049] In view of the problems existing in the above-mentioned prior art, this embodiment provides a method for quickly determining an integer-order viscoelastic model of a viscoelastic material. This method aims to quickly obtain a constitutive model that can describe the viscoelastic behavior of a viscoelastic material through optimization. Based on the time-temperature equivalence principle, the test results at different temperatures are translated to a reference temperature to form a smooth curve, thereby breaking through the limitations of the test instrument and achieving the solution of the dynamic modulus of the material at different frequencies.

[0050] The integer-order viscoelastic model of viscoelastic materials is a mathematical model used to describe the viscoelastic behavior of viscoelastic materials under different stress and temperature conditions. The integer-order viscoelastic model of viscoelastic materials is an important tool for describing the viscoelastic behavior of viscoelastic materials. By establishing a mathematical model, we can better understand and predict the mechanical properties of viscoelastic materials in practical applications.

[0051] This method obtains the target dynamic modulus master curve data and experimental condition data, and uses the time-temperature equivalence principle to translate the test results of different temperatures to a reference temperature to form a smooth curve, thereby breaking through the limitations of the test instrument and achieving the solution of the dynamic modulus of the material at different frequencies. The Sigmoidal function is a curve that is used more frequently to solve the dynamic modulus master curve of viscoelastic materials, because it is widely used as an integer-order Prony series. Therefore, this paper uses the Sigmoidal model to fit and solve the master curve of the dynamic modulus of viscoelastic materials; based on the dynamic modulus master curve obtained from the experiment, the search space including multiple dynamic modulus master curves is initialized; the objective function value of the dynamic modulus master curve corresponding to the dynamic modulus curve combination and the target dynamic modulus master curve is minimized as the optimization target, and a new dynamic modulus master curve combination is generated based on the evolutionary strategy to form a new search space and complete an iteration; the iteration is repeated multiple times, and finally the dynamic modulus master curve with the highest similarity to the target dynamic modulus master curve is obtained.

[0052] See also Figure 1 , the method comprises the following steps:

[0053] Step S0: Before the formal calculation, the target dynamic modulus value of the viscoelastic material (i.e., the target dynamic modulus master curve) and the key factors affecting the calculation of the dynamic modulus of the viscoelastic material are determined in advance according to the conditions of the dynamic modulus curve experiment of the viscoelastic material, and the target dynamic modulus master curve is used as the optimization final value. Among them, the key factors include parameters such as experimental conditions, Sigmoidal model, and viscoelastic material gradation type.

[0054] Using relevant software, a genetic algorithm is used to establish the data architecture of the key factors and the optimization method of the dynamic modulus master curve of viscoelastic materials. The main significance of the data architecture is that it tells how to use genetic algorithms to solve a complex optimization problem. Through iterative evolution, the optimal solution of the problem is gradually found. The algorithm initially performs some initialization settings, including the setting of parameters such as the search space size, evolution probability, single solution dimension, search space range, and number of iterations.

[0055] Specifically, this step first obtains the dynamic modulus curve data and experimental condition data of the target material, and uses the Sigmoidal model to solve the dynamic modulus value (E*): Introduce random variables to fit and solve the dynamic modulus master curve, where δ, α, β, and γ are fixed unknowns in the model, and a T are the displacement factors at different temperatures.

[0056] Step S1: Based on the experimental condition data, the search space including multiple dynamic modulus master curve data is initialized. The main program is looped to seek the optimal solution. Further, the algorithm adopts an evolutionary strategy to select a single solution data using fitness value. The fitness value is usually realized by the objective function of the problem, which indicates the performance or quality of any single solution in the search space. It is ensured that after the genetic algorithm iteration is completed, the final code finds the location and value of the optimal solution and displays it on the screen.

[0057] Furthermore, the dynamic modulus of the viscoelastic material at different frequencies f and temperatures T is obtained: T = [T1, T2, T3, ... T m ],f=[f1,f2,f3,…f n ] experimental conditions, (i.e., obtaining experimental condition data), and then using the random variables generated by the Sigmoidal model to calculate the single dynamic modulus values ​​at different temperatures and frequencies in turn, and then calculate the proportion matrix P, P with a number of m×n ijRepresents the data in the i-th row and j-th column of the matrix; where i=1,2,3…m, j=1,2,3,…n. Then, according to the values ​​of each row of the matrix P, the Sigmoidal model is used for successive calculations to obtain m dynamic modulus master curves E m , thus obtaining the search space.

[0058] Each dynamic modulus master curve data includes m sub-data E i ,

[0059] Furthermore, the search space is calculated as follows:

[0060]

[0061] Where E is the dynamic modulus master curve, P is the m×n matrix that satisfies the distribution, f=[f1,f2,f3,…f k ] is the frequency change value during the dynamic modulus experiment, and the i-th row P of the matrix P i =[P i1 ,P i2 ,P i3 ,…P in ], i = 1, 2, 3…m. When calculating the specific value of E, the values ​​of columns 1 to 4 of the matrix P are fixed each time, and the values ​​of 1 to k of f and the values ​​of columns 4 to n of each row of P are gradually selected for calculation. Columns 1 to 4 of the matrix P represent random variables with fixed values ​​in the equation, and columns 5 to 8 are displacement factors for calculating the dynamic modulus master curve, which are calculated one by one according to the values ​​of each row of the matrix P. Get m dynamic modulus master curves E m .

[0062] Calculate E i With the average The sum of squares of errors (SSE) of the data points between them is calculated by the formula: The optimization goal is to minimize the SSE.

[0063] Algorithm parameters are predefined, including search space size, evolution probability, single solution dimension, search space range, and number of iterations.

[0064] Sigmoidal model random variables are randomly generated, and the master curve of the dynamic modulus of the viscoelastic material calculated according to the combination of the Sigmoidal model random variables is a set of multiple solutions, where each single solution is a decimal, so as to calculate the objective function value.

[0065] Calculate the objective function value of the master curve of the dynamic modulus of the initial viscoelastic material.

[0066] An image of the initial dynamic modulus master curve of the calling function, including the distribution of the dynamic modulus master curve in the search space and the change in the objective function value.

[0067] Initialization records the optimal dynamic modulus master curve and solution values ​​of each generation, and records the default optimal dynamic modulus master curve.

[0068] Enter the main loop and execute the iterative process of the genetic algorithm. In each generation:

[0069] Compute the objective function value of a single solution from the previous generation.

[0070] The fitness value (i.e., the objective function value) is calculated based on the objective function value.

[0071] Duplicate a single solution to create a new generation of search space.

[0072] Perform evolutionary strategy operations.

[0073] Select the best single solution and keep it.

[0074] Update the search space, calculate the objective function value of the search space, and record the optimal value and the corresponding solution.

[0075] After the loop is finished, the value of the optimal solution and the corresponding random variable value are found and displayed.

[0076] Step S2: Use the evolutionary strategy in the genetic algorithm to select excellent solution combinations. The process of seeking the optimal solution mainly includes evolution and update strategies. The evolutionary strategy calculates the fitness value and replicates the solution with a lower fitness value with a higher probability.

[0077] Among them, the selection strategy of excellent solutions will play a decisive role in the performance of the algorithm. In order to transform the existing search space into the next generation search space, this method selects excellent single solutions from the old search space for replication. The selection is based on the fitness value of the single solution. The single solution with low fitness value is replicated to make it multiply; the single solution with high fitness value is covered by the single solution with low fitness value, making it disappear.

[0078] In this embodiment, fitness ratio selection is adopted, in which the expected value of any single solution being selected is related to the ratio of its fitness and the average fitness of the search space, and is implemented by an update strategy. First, the fitness of each single solution is calculated, and then the proportion of this fitness value in the total fitness of the search space is calculated, which represents the probability of the single solution being selected in the selection process. The selection process embodies the idea of ​​"survival of the fittest" in the biological evolution process, and ensures that good genes are inherited by the next generation of single solutions.

[0079] Evolutionary strategies are more likely to select single solutions with the same fitness value, which increases the representativeness of these single solutions in the next generation and helps the genetic algorithm find better solutions faster. Although the evolutionary strategy method tends to select single solutions with lower fitness values, it still provides a certain opportunity for single solutions with higher fitness values ​​to be selected to maintain the diversity of the population and prevent premature gradient local optimal solutions. At the same time, the evolutionary strategy introduces a certain degree of randomness, so that the selection of a single solution is not completely deterministic, which helps to avoid the algorithm taking the same strategy in each generation, thereby better exploring the space.

[0080] Specifically, the evolution strategy first needs to calculate the fitness value of each single solution. Next, the selection probability is calculated for each single solution. The probability is usually inversely proportional to the fitness value of the single solution, that is, the single solution with a lower fitness value has a greater probability of being selected.

[0081] This can be achieved by doing the following:

[0082] Normalize the fitness values ​​of all individual solutions in the search space. This can be done by dividing the fitness value of each individual solution by the sum of the fitness values ​​of all individual solutions. Create an evolution strategy selection method with a space size equal to the number of individual solutions in the search space. The size of each region of the evolution strategy is proportional to the selection probability of each individual solution. Generate a random probability value (usually a random number between 0 and 1) and then select it individually on the evolution strategy. The selection method determines whether a single solution is selected by comparing the random probability value with the boundaries of each region on the evolution strategy. If the random probability value belongs to a certain region, then the corresponding single solution will be selected. Repeat the above selection process until a sufficient number of single solutions are selected to build the next generation search space. Generally, individual solutions with lower fitness values ​​have a greater probability of being selected and are therefore more likely to pass their genetic information to the next generation.

[0083] Specifically, the process of selecting the dynamic modulus master curve based on the evolution strategy includes:

[0084] Calculate the value of the objective function corresponding to each solution in the current search space and perform normalization;

[0085] Generate random probability values, select a single solution based on the probability values ​​and the normalized value of the objective function, and repeat this operation multiple times.

[0086] During the screening process, the probability of a single solution being selected is inversely proportional to the value of the corresponding objective function.

[0087] Step S3, crossover and mutation optimization are performed on the single solution in the search space to ensure that the single solution in the search space has a high fitness value, and the suitable single solution in the search space is continuously copied to implement the survival of the fittest system to ensure that the final output result is the optimal solution. Evolutionary strategies are divided into intra-group and inter-group evolutionary strategies, that is, any identical position value between two solutions is crossovered with a certain probability and any position value within a single solution in the group is mutated with a certain probability.

[0088] The new search space generated by replication in S2 improves its performance, but it cannot generate new single solutions. In order to generate new single solutions, the genetic algorithm imitates the gene recombination process of sexual reproduction in nature, performs transposition optimization on the random distribution of chromosomes (strings), inherits the original good genes to the next generation of single solutions, and generates new single solutions containing more complex gene structures. Whether a single solution in the genetic algorithm mutates can be randomly selected or determined by selection operator calculation. The optimized mothers are all new generation single solutions generated by replication from the previous generation. The operation of evolutionary strategies can ensure that the optimization process of the genetic algorithm can converge to the global optimal point, and plays an important role in improving the convergence speed of the optimization process.

[0089] In order to ensure the quality and diversity of solutions, a group of Sigmoidal model single solutions are internally evolved using optimization strategies to calculate the dynamic modulus of the mixture, so as to prevent the algorithm gradient from reaching the local optimal solution, improve the global search capability, give full play to the advantages of direct search and random search, and continuously establish and improve single solutions. Evolutionary strategy operations help generate better solutions, which can produce results close to more optimal solutions in optimization problems.

[0090] Operation S4, repeating the above steps until the search space converges to the global optimal solution.

[0091] By running the completed genetic algorithm, many different dynamic modulus master curves are generated with random dynamic moduli on a global scale. The mean square error between the solved dynamic modulus master curve and the target dynamic modulus master curve is the smallest, indicating that the final drawn dynamic modulus master curve is basically similar to the target dynamic modulus master curve. At this time, it means that a set of data closest to the target dynamic modulus master curve of the viscoelastic material has been found, and outputting this set of data is the optimal solution.

[0092] In summary, this method uses the Sigmoidal curve to fit the dynamic modulus. The Sigmoidal curve includes multiple unknowns. This method first fits its unknowns, and then brings the S curve into the calculation of the corresponding dynamic modulus data under different temperatures and frequencies. Finally, after all the calculations are completed, a dynamic modulus master curve is formed.

[0093] In iterative optimization, the root mean square of the experimental data obtained in advance and the fitted master curve is calculated. After multiple fittings of the unknowns of the Sigmoidal model, the dynamic modulus data calculated by the Sigmoidal model is closer and closer to the experimental data (the root mean square is getting smaller and smaller), and then the unknowns in the model can be directly determined, and finally the dynamic modulus at different temperatures and frequencies can be directly calculated. Among them, the experimental data is obtained through simulation. Specifically, one hundred dynamic modulus data will be generated each time, that is, there are one hundred data on each data node. The experimental data is obtained by calculating the average value of the data on each data node.

[0094] The above process is explained below with a specific example.

[0095] Step 0: According to the requirements of road engineering for dynamic modulus, the dynamic modulus of the viscoelastic material and the key factors affecting the dynamic modulus of the viscoelastic material are determined through experiments, and the target dynamic modulus master curve is used as the optimization final value.

[0096] This example takes AC-13 viscoelastic material as an example. AC-13 viscoelastic material is commonly used in road construction such as highways, expressways and airport runways. It generally has high strength and durability and can withstand the impact of traffic loads and climate change on the road surface. Its surface roughness is moderate and can provide sufficient friction, making the vehicle more stable and safer during driving. This characteristic plays a positive role in improving road safety and reducing the occurrence of traffic accidents. It is a ratio combination used more frequently in road construction.

[0097] This example takes the dynamic modulus master curve of AC-13 viscoelastic material as the target for optimization.

[0098] The key factors affecting the dynamic modulus of viscoelastic materials mainly include the following:

[0099] Properties: The viscosity, viscoelasticity and cohesion of the material will affect the dynamic modulus of the mixture. Generally speaking, the greater the viscosity, the higher the viscoelasticity and the stronger the cohesion of the material, the higher the dynamic modulus of the mixture.

[0100] Interaction between materials and aggregates: The interaction between materials and aggregates, such as bonding, friction, and stress distribution, will also affect the dynamic modulus of the mixture. The greater the bonding force, the smaller the friction force, and the more uniform the stress distribution, the higher the dynamic modulus of the mixture.

[0101] Experimental conditions: Under different temperatures and frequencies, the calculated dynamic moduli of viscoelastic materials vary greatly.

[0102] The above factors have a comprehensive impact on the dynamic modulus master curve of the viscoelastic material. Since this method uses the Sigmoidal model to calculate the dynamic modulus master curve, which is greatly affected by temperature and frequency, the choice of temperature and frequency in the dynamic modulus experiment of viscoelastic materials is particularly important for the calculation. By reasonably controlling and adjusting these factors, viscoelastic materials that meet different engineering needs can be obtained.

[0103] Different viscoelastic materials in engineering have different types of dynamic modulus master curves. The traditional calculation method is relatively rough, and the calculation efficiency needs to be improved. In addition, in actual engineering, for the sake of convenience and speed, the construction party generally does not make accurate calculations. In order to improve the quality of the project, it is necessary to use the aforementioned method of quickly determining the integer-order viscoelastic model of viscoelastic materials for design.

[0104] Using relevant software and genetic algorithm, a data model of the optimization method of the above factors and experimental conditions is established, and a series of variables are defined: including the size of the search space, the probability of evolution, the dimension of a single solution, the range of the search space and the number of iterations. These variables will be used to define the parameters of the algorithm and the problem setting.

[0105] When the Sigmoidal model is used to calculate the dynamic modulus master curve of viscoelastic materials, the number of random variables with fixed values ​​inside the model is 4, and there are several displacement factors. The number of displacement factors depends on the experimental temperature. This example conducted five temperature experiments, so the number of displacement factors is 5. Because the displacement factor of the dynamic modulus master curve is 0, no assumption is needed to solve it, so the number of random variables inside the actual model is 8. Therefore, a 150×8 matrix is ​​set as the search space in this example, which means that each iterative search space has 150 single solutions. The Sigmoidal model viscoelastic material has a total of 8 random variables, so the dimension of each single solution is 8.

[0106] A matrix F is defined to represent the frequency variation values ​​in the experiment. The same parallel experiments were conducted at five different temperatures as described in Table 1.

[0107] Table 1 Experimental frequency F at different temperatures during the experiment

[0108]

[0109] A 1-row 30-column matrix is ​​defined to represent the master curve of the dynamic modulus of the target viscoelastic material. In this example, the matrix B is obtained through five experiments at different temperatures and six different frequencies.

[0110] The data of each generation of search space are stored in a 150×30 matrix, which represents the dynamic modulus master curve of a single solution in the search space. The matrix is ​​calculated by bringing the random variables of the 150×8 Sigmoidal model into the model one by one.

[0111] The initial population combination is updated in a loop, and the specific update operations are as follows.

[0112] Step 1. On the premise that some conclusions have been drawn from the experiment, the following operations are performed: define the upper and lower limits of eight random variables respectively, randomly select the variables within the upper and lower limits of the random variables, and calculate the dynamic modulus of the viscoelastic material one by one after determining the variable values. At this point, the eight random variables of the first solution of the first-generation search space have been updated, and the eight random variables of the second solution of the first-generation search space are calculated. The cycle is stopped after one hundred and fifty operations. At this time, all individual solutions in the first-generation search space have been updated. Some data are listed here, as described in Table 2.

[0113] Table 2 Primary dynamic modulus master curve values ​​(rows 1-2, 49-51, 99-101, 149-150)

[0114]

[0115] The function is used to calculate the function value of the dynamic modulus of each viscoelastic material and assign the function value to the search space. The specific calculation method is as follows:

[0116] According to the experimental conditions of the dynamic modulus of the viscoelastic material, the experimental conditions are determined, f = [f1, f2, f3, ... f6] (i.e., the experimental condition data is obtained), and then the random variables generated by the Sigmoidal model are calculated to obtain a matrix P of m × n, P ij represents the data of the i-th row and j-th column of the matrix; i = 1, 2, 3…150, j = 1, 2, 3,…30. Then, the values ​​of each row of the matrix P are calculated one by one. Get 150 dynamic modulus master curves E m , thus obtaining the search space. Calculate E i With the average The sum of squared errors SSE of each data point between them. The specific value of SSE is calculated according to the formula: Take "minimum SSE" as the optimization goal.

[0117] Use the function to draw the master curve of the dynamic modulus of the initial viscoelastic material and the iterative evolution error value.

[0118] In the iterative process, the search space is copied, crossed, and mutated, as follows: After the initial function update is completed, the main program loop begins. The loop operation is continuously performed to calculate the objective function value of a single solution within the i-1 generation population combination. Based on the calculated function value, the fitness value of the i-1 generation is further calculated to determine the fitness value. A single solution with a lower fitness value is copied, and a single solution with a higher fitness value is covered by a solution with a lower fitness value. After the end, the i-th generation population combination is created, and the i-th generation fitness value is calculated. When i<100, the same steps are repeated, and a higher fitness value is covered, and a lower fitness value is used to generate a new population combination through copying, crossover, and mutation operations. When i≥100, the optimal value is output.

[0119] The function is used to calculate the function value of the current dynamic modulus master curve and stored in the search space.

[0120] The fitness value of each dynamic modulus master curve is calculated using the function. According to the algorithm explanation, the function value itself is directly used as the fitness value.

[0121] Use the function to generate new population individuals and store them in a new array. The specific implementation is as follows:

[0122] Calculate the probability p of a single solution being selected i , calculated as follows: single solution fitness value / search space total fitness value. The generated p is converted into i Gradually add to generate a new array P i , P i Each element position in corresponds to p i For example, if p1 = 0.2, p2 = 0.4, p3 = 0.1, p4 = 0.3, then the new array is P1 = 0.2, P2 = 0.6, P3 = 0.7, P4 = 1, and a random variable R i Satisfy uniform distribution on [0~1], randomly generate R i , and sort the generated random numbers in descending order and store them in a 100×1 matrix (since the number of single solutions in the above population is 100, 100 random numbers are generated and the probability p of each single solution being selected i Compare, 1 is to generate a random number each time. )

[0123] Compare R i With P i If the random number R i <P i , which means selecting the single solution and copying it to the corresponding position of the new array. i >P i, it means that the single solution is not selected for replication. At this point, the calculation of whether the first solution in the search space is replicated is completed, and the calculation of whether the second solution is replicated begins, and the cycle stops after one hundred operations. At this time, the optimization of individual solutions in the search space is achieved.

[0124] Eventually, the new array will contain a single solution that has been selected with a probability proportional to its fitness value. This selection process is an important step in the genetic algorithm to create the next generation of single solutions, thereby gradually improving the fitness of the population during the evolution process.

[0125] Step S2: Use the replication in the algorithm to select an excellent dynamic modulus master curve combination, and at the same time perform crossover and mutation optimization on the Sigmoidal model random variables to ensure that a single solution within the population has a lower fitness value, and continuously replicate a single solution within the appropriate dynamic modulus master curve combination to implement a survival of the fittest system to ensure that the final output result is the optimal solution.

[0126] Randomly generate variable c i , let c i Satisfies uniform distribution on [0~1], and assumes the crossover probability q i =0.4, if c i <q i , then perform a crossover operation, the specific operations are as follows:

[0127] The function is used to perform crossover operation on the new population. There are eight random variables in the Sigmoidal model, and the crossover site is randomly selected within the group for crossover operation. The specific operation method is as follows: Assume that the eight random variables are P1, P2, P3, P4, α T1 ,α T2 ,α T3 ,α T4 Represents the 1st to 8th random numbers. Choose any two Xs to cross-exchange. The results after cross-exchange are P1, P3, P2, P4, α T1 ,α T2 ,α T3 ,α T4 Represent the 1st to 8th random numbers respectively.

[0128] Randomly generate variable b i , let b i Satisfies uniform distribution on [0~1], let the mutation probability m i =0.4, if b i <m i , then perform mutation operation, the specific operations are as follows:

[0129] The new population is mutated using the function. The Sigmoidal model has eight random variables, and the mutation site is randomly selected between groups for mutation operation. The specific operation is as follows: Assume that the two groups of eight random variables are P1, P2, P3, P4, α T1 ,α T2 ,α T3 ,α T4 , represents the 1st to 8th random numbers, and any variable is selected between the groups for mutation. The results after mutation are P1, P2, Q3, P4, α T1 ,α T2 ,α T3 ,α T4 Represent the 1st to 8th random numbers respectively.

[0130] After the crossover and mutation in step 2 are completed, multiple new single solutions will be generated. In order to ensure that the population size is fixed, some single solutions need to be covered. By comparing the fitness value calculated above, it is determined whether a single solution should be covered.

[0131] Replication may select more single solutions with lower fitness values, thereby increasing the representativeness of these single solutions in the next generation. Selection helps the genetic algorithm find better solutions faster. Although the replication method tends to select single solutions with lower fitness values, it still provides a certain opportunity for single solutions with higher fitness values ​​to be selected to maintain the diversity of the population and prevent the local optimal solution of the gradient from appearing too early.

[0132] Step 3: Repeat step 2 until the search space converges to the global optimal solution.

[0133] After the replication, crossover, and mutation operations are completed, the function calculation results are used and assigned to the search space as the new objective function.

[0134] The function is used to calculate the fitness value of a single solution in the search space. According to the algorithm interpretation, the function value itself is directly used as the fitness value.

[0135] Compare the new fitness value with the previous fitness value, copy the single solution with smaller fitness value into the storage array and cover the single solution with larger fitness value. The search space is updated while ensuring that the size of the search space remains unchanged, and the function value of the updated search space is calculated at the same time.

[0136] Use the function to draw the dynamic modulus master curve and iterative error value of the updated search space.

[0137] Find the value and position of the optimal function value (minimum function value) of each generation, and record the optimal function value of each generation.

[0138] like Figure 3, Table 3, and Table 4, where Table 3 only lists part of the data.

[0139] Table 3 Optimal values ​​of some random variables in each generation (1st-3rd, 48th-51st, 98th-100th generations)

[0140]

[0141] Table 4 Optimal values ​​of random variables

[0142]

[0143] The Sigmoidal model is used to convert the random variables with the best fitness value in each generation into the dynamic modulus value of the viscoelastic material. In order to record and further analyze the actual value of the best solution and draw the dynamic modulus master curve, the specific operations are as follows:

[0144] It is known that P is an m×n matrix, f=[f1,f2,f3,…f k ] is the frequency change value during the dynamic modulus experiment, and the i-th row P of the matrix P i =[P i1 ,P i2 ,P i3 ,…P in ], i = 1, 2, 3…m. When calculating all the values ​​of E, the values ​​of the 1st to 4th columns of the matrix P are fixed each time, and the values ​​of the matrix F and the 4th to nth columns of each row of the matrix P are gradually selected for calculation. The 1st to 4th columns of the matrix P represent the random variables with fixed values ​​in the model, and the 5th to 8th columns are the displacement factors when calculating the dynamic modulus master curve. Among them, by calculating the values ​​of each row of the matrix P one by one, m synthetic dynamic modulus master curves E are obtained. m .

[0145] See also Figure 5 , Figure 6 The main curve of the evolutionary dynamic modulus and the evolutionary error value after the first iteration. Figure 7 , Figure 8 The fifth iteration evolution dynamic modulus master curve and iterative evolution error value. Fig. 9 , Fig.10 These are the main curve of the evolutionary dynamic modulus and the evolutionary error value curve after thirty iterations.

[0146] See also Fig.11 , Fig.12 They are the main curve of the evolutionary dynamic modulus and the evolutionary error value curve after sixty iterations. Tables 5 and 6 are some data after the sixtieth iteration.

[0147] Table 5 Sixtieth generation partial dynamic modulus master curve values ​​(rows 1-2, 49-51, 99-101, 149-150)

[0148]

[0149] Table 6 Optimal dynamic modulus data values ​​for the 50th generation

[0150]

[0151] Output the best random number combination, such as Figure 4 As described above, upon comparison, the target dynamic modulus master curve and the dynamic modulus master curve obtained by using the genetic algorithm substantially coincide with each other in percentage.

[0152] After the cycle is completed, the function value and position of the optimal dynamic modulus master curve are found, and the minimum error, the optimal dynamic modulus master curve and the corresponding optimal random number value are displayed. This information is related to the best single solution, and the function is used to draw a graph to represent the relationship between the optimal dynamic modulus master curve and the target dynamic modulus master curve. See Table 7 and Table 8 for some data after the 100th iteration. Fig.13 , Fig.14 , Fig.15 They are respectively the main curve of the 100th iterative evolution dynamic modulus, iterative evolution error, and fitness value evolution curve. Fig.16 Schematic diagram of the final target curve and the optimization curve.

[0153] Table 7: The main curve values ​​of the dynamic modulus of the first 100th generation (rows 1-2, 49-51, 99-101, 149)

[0154]

[0155] Table 8 Optimal dynamic modulus data values ​​for the 100th generation

[0156]

[0157] In summary, this method can accurately predict the dynamic modulus master curve of the final designed viscoelastic material through design parameters, which is conducive to quickly optimizing the calculation of the dynamic modulus master curve of the viscoelastic material and obtaining the expected effect; it has a positive significance for improving the accuracy and speed of the calculation of the dynamic modulus master curve of the mixture. By using the evolutionary strategy and mutation method in the genetic algorithm and introducing randomness, the local optimal solution can be avoided, thereby increasing the possibility of finding the global optimal solution.

[0158] This approach has many advantages, including improved design accuracy, flexibility, efficiency, and repeatability. This enables engineers to better design materials that meet differentiated performance requirements to meet project needs, while reducing the risk of errors, saving time and costs. Therefore, a rapid determination method based on the integer-order viscoelastic model of viscoelastic materials is particularly important for accurately and quickly determining the dynamic modulus master curve of viscoelastic materials.

[0159] Example 2

[0160] This embodiment provides an electronic device, including: one or more processors and a memory, wherein the memory stores one or more programs, and the one or more programs include instructions for executing the method for quickly determining an integer-order viscoelastic model of a viscoelastic material as described in Example 1.

[0161] Example 3

[0162] This embodiment provides a computer-readable storage medium, including one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the method for quickly determining an integer-order viscoelastic model of a viscoelastic material as described in Example 1.

[0163] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for quickly determining an integer-order viscoelastic model of a viscoelastic material, characterized in that: The steps include: Step S0, obtaining a target dynamic modulus master curve of the viscoelastic material, constructing an optimization problem of the dynamic modulus master curve of the viscoelastic material based on a genetic algorithm, obtaining experimental condition data of the dynamic modulus of the viscoelastic material, and initializing a proportional matrix of unknown numbers for fitting the dynamic modulus of the viscoelastic material; Step S1, constructing multiple dynamic modulus master curves based on the ratio matrix as the search space of the optimization problem, with the goal of minimizing the error between the dynamic modulus master curve and the target curve obtained in advance through experiments, and calculating the fitness value of a single solution; Step S2, by calculating the fitness value and selecting by probability, a single solution of the next generation is screened and a new search space is constructed; Step S3, performing crossover processing and mutation processing on a single solution in the current search space; Step S4, repeat steps S1-S3 until the search space converges to the global optimal solution, and the viscoelastic model is determined. Wherein, in the step S1, the dynamic modulus master curve in the search space is modeled as: In the above formula, E j is the jth dynamic modulus master curve in the search space, P ji represents the data in the jth row and ith column of the ratio matrix, f 1～k =[f1,f2,f3,…f k ] is the frequency vector used as experimental condition data, The error between the dynamic modulus master curve and the target curve obtained by experiment is minimized as follows: In the above formula, SSE j is the jth dynamic modulus master curve E j The error value, is the target dynamic modulus master curve obtained experimentally, In step S2, the process of calculating the fitness value and selecting according to probability to screen and obtain a single solution of the next generation includes: Step S201, calculating the proportion of the fitness value in the total fitness of the search space as the probability of being selected; Step S202, based on the calculated probability of being selected, by comparing the probability with the regional boundary on the preset evolutionary strategy, it is determined whether the solution is selected, and all selected single solutions are used as single solutions of the next generation, wherein the probability of a solution being selected is inversely proportional to the fitness.

2. The method for quickly determining an integer-order viscoelastic model of a viscoelastic material according to claim 1, characterized in that: The crossover process involves exchanging the positions of variables in a single solution with a preset probability.

3. The method for quickly determining an integer-order viscoelastic model of a viscoelastic material according to claim 1, characterized in that: The mutation process includes exchanging two solutions with a preset probability.

4. The method for quickly determining an integer-order viscoelastic model of a viscoelastic material according to claim 1, characterized in that: In the step S1, a plurality of dynamic modulus master curves are constructed based on the proportion matrix using the Sigmoidal model.

5. The method for quickly determining an integer-order viscoelastic model of a viscoelastic material according to claim 1, characterized in that: The experimental condition data include multiple temperature and frequency coupling combinations.

6. An electronic device, characterized in that: include: One or more processors and a memory, wherein the memory stores one or more programs, wherein the one or more programs include instructions for executing the method for quickly determining an integer-order viscoelastic model of a viscoelastic material as claimed in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that: It comprises one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs comprise instructions for executing the method for quickly determining an integer-order viscoelastic model of a viscoelastic material as claimed in any one of claims 1 to 5.

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