Edited from: https://vsystemes.com/35621/
1 Overview**
After 20 years of development, for domestic CAE simulation, many enterprises no longer only focus on the simulation itself, but focus more on the following three aspects:
(1) The focus of attention is slowly transitioning from ordinary simulation analysis to optimization analysis;
(2) CAE simulation analysis is more professional, standardized and streamlined;
(3) The complexity of CAE simulation analysis problems involves interdisciplinary and multidisciplinary compound problems.
We will explain the above three aspects respectively.
1.1 Transition from simulation analysis to optimization
Nowadays, computer-aided simulation analysis technology has been widely used in various industries, and everyone will simulate the ultimate goal of digital prototype virtual test instead of physical prototype real test.
With the improvement of domestic CAE simulation analysis level, on the basis of relatively mature simulation analysis methods and models, in order to more effectively apply simulation analysis results and achieve the purpose of simulation analysis results guiding product design, optimization methods and corresponding optimization software are gradually being used. Introduced into the work of the CAE department.
How to apply optimization software to build an optimization process, and what optimization method and mode to implement the optimization process have become the concerns of many enterprise CAE teams.
According to the above requirements, Dassault Systèmes provides Isight software, as a multi-parameter and multi-disciplinary optimization tool platform, which can be combined with simulation analysis tools (such as ABAQUS) to realize the establishment of simulation optimization process and solve the problem of joint optimization of product design and simulation.
1.2 Simulation standardization and process
With the increasing growth and maturity of the enterprise CAE team and the accumulation of simulation data, these enterprises have put forward an urgent need for the establishment of the simulation specification process.
Nowadays, high-performance computing resources are extremely abundant, and it is foreseeable that the development and practical application of quantum computers will bring about a leap in computing resources in the near future. For the CAE industry, computer hardware will no longer be the bottleneck and shackle of simulation analysis, and a large number of simulation model processing tasks and a large amount of simulation data to be processed will become a great burden on the CAE team.
First, how to standardize the simulation process; second, how to combine software tools to solidify the corresponding process; finally, how to automate the simulation process as much as possible. The above three points have become problems that the CAE industry must solve if it wants to grow and develop.
In Isight, we can create a simulation process template through the organic combination of application process components and application components, realize the call and information interaction with third-party software through the original application components and secondary development, and create through the rich development interface of Isight and develop simulation templates and custom modules.
1.3 Multidisciplinary and multi-field interaction
CAE simulation analysis method can be applied in many fields and specialties, such as structure, fluid, heat transfer, electromagnetic and so on. Solving multidisciplinary problems through simulation analysis involves physical mechanisms and professional theories in different fields, and also uses different types of analysis and calculation software from various industries.
The focus of the CAE industry on simulation analysis objects has gradually shifted from the simulation of a single type of simple physical process in a single discipline to the simulation of a multi-disciplinary complex physical process across domains.
In order to achieve multidisciplinary co-simulation optimization, it is often necessary to connect different software in series under the same simulation platform, and then combine corresponding optimization algorithm tools to finally realize the establishment of the optimization process.
Isight provides interfaces for a large number of third-party software in the form of application components, and can easily connect various commonly used software in series in Isight's optimization or experimental design processes, so as to realize the data flow transfer between each software and complete multi-disciplinary and multi-disciplinary Domain co-simulation and optimization process.
The tool modules in Isight software are mainly divided into two categories: process components and application components. The different functional components and modules of Isight will be introduced below.
2. Isight process components
The main function of the process component in Isight software is to define different control processes such as optimization or design of experiments. As shown in the figure below, the main process components of Isight are: optimization method (Optimization), design of experiment (DOE), approximate fitting (Approximation), robust design (including Monte Carlo method, Taguchi robust design, 6S robust design ).
2.1 Optimization method
The Isight optimization component integrates a large number of numerical optimization algorithms, which can be generally divided into three categories from the theoretical aspect: gradient optimization algorithm, direct search method and global optimization algorithm. The Isight optimization component supports multiple input variables (design variables), multiple constraints and multiple objective functions. In particular, Isight not only provides an optimization algorithm for a single objective function, but also supports a real optimization algorithm for multiple objective functions. Theoretically, the optimization module of Isight supports infinite input design variables as input and infinite objective function as output.
2.1.1 Gradient optimization algorithm
Usually, after we abstract engineering problems into nonlinear, continuously derivable mathematical problems, the gradient optimization algorithm is an efficient method to solve such problems. The gradient optimization algorithms integrated in Isight include: MMFD Modified Method of Feasible Direction, LSGRD Large Scale Generalized Reduced Gradient, NLPQL Sequential Quadratic Programming, MOST multi-kinetic Optimization system technology (Multifunction Optimization System Tool), MISQP mixed integer sequence quadratic programming (Mixed-Interger Sequential Quadratic Programming).
In general, the optimization efficiency of the gradient algorithm is high, but the objective function is required to be derivable, and it is easy to fall into a local optimal solution. When we know enough about the optimization space and further restrict the value range of the design variables, the optimal solution can be obtained as quickly as possible through the gradient algorithm.
2.1.2 Direct search method
The direct search method does not need to calculate the gradient of the function, but only needs to judge and adjust the search direction and step size through the value of a certain function expression on the design point. When the objective function in the optimization problem is complex or has no direct function expression, the optimal solution can be obtained by direct search method.
The Isight optimization module integrates the following direct search methods: Hooke-Jeeves Direct Search Method (Hooke-Jeeves Direct Search Method), Downhill Simplex method (Downhill Simplex).
The direct search method does not need the derivability of the objective function, and the search step size is larger than that of the gradient method, so the direct search method can obtain the information of a larger range of design space with less restrictions. Similarly, the direct search method is also easy to fall into a local optimal solution, and cannot be optimized by parallel methods.
2.1.3 Global optimization algorithm
The engineering problems we encounter are often complex. The objective function in the design space may be multimodal, nonlinear, discontinuous, and non-differentiable; the design variables and constraint functions may also be linear, nonlinear, continuous, and discrete. When the optimization problem is very complex, there is no derivative and gradient information available, and the problem has the possibility of multi-peak, neither the gradient algorithm nor the direct method can obtain the global optimal solution. At this time, the global optimization algorithm should be used to solve the problem.
The Isight optimization module integrates the following global optimization algorithms: 1. Multi-Island Genetic Algorithm MIGA (Multi-Island Genetic Algorithm); 2. Adaptive Simulated Annealing ASA (Adaptive Simulated Annealing); 3. Particle Swarm Optimization PSO (Particle Swarm Optimization ); 4. Evol (Evolutionary Optimization); 5. Automatic optimization expert algorithm Pointer (Pointer Automatic Optimizer).
The global optimization algorithm has strong adaptability and can be used for various optimization problems. It only evaluates the design points without calculating the gradient. The global optimization algorithm can jump out of the peak-valley area (local optimal solution) of the design space when searching, so the global optimal solution can be obtained finally. The number of iterations required by the global optimization algorithm is often very large, so the optimization rate is low and the calculation cost is very high.
2.1.4 Multi-objective optimization algorithm
Most of the practical engineering problems we encounter are multi-objective problems, that is, to optimize multiple sub-objectives (objective functions) at the same time, and these objective functions are often not monotonically consistent and conflict with each other.
Generally, multi-objective optimization methods can be divided into two categories: 1. Normalization method (weighting method), that is, by weighting and summing multiple objective functions, a new single objective function is created, and then the single-objective optimization method is applied. optimize this objective function;
2. Non-normalization method, that is, the real optimization of multi-objective functions without weighting
The single-objective optimization algorithm in Isight supports weighted summation of multi-objective functions, so for simple multi-objective optimization problems, and the multi-objective functions are monotonously consistent, you can use Section 2.1.1-2.1.3 A variety of different algorithms are introduced for normalized multi-objective optimization.
For non-normalization methods, Isight provides the following algorithms: NSGA-II (Non-Dominated Sorting Genetic Algorithm), Neighborhood Cultivation Genetic Algorithm (Neighborhood Cultivation Genetic Algorithm), Archive Micro Genetic algorithm AMGA (Archive-Based Micro Genetic Algorithm), global multi-objective gradient exploration algorithm PE (Hybrid Multi-Gradient Pareto Exploration).
The non-normalization method in Isight adopts the concept of Pareto optimal solution set, which can directly deal with multiple objective functions, so that the frontier of the optimized solution set can be as close as possible to and evenly cover the Pareto frontier, and it supports solving complex Pareto frontiers (concave part).
2.2 Experimental design
Isight provides us with Design of Experiments (DOE) tools to facilitate reasonable and effective acquisition of data information, which is an important statistical method in product development and process optimization. Through the Isight experimental design module, we can achieve the following effects: obtain the overall information of the design space; analyze the parameter relationship between input design variables and output responses; identify key factors (design variables); construct empirical formulas and approximate models, etc.
By applying the tools provided by the Isight experimental design module, in the experimental planning stage, we can freely define the experimental design factors and their types and levels, choose different experimental design methods, specify the interaction of interest, automatically generate the experimental design matrix, set Analysis of the response trend; in the result processing stage, we can perform numerical analysis on the DOE results with the assistance of result analysis tools, and draw corresponding conclusions. We can get test data tables, scatter diagrams, ANOVA analysis tables, and Pareto diagrams , main effects plots, interaction effects plots, and correlation plots, etc.
Isight integrates a variety of DOE method algorithms, and provides a secondary development interface to facilitate user-defined DOE methods. The integrated experimental design methods include: parameter study, full factorial design, fractional factorial, orthogonal arrays, central composite design , Box-Behnken method, Latin hypercube design, optimal latin hypercube design, custom data file (data file).
After applying the DOE method, Isight can provide rich results analysis data and graphs. Isight can establish a multiple quadratic regression model through sample points, and give the coefficient value of the regression model expression through the coefficient table. Isight can give a Pareto diagram based on the experimental design results, reflecting the influence and contribution of each factor on each response in the actual space, and it is given in the form of a percentage chart, so that users can clearly understand the factor-response relationship at a glance. Isight provides a variance analysis tool, which is convenient for users to judge whether the error of the fitting result of the experimental design meets the requirements. Isight can give the main effect diagram and the interaction effect diagram, which is convenient for users to analyze the change of the response value when the level of a single factor is changed, and the change of other factors is averaged. Similarly, the interaction and interaction between factors and factors and factors and responses can be learned through the interaction effect diagram. When Isight is doing fitting error analysis, it will also give a correlation chart to show the correlation coefficient r of all input parameters (factors) to output parameters (response).
2.3 Approximate fit
Approximate fitting is to establish a mathematical expression relationship between input variables and output variables through approximate fitting. In the approximate fitting process in Isight, we can use different methods to collect sample data. The sample points can come from the experimental design matrix, random points, real test points, and empirical databases; we can choose different approximate models; we Approximate fit models can be validated with error analysis tools.
Once the approximate fitting model is established to replace the actual simulation or test model, and then optimize based on the approximate fitting model, it is no longer necessary to call the simulation software for repeated calculations, saving time and improving optimization efficiency. And because the approximate fitting model is smoother than the original data sampling model, the numerical noise is reduced, and the optimization solution process is easier to converge.
Isight provides the following approximate model methods: 1. Response surface model RSM (Response surface); 2. Radial basis/elliptic basis neural network model RBF/EBF (RBF/EBF Nueral Network); 3. Orthogonal polynomial model Orthogonal (Chebyshev /Orthogonal Polynomial); 4. Kriging model.
In the above approximate model method, the response surface model is realized by polynomial fitting, which is simple to calculate and has good robustness, and has a wide range of applications, but it cannot guarantee that the response surface passes through all sample points, and the approximate results are prone to errors for highly complex problems. The neural network model has strong approximation, which can ensure that the response surface passes through all sample points and has strong fault tolerance. Even if the samples contain non-smooth noise, the approximation result will not be affected. However, it takes a long time to establish the approximation model. When there are many input variables (many factors), the orthogonal polynomial model can be used instead of the response surface model to speed up the establishment of the approximate model. The Kriging method, also known as the spatial local interpolation method, is often used when the design space has spatial correlation. It originated from and is mainly used in geostatistics.
After Isight completes the approximate fitting, it will automatically evaluate the error of the approximate fitting model, and we can easily determine the availability of the approximate model through the automatic evaluation results.
2.4 Random sampling analysis, robust design and quality design
There are three modules related to stochastic analysis in Isight: Monte Carlo Simulation, Taguchi Robust Design and 6 Sigma Quality Design DFSS (Design For Six Sigma).
Among them, the function of the Monte Carlo simulation component is: the system studies the random probability distribution of output variables under the condition that a group of variables distributed according to random probability are used as input parameters. It can also be used to analyze the influence factors of different random input variables on the output response, as well as analyze the failure probability and reliability of design point accessories. For the two key factors of Monte Carlo simulation, probability distribution function and sampling rules, Isight provides rich support. Isight provides 7 commonly used probability distribution functions: normal distribution, lognormal distribution, Weibull distribution, Gumbel distribution, exponential distribution, uniform distribution and triangular distribution. The Isight Monte Carlo simulation component provides two sampling techniques: simple random sampling and descriptive sampling.
Isight's Taguchi robust design component provides automated tools for the second and third stages of the three major stages of system design, parameter design, and tolerance design in Taguchi's robust design method. By setting the design parameters, creating an orthogonal experimental design matrix table, and taking the signal-to-noise ratio (SNR) as the analysis index, the goal of reducing the random difference of the target (reducing the influence of the noise factor on the target function) and enhancing the robustness of the product is achieved. Users can set signal factors, control factors, noise factors and other factors in Isight, generate Taguchi method orthogonal table, and order the program to execute the test plan to obtain the test results. Users can observe the signal-to-noise ratio SNR, sensitivity β and factor effect table output by Isight to analyze and judge the robustness design results.
Isight provides a complete 6 Sigma analysis and optimization algorithm framework, which can significantly improve the efficiency and effectiveness of enterprises implementing 6 Sigma quality design. Isight's DFSS component includes two modules: 6 Sigma analysis module and 6 Sigma optimization module. The main function of the 6 Sigma analysis module is to apply a random method to evaluate the quality of the design scheme. Isight supports three different calculation methods: based on reliability analysis (Reliability Analysis), based on Monte Carlo sampling (MCS, Monte Carlo Sampling) and based on experiments Design (DOE, Design of Experiments). The main function of the 6 Sigma optimization module is to search for the area with the least fluctuation of random factors in the design space, that is, the area where the uncertain factors introduced by random design variables have the least impact on the output response, which is the subsequent step of the 6 Sigma analysis.
3. Isight application components
For third-party applications on the market, Isight provides a large number of interface modules of such programs, which are integrated in the Isight platform in the form of Isight application components. By applying these components, users can organically combine and apply Isight process components, Isight embedded application components and call third-party applications for simulation process construction and optimization tasks.
Some commonly used application component libraries in Isight are shown in the figure below:
It can be seen that the Isight application component library includes the interfaces of mainstream CAD and CAE software, and users can complete the calling of these software through simple settings.
It is important to note that Isight also provides a universal interface component called Simcode. Through the Simcode component, users can call any third-party software (only this third-party software can be run through the OS Command command line). The Simcode component consists of three modules: the DataExchanger module for rewriting program input files, the OS Command module for executing application programs, and the DataExchanger module for reading program output files.
Theoretically, through the secondary development of Simcode components, Isight custom components and the development of Isight simulation optimization process templates, integration with any software and customization of any simulation optimization process can be realized.
4. Summary
This article briefly introduces the main functions of the multi-parameter and multi-disciplinary optimization software Isight under the Dassault Systèmes SIMULIA platform, and introduces two types of component libraries in Isight respectively. The process components are: optimization algorithm components, experimental design methods Components, Approximate Fitting Components and Random Algorithms, Robust Design, Quality Design Components, and the Isight Application Component Library are introduced. We can see that Isight has two advantages and features: 1. Powerful and perfect support for optimization algorithms and experimental design methods; 2. Support for any third-party software integration. Through Isight software, users can complete the template integration of any simulation process, automate the simulation process, and improve the efficiency of the simulation process. In combination with the optimization algorithm and experimental design method provided by Isight, the exploration and optimization of any parametric physical problems can be achieved.
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