基于基因表达式编程技术的非线性系统辨识研究
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摘要
随着科学技术的发展,现代工业过程变得越来越复杂,了解复杂对象的详细行为特征也越来越困难。基于观测数据通过系统辨识方法获取的对象数学模型,是人们对系统分析及控制的基础。近几十年来系统辨识方法已成为复杂非线性系统研究的重要手段,在各工程领域都得到广泛应用,然而,由于实际对象的复杂性,现有的辨识方法还存在着难以克服的困难,还有进一步研究的必要。
基因表达式编程(GEP)技术是近几年来发展起来的全局优化搜索技术,其超强的搜索能力和极高的进化效率,使它迅速在许多领域里得到了应用。本文利用GEP技术,以模型的可解释性、简单实用性和辨识智能化为研究目标,研究了非线性模型辨识的进化方法,其主要内容可概括如下:
1.给出了利用GEP进行系统辨识的基本思想和实现框架,结合遗传算法、模拟退火算法和粒子群优化算法,提出了一种从GEP表达式中进行常量提取和常量优化的方法,进行了静态非线性系统和时间序列预测模型辨识的研究,通过实验验证了算法的稳定性和优越性。
2.分析了进化算法对动态系统进行建模的不足,提出了一种独特的动态项生成方案,引入可变终止符集概念,可以自由地生成动态系统所需的动态项。通过仿真实验验证了可变终止符集具有较高的性能。
3.根据NARMAX模型和GEP多基因染色体的特点,提出了利用GEP进行各类NARMAX模型的系统辨识方法,给出了更加有效的模型描述方式,简化了染色体到模型的映射机制。
4.提出了GEP算法进行Hammerstein模型辨识的方案,通过加入一些超越函数,扩展了Hammerstein模型非线性部分的函数形式,有效地降低了模型非线性部分的项数。
5.分析了现有系统建模中多目标方案的不足,提出了更加有效的综合精度和复杂度指标的多目标优化方案,并以多项式NARMAX模型的辨识算法为例,给出了具体的实现过程。定义了精度阈值和复杂度指标上限值,通过自调整方式,将进化种群中的有效解控制在预定义的范围内。克服了原有多目标优化算法有效解过多、容易使进化早熟的缺点,最终得到一组复杂度和精确度取得很好平衡的模型。
With the development of science and technology, modern industrial processes become more complex, and detailed understanding of complex object characteristics also becomes increasingly difficult. The object model obtained through system identification is the basis of its analysis and control. In recent decades, system identification methods have become important tools of studying complicated nonlinear systems, and are widely used in various areas of engineering. However, because of the complexity of actual objects, some difficulties still exist in the existing identification methods, and therefore further research is necessary.
Gene Expression Programming (GEP) is a global optimization search technology developed in the past few years, and has been applied in many areas because of its powerful search capabilities and high evolution efficiency. In this paper, evolutionary nonlinear identification methods based on GEP are studied, and models’interpretability, simple practicality and intelligent identification progress are targets for research. The main content can be summarized as follows.
1. The basic idea and the realizing framework of system identification using GEP is given, and the mixed GEP algorithm is also presented. Combining genetic algorithm, simulated annealing and PSO algorithm, a method of constant extraction and constant optimization from GEP expression is proposed. The mixed GEP identification algorithm for static nonlinear systems and time series prediction model is also studied. The experiment results illustrated the stability and superiority of the proposed algorithm.
2. The drawbacks of the representation of dynamic system modeling using evolutionary algorithm are analyzed, and an especial method of dynamic items generation is proposed. Through introduction of variable terminals set, the algorithm can generate freely the necessary dynamic items of dynamic system. The simulation experiments illustrated that the variable terminals set has a higher performance.
3. Based on the characteristics of NARMAX model and the multi-gene chromosome of GEP, a NARMAX model identification algorithm is proposed. The algorithm can give a more reasonable description of the model, and simplify the mapping mechanism between models and chromosomes.
4. The coding schemes about Hammerstein model using GEP is given. Adding some transcendental functions in the terminals set, the algorithm expands the function expression of the Hammerstein model’s nonlinear part, and can effectively reduce the number of the nonlinear items.
5. The deficiency of the existing multiobjective system modeling algorithm is analyzed, and a more reasonable multiobjective evolutionary algorithm is proposed, and an implementation process about polynomial NARMAX model identification is given in detail. By defining the threshold of accuracy and the upper-limit value of complexity index, this algorithm can automatically maintain the number of effective solutions of the evolution population in an effective range through an automatic adjustment, and overcome the deficiency of early convergence of the original multi-objective optimization algorithm because of the superabundant effective solutions. The factors of models’accuracy and complexity are taken into account, and the algorithm can make the final solutions achieve a trade-off between the accuracy and the complexity.
基因表达式编程(GEP)技术是近几年来发展起来的全局优化搜索技术,其超强的搜索能力和极高的进化效率,使它迅速在许多领域里得到了应用。本文利用GEP技术,以模型的可解释性、简单实用性和辨识智能化为研究目标,研究了非线性模型辨识的进化方法,其主要内容可概括如下:
1.给出了利用GEP进行系统辨识的基本思想和实现框架,结合遗传算法、模拟退火算法和粒子群优化算法,提出了一种从GEP表达式中进行常量提取和常量优化的方法,进行了静态非线性系统和时间序列预测模型辨识的研究,通过实验验证了算法的稳定性和优越性。
2.分析了进化算法对动态系统进行建模的不足,提出了一种独特的动态项生成方案,引入可变终止符集概念,可以自由地生成动态系统所需的动态项。通过仿真实验验证了可变终止符集具有较高的性能。
3.根据NARMAX模型和GEP多基因染色体的特点,提出了利用GEP进行各类NARMAX模型的系统辨识方法,给出了更加有效的模型描述方式,简化了染色体到模型的映射机制。
4.提出了GEP算法进行Hammerstein模型辨识的方案,通过加入一些超越函数,扩展了Hammerstein模型非线性部分的函数形式,有效地降低了模型非线性部分的项数。
5.分析了现有系统建模中多目标方案的不足,提出了更加有效的综合精度和复杂度指标的多目标优化方案,并以多项式NARMAX模型的辨识算法为例,给出了具体的实现过程。定义了精度阈值和复杂度指标上限值,通过自调整方式,将进化种群中的有效解控制在预定义的范围内。克服了原有多目标优化算法有效解过多、容易使进化早熟的缺点,最终得到一组复杂度和精确度取得很好平衡的模型。
With the development of science and technology, modern industrial processes become more complex, and detailed understanding of complex object characteristics also becomes increasingly difficult. The object model obtained through system identification is the basis of its analysis and control. In recent decades, system identification methods have become important tools of studying complicated nonlinear systems, and are widely used in various areas of engineering. However, because of the complexity of actual objects, some difficulties still exist in the existing identification methods, and therefore further research is necessary.
Gene Expression Programming (GEP) is a global optimization search technology developed in the past few years, and has been applied in many areas because of its powerful search capabilities and high evolution efficiency. In this paper, evolutionary nonlinear identification methods based on GEP are studied, and models’interpretability, simple practicality and intelligent identification progress are targets for research. The main content can be summarized as follows.
1. The basic idea and the realizing framework of system identification using GEP is given, and the mixed GEP algorithm is also presented. Combining genetic algorithm, simulated annealing and PSO algorithm, a method of constant extraction and constant optimization from GEP expression is proposed. The mixed GEP identification algorithm for static nonlinear systems and time series prediction model is also studied. The experiment results illustrated the stability and superiority of the proposed algorithm.
2. The drawbacks of the representation of dynamic system modeling using evolutionary algorithm are analyzed, and an especial method of dynamic items generation is proposed. Through introduction of variable terminals set, the algorithm can generate freely the necessary dynamic items of dynamic system. The simulation experiments illustrated that the variable terminals set has a higher performance.
3. Based on the characteristics of NARMAX model and the multi-gene chromosome of GEP, a NARMAX model identification algorithm is proposed. The algorithm can give a more reasonable description of the model, and simplify the mapping mechanism between models and chromosomes.
4. The coding schemes about Hammerstein model using GEP is given. Adding some transcendental functions in the terminals set, the algorithm expands the function expression of the Hammerstein model’s nonlinear part, and can effectively reduce the number of the nonlinear items.
5. The deficiency of the existing multiobjective system modeling algorithm is analyzed, and a more reasonable multiobjective evolutionary algorithm is proposed, and an implementation process about polynomial NARMAX model identification is given in detail. By defining the threshold of accuracy and the upper-limit value of complexity index, this algorithm can automatically maintain the number of effective solutions of the evolution population in an effective range through an automatic adjustment, and overcome the deficiency of early convergence of the original multi-objective optimization algorithm because of the superabundant effective solutions. The factors of models’accuracy and complexity are taken into account, and the algorithm can make the final solutions achieve a trade-off between the accuracy and the complexity.
引文
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