基于智能算法的非线性模型研究及预测控制
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摘要
近年来,随着生命科学和计算机技术的迅速发展,大规模并行处理技术的产生,以不确定性、非线性、时间不可逆性为内涵,以复杂问题为对象的“复杂性研究”新兴边缘交叉学科的出现,尤其是以粒子群算法(Particle Swarm Optimization,简称PSO)、遗传算法(Genetic Algorithm,简称GA)和神经网络(Artificial Neural Network,简称ANN)等为代表智能仿生技术的引入,具有随机搜索性能的智能优化分析方法逐渐发展起来,为具有时变特性的土木工程问题解决,提供了一种全新的研究思路和方法,并已取得了重大的科研成果。
正是基于这样一个背景,本文结合智能研究的发展成果,针对工程的复杂性、时变性特点,将变异粒子群算法(Variation PSO,简称VPSO)引入反分析研究,与具有动态反馈特性的Elman神经网络(Elman Neural Network,简称ENN)进行融合,提出了新的耦合算法“VPSO-ENN”,用于岩土工程智能分析,成功实现了大型工程问题的非线性参数辨识和变形预测控制。本文主要完成以下几个方面工作:
(1)系统地研究了标准粒子群算法(Standard PSO,简称SPSO)生物运行机理,针对SPSO算法在求解高维、多峰等复杂非线性优化问题时,易陷入局部最优解、早熟等缺陷,本文采用粒子速度随机变异策略,对SPSO算法进行改进,提出了一种具有全局快速收敛的VPSO算法。通过对5个高维复杂Benchmark测试函数的优化,结果表明VPSO算法具有搜索机理简单、算法参数调整少、无需梯度信息的特点,与SPSO相比,VPSO算法的收敛精度、收敛速度以及算法稳定性,均得到显著地提高。
(2)将VPSO算法与Elman反馈网络进行融合,提出了一种新的耦合算法“VPSO-ENN”。采用VPSO算法优化并确定ENN权值和阈值,使其学习训练不再依赖于梯度信息。通过VPSO搜寻ENN最优的一组权值和阈值,能有效找到问题的全局最优解,克服了ENN算法易于陷入局部极小和收敛速度慢的缺点,可提高网络的训练速度、非线性映射和泛化能力,实现任意非线性函数的逼近。
(3)建立了基于“VPSO-ENN”非线性参数辨识模型,采用隐性数学表达式建模方式,通过对其目标隐函数进行寻优,实现了时变系统的辨识输出值与实际输出值的高精度拟合,达到非线性参数辨识的目的。结果表明,VPSO-ENN辨识模型具有很强的非线性参数辨识能力,该方法简单易操作且识别准确率高,用以反推时变系统的未知参数是可行的,具有工程实用性。
(4)根据VPSO算法仿生优化原理和网络控制理论,采用预测智能控制的思想,建立了一个多输入多输出(MIMO)的“VPSO-ENN”预测智能控制系统。将预测系统中过去时刻输出的一阶导数和二阶导数加入到模型的输入,使预测模型VPSO-ENNPM具有动态反馈特性。通过优化含有预测信息的目标函数,系统获得预测控制律,成功地避免了递推预测模型误差迭加增大的问题,实现了时变系统预测智能控制。
(6)利用VPSO算法和Elman神经网络控制技术,采用时间窗口滚动技术,建立了一套集深基坑施工变形预测与控制于一体的“VPSO-ENN”多步预测控制系统,通过建立期望输出与超前预测输出之间的非线性隐式方程表达式,成功地避开了复杂的岩土本构关系和力学计算。采用MATIAB7.0编制程序,利用基坑有限的历史监测变形数据和最新的观测数据,成功地实现了基坑施工变形的多步预测。
工程实例分析表明,基于“VPSO-ENN”智能预测方法具有较高的预测精度、很强的泛化能力,适于对时变系统未来变化趋势的预测控制智能化,可实现大型土木工程施工过程的实时控制。
The life science and the computer technique have developed rapidly,and massively parallel processing technology(MPP) has been presented.Complexity research presented is a new interdisciplinary science,which takes the uncertainty,nonlinearity,time irreversibility as connotations and takes complex problems as objects.Especially,the simulating biology intelligent techniques have been introduced gradually,such as Particle Swarm Optimization(PSO),Genetic Algorithm(GA) and Artificial Neural Network (ANN).The algorithms have random search performance.The techniques provide a new research way in solving problems for the civil engineering of time variant characteristics. Moreover the important achievements have been obtained in the scientific research.
Based on the above background,combining development achievements of the intelligent study,Variation PSO(VPSO) is introduced into the back-analysis according to engineering complexity and time variation in this dissertation.A new algorithm is presented,VPSO combines Elman feedback network(ENN) and forms VPSO-ENN.The method is employed in the intelligent analysis of geotechnical engineering.It is successfully realized in the nonlinear parameter identification and deformation predictive control.The dissertation includes the following contents:
Firstly,the biological operation mechanism of the standard PSO(SPSO) has been systematically studied.SPSO is easy to get locked into the local optimum value and premature convergence,when the nonlinear optimization problems of the high-dimension and multi-peak are solved.The random variation strategy of particle velocity is adopted to improve SPSO in this dissertation.VPSO,which has rapid global convergence,is presented.According to optimize five Benchmark testing functions of the high-dimension and complexity,the results show that VPSO has simple search mechanism,few adjusting parameters and no gradient information.Compared with SPSO,the VPSO performance is significantly improved in convergence precision, convergence speed and computational stability.
Secondly,a new algorithm is presented by combining VPSO algorithm with the ENN.VPSO is used to optimize and determine ENN structure,which does not depend on the gradient information.Using VPSO to search a group of the optimal weights and thresholds,the global optimal solution can effectively be found.The ENN defects of the low learning convergence speed and the easily appearing local minimum has been overcome.Moreover,the method can improve network training speed,increase nonlinear mapping and generalization ability,and approach arbitrary nonlinear functions.
Thirdly,the identification model of nonlinear parameters is constructed based on the VPSO-ENN,the implicit mathematical expressions are established.Optimizing the implicit objective function,the high precision fitting is realized between expected output value of the actual system and output value of the identification model.The goal of the nonlinear parameter identification is achieved.The results show that the VPSO-ENN identification model has strong identification ability,simple operation and high identification accuracy.It is feasible to identify unknown parameters of geotechnical engineering.
Fourthly,according to the bionic optimization principle of VPSO algorithm and networked control theory,intelligent predictive control has been used to establish VPSO-ENN system,which is one of the multi-input/multi-outinput(MIMO) model.The first derivative and the second derivatives,which are of the past output values in system, are added to the input of the prediction model(PM).Then VPSO-ENN prediction model, called VPSO-ENNPM,has dynamic feedback characteristics.The control law of the prediction system can be obtained based on the optimized objective function of prediction information.The increases of iterative error of recursive prediction model can been avoided effectively.The intelligent predictive control of time-varying system is realized.
Finally,using VPSO-ENN control technology and applying time-scroll technology, a set of VPSO-ENN multi-step prediction control system has been established.The syetem integrates foundation pit deformation prediction and control together.The nonlinear implicit equations are constructed between the target output and prediction output.This approach can be avoided the complicated structure relation and mechanical calculation in geotechnical engineering successfully.The program has been compiled with MATIAB7.0.Using the limited history and the latest observation data,the multi-step prediction of foundation pit construction is successfully realized.
The results of engineering cases indicate that intelligent prediction method based on the VPSO-ENN has high prediction accuracy and strong generalization ability.It is suitable for the prediction intelligent control of future tendency.The large construction process of civil engineering can be controlled in real-time.
正是基于这样一个背景,本文结合智能研究的发展成果,针对工程的复杂性、时变性特点,将变异粒子群算法(Variation PSO,简称VPSO)引入反分析研究,与具有动态反馈特性的Elman神经网络(Elman Neural Network,简称ENN)进行融合,提出了新的耦合算法“VPSO-ENN”,用于岩土工程智能分析,成功实现了大型工程问题的非线性参数辨识和变形预测控制。本文主要完成以下几个方面工作:
(1)系统地研究了标准粒子群算法(Standard PSO,简称SPSO)生物运行机理,针对SPSO算法在求解高维、多峰等复杂非线性优化问题时,易陷入局部最优解、早熟等缺陷,本文采用粒子速度随机变异策略,对SPSO算法进行改进,提出了一种具有全局快速收敛的VPSO算法。通过对5个高维复杂Benchmark测试函数的优化,结果表明VPSO算法具有搜索机理简单、算法参数调整少、无需梯度信息的特点,与SPSO相比,VPSO算法的收敛精度、收敛速度以及算法稳定性,均得到显著地提高。
(2)将VPSO算法与Elman反馈网络进行融合,提出了一种新的耦合算法“VPSO-ENN”。采用VPSO算法优化并确定ENN权值和阈值,使其学习训练不再依赖于梯度信息。通过VPSO搜寻ENN最优的一组权值和阈值,能有效找到问题的全局最优解,克服了ENN算法易于陷入局部极小和收敛速度慢的缺点,可提高网络的训练速度、非线性映射和泛化能力,实现任意非线性函数的逼近。
(3)建立了基于“VPSO-ENN”非线性参数辨识模型,采用隐性数学表达式建模方式,通过对其目标隐函数进行寻优,实现了时变系统的辨识输出值与实际输出值的高精度拟合,达到非线性参数辨识的目的。结果表明,VPSO-ENN辨识模型具有很强的非线性参数辨识能力,该方法简单易操作且识别准确率高,用以反推时变系统的未知参数是可行的,具有工程实用性。
(4)根据VPSO算法仿生优化原理和网络控制理论,采用预测智能控制的思想,建立了一个多输入多输出(MIMO)的“VPSO-ENN”预测智能控制系统。将预测系统中过去时刻输出的一阶导数和二阶导数加入到模型的输入,使预测模型VPSO-ENNPM具有动态反馈特性。通过优化含有预测信息的目标函数,系统获得预测控制律,成功地避免了递推预测模型误差迭加增大的问题,实现了时变系统预测智能控制。
(6)利用VPSO算法和Elman神经网络控制技术,采用时间窗口滚动技术,建立了一套集深基坑施工变形预测与控制于一体的“VPSO-ENN”多步预测控制系统,通过建立期望输出与超前预测输出之间的非线性隐式方程表达式,成功地避开了复杂的岩土本构关系和力学计算。采用MATIAB7.0编制程序,利用基坑有限的历史监测变形数据和最新的观测数据,成功地实现了基坑施工变形的多步预测。
工程实例分析表明,基于“VPSO-ENN”智能预测方法具有较高的预测精度、很强的泛化能力,适于对时变系统未来变化趋势的预测控制智能化,可实现大型土木工程施工过程的实时控制。
The life science and the computer technique have developed rapidly,and massively parallel processing technology(MPP) has been presented.Complexity research presented is a new interdisciplinary science,which takes the uncertainty,nonlinearity,time irreversibility as connotations and takes complex problems as objects.Especially,the simulating biology intelligent techniques have been introduced gradually,such as Particle Swarm Optimization(PSO),Genetic Algorithm(GA) and Artificial Neural Network (ANN).The algorithms have random search performance.The techniques provide a new research way in solving problems for the civil engineering of time variant characteristics. Moreover the important achievements have been obtained in the scientific research.
Based on the above background,combining development achievements of the intelligent study,Variation PSO(VPSO) is introduced into the back-analysis according to engineering complexity and time variation in this dissertation.A new algorithm is presented,VPSO combines Elman feedback network(ENN) and forms VPSO-ENN.The method is employed in the intelligent analysis of geotechnical engineering.It is successfully realized in the nonlinear parameter identification and deformation predictive control.The dissertation includes the following contents:
Firstly,the biological operation mechanism of the standard PSO(SPSO) has been systematically studied.SPSO is easy to get locked into the local optimum value and premature convergence,when the nonlinear optimization problems of the high-dimension and multi-peak are solved.The random variation strategy of particle velocity is adopted to improve SPSO in this dissertation.VPSO,which has rapid global convergence,is presented.According to optimize five Benchmark testing functions of the high-dimension and complexity,the results show that VPSO has simple search mechanism,few adjusting parameters and no gradient information.Compared with SPSO,the VPSO performance is significantly improved in convergence precision, convergence speed and computational stability.
Secondly,a new algorithm is presented by combining VPSO algorithm with the ENN.VPSO is used to optimize and determine ENN structure,which does not depend on the gradient information.Using VPSO to search a group of the optimal weights and thresholds,the global optimal solution can effectively be found.The ENN defects of the low learning convergence speed and the easily appearing local minimum has been overcome.Moreover,the method can improve network training speed,increase nonlinear mapping and generalization ability,and approach arbitrary nonlinear functions.
Thirdly,the identification model of nonlinear parameters is constructed based on the VPSO-ENN,the implicit mathematical expressions are established.Optimizing the implicit objective function,the high precision fitting is realized between expected output value of the actual system and output value of the identification model.The goal of the nonlinear parameter identification is achieved.The results show that the VPSO-ENN identification model has strong identification ability,simple operation and high identification accuracy.It is feasible to identify unknown parameters of geotechnical engineering.
Fourthly,according to the bionic optimization principle of VPSO algorithm and networked control theory,intelligent predictive control has been used to establish VPSO-ENN system,which is one of the multi-input/multi-outinput(MIMO) model.The first derivative and the second derivatives,which are of the past output values in system, are added to the input of the prediction model(PM).Then VPSO-ENN prediction model, called VPSO-ENNPM,has dynamic feedback characteristics.The control law of the prediction system can be obtained based on the optimized objective function of prediction information.The increases of iterative error of recursive prediction model can been avoided effectively.The intelligent predictive control of time-varying system is realized.
Finally,using VPSO-ENN control technology and applying time-scroll technology, a set of VPSO-ENN multi-step prediction control system has been established.The syetem integrates foundation pit deformation prediction and control together.The nonlinear implicit equations are constructed between the target output and prediction output.This approach can be avoided the complicated structure relation and mechanical calculation in geotechnical engineering successfully.The program has been compiled with MATIAB7.0.Using the limited history and the latest observation data,the multi-step prediction of foundation pit construction is successfully realized.
The results of engineering cases indicate that intelligent prediction method based on the VPSO-ENN has high prediction accuracy and strong generalization ability.It is suitable for the prediction intelligent control of future tendency.The large construction process of civil engineering can be controlled in real-time.
引文
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