电气工程及其自动化毕业设计（论文）外文翻译遗传算法在非线性模型中的应用

1、郑州航空工业管理学院英 文 翻 译 2011 届 电气工程及其自动化 专业 0706073 班级题 目 遗传算法在非线性模型中的应用 姓 名 学号 指导教师 职称 副教授 二一 一 年 三 月 三十 日英语原文：application of genetic programming to nonlinear modelingintroductionidentification of nonlinear models which are based in part at least on the underlying physics of the real system presents many

2、 problems since both the structure and parameters of the model may need to be determined. many methods exist for the estimation of parameters from measures response data but structural identification is more difficult. often a trial and error approach involving a combination of expert knowledge and

3、experimental investigation is adopted to choose between a number of candidate models. possible structures are deduced from engineering knowledge of the system and the parameters of these models are estimated from available experimental data. this procedure is time consuming and sub-optimal. automati

4、on of this process would mean that a much larger range of potential model structure could be investigated more quickly.genetic programming (gp) is an optimization method which can be used to optimize the nonlinear structure of a dynamic system by automatically selecting model structure elements from

5、 a database and combining them optimally to form a complete mathematical model. genetic programming works by emulating natural evolution to generate a model structure that maximizes (or minimizes) some objective function involving an appropriate measure of the level of agreement between the model an

6、d system response. a population of model structures evolves through many generations towards a solution using certain evolutionary operators and a “survival-of-the-fittest” selection scheme. the parameters of these models may be estimated in a separate and more conventional phase of the complete ide

7、ntification process.applicationgenetic programming is an established technique which has been applied to several nonlinear modeling tasks including the development of signal processing algorithms and the identification of chemical processes. in the identification of continuous time system models, th

8、e application of a block diagram oriented simulation approach to gp optimization is discussed by marenbach, bettenhausen and gray, and the issues involved in the application of gp to nonlinear system identification are discussed in grays another paper. in this paper, genetic programming is applied t

9、o the identification of model structures from experimental data. the systems under investigation are to be represented as nonlinear time domain continuous dynamic models.the model structure evolves as the gp algorithm minimizes some objective function involving an appropriate measure of the level of

10、 agreement between the model and system responses. one examples is (1) where is the error between model output and experimental data for each of n data points. the gp algorithm constructs and reconstructs model structures from the function library. simplex and simulated annealing method and the fitn

11、ess of that model is evaluated using a fitness function such as that in eq.(1). the general fitness of the population improves until the gp eventually converges to a model description of the system.the genetic programming algorithm for this research, a steady-state genetic-programming algorithm was

12、used. at each generation, two parents are selected from the population and the offspring resulting from their crossover operation replace an existing member of the same population. the number of crossover operations is equal to the size of the population i.e. the crossover rate is 100. the crossover

13、 algorithm used was a subtree crossover with a limit on the depth of the resulting tree. genetic programming parameters such as mutation rate and population size varied according to the application. more difficult problems where the expected model structure is complex or where the data are noisy gen

14、erally require larger population sizes. mutation rate did not appear to have a significant effect for the systems investigated during this research. typically, a value of about 2 was chosen. the function library varied according to application rate and what type of nonlinearity might be expected in

15、the system being identified. a core of linear blocks was always available. it was found that specific nonlinearity such as look-up tables which represented a physical phenomenon would only be selected by the genetic programming algorithm if that nonlinearity actually existed in the dynamic system. t

16、his allows the system to be tested for specific nonlinearities.programming model structure identification each member of the genetic programming population represents a candidate model for the system. it is necessary to evaluate each model and assign to it some fitness value. each candidate is integ

17、rated using a numerical integration routine to produce a time response. this simulation time response is compared with experimental data to give a fitness value for that model. a sum of squared error function (eq.(1) is used in all the work described in this paper, although many other fitness functi

18、ons could be used. the simulation routine must be robust. inevitably, some of the candidate models will be unstable and therefore, the simulation program must protect against overflow error. also, all system must return a fitness value if the gp algorithm is to work properly even if those systems ar

19、e unstable.parameter estimation many of the nodes of the gp trees contain numerical parameters. these could be the coefficients of the transfer functions, a gain value or in the case of a time delay, the delay itself. it is necessary to identify the numerical parameters of each nonlinear model befor

20、e evaluating its fitness. the models are randomly generated and can therefore contain linearly dependent parameters and parameters which have no effect on the output. because of this, gradient based methods cannot be used. genetic programming can be used to identify numerical parameters but it is le

21、ss efficient than other methods. the approach chosen involves a combination of the nelder-simplex and simulated annealing methods. simulated annealing optimizes by a method which is analogous to the cooling process of a metal. as a metal cools, the atoms organize themselves into an ordered minimum e

22、nergy structure. the amount of vibration or movement in the atoms is dependent on temperature. as the temperature decreases, the movement, though still random, become smaller in amplitude and as long as the temperature decreases slowly enough, the atoms order themselves slowly enough, the atoms orde

23、r themselves into the minimum energy structure. in simulated annealing, the parameters start off at some random value and they are allowed to change their values within the search space by an amount related to a quantity defined as system temperature. if a parameter change improves overall fitness,

24、it is accepted, if it reduces fitness it is accepted with a certain probability. the temperature decreases according to some predetermined cooling schedule and the parameter values should converge to some solution as the temperature drops. simulated annealing has proved particularly effective when c

25、ombines with other numerical optimization techniques. one such combination is simulated annealing with nelder-simplex is an (n+1) dimensional shape where n is the number of parameters. this simples explores the search space slowly by changing its shape around the optimum solution .the simulated anne

26、aling adds a random component and the temperature scheduling to the simplex algorithm thus improving the robustness of the method . this has been found to be a robust and reasonably efficient numerical optimization algorithm.the parameter estimation phase can also be used to identify other numerical

27、 parameters in part of the model where the structure is known but where there are uncertainties about parameter values.representation of a gp candidate modelnonlinear time domain continuous dynamic models can take a number of different forms. two common representations involve sets of differential e

28、quations or block diagrams. both these forms of model are well known and relatively easy to simulate .each has advantages and disadvantages for simulation, visualization and implementation in a genetic programming algorithm. block diagram and equation based representations are considered in this pap

29、er along with a third hybrid representation incorporating integral and differential operators into an equation based representation.choice of experimental data setexperimental designthe identification of nonlinear systems presents particular problems regarding experimental design. the system must be

30、 excited across the frequency range of interest as with a linear system, but it must also cover the range of any nonlinearities in the system. this could mean ensuring that the input shape is sufficiently varied to excite different modes of the system and that the data covers the operational range o

31、f the system state space.a large training data set will be required to identify an accurate model. however the simulation time will be proportional to the number of data points, so optimization time must be balanced against quantity of data. a recommendation on how to select efficient step and prbs

32、signals to cover the entire frequency rage of interest may be found in godfrey and ljungs texts.model validation an important part of any modeling procedure is model validation. the new model structure must be validated with a different data set from that used for the optimization. there are many te

33、chniques for validation of nonlinear models, the simplest of which is analogue matching where the time response of the model is compared with available response data from the real system. the model validation results can be used to refine the genetic programming algorithm as part of an iterative mod

34、el development process.selected from “control engineering practice, elsevier science ltd. ,1998”中文翻译：遗传算法在非线性模型中的应用导言：非线性模型的辨识，至少是部分基于真实系统的基层物理学，自从可能需要同时决定模型的结构和参数以来，就出现了很多问题。尽管从测量的响应数据来估计模型参数有很多方法，但是结构的辨识却更为棘手。选择模型通常是通过专家知识和实验研究结合的试验和误差逼近法从大量的候选模型中去选择的。可能的模型结构是从系统的工程知识演绎出来的，而这些模型的参数是从现有的实验数据得来的。这样的

35、方法是如此耗时却未达到最佳标准，可能只有这个过程的自动控制才能更快地从更大范围的可能模型结构中去研究。遗传算法（gp）是一种最优化的方法，它可以通过从数据库自动选择模型结构元件用来使动态系统的非线性结构及元件之间的结合最优化，然后形成一个完善的数学模型。遗传算法是通过效仿自然界的进化去产生一个使一些目标函数最大化（或最小化）的模型结构，这些目标函数包括模型和系统响应之间的协调水平的适当测量。一些模型结构通过很多代向着一种解决方案而发展,这种方案是利用可靠的进化操作者和“适者生存”的选择规则进行。这些模型的参数可能通过被分离和更多完全的辨识过程的传统状态而估计出来。应用： 遗传算法是一种早已投入

36、使用的技术，这种技术已经在一些包括信号处理运算规则和化学加工辨识在内的非线性建模任务中得到应用。在连续时间系统模型的辨识中，玛伦巴赫、贝特哈慈和格雷研究了应用方框图导向仿真以达到遗传算法最优化问题，另外关于遗传算法在非线性系统辨识中的应用问题在格雷的另一片论文中得以讨论。在这篇文章中，遗传算法是应用在从实验数据得来的模型结构的辨识中，其中被研究的系统是用来代表非线性连续时域动态模型的。这些模型结构逐渐发展成为遗传算法运算规则，使得包括模型和系统响应之间的协调水平的适当测量在内的目标函数最小化。举例说明： （1）在此式子中，是指n次数据点中每一次模型输出和实验数据之间的误差。遗传算法运算规则是在

37、函数库的基础上实现构造和重建的，那种模型的单一和模仿的及恰当的退火方法是用来估计一个合适的函数如同方程（1）所示。通常遗传算法是在不断的完善，直到这个遗传算法最后汇聚到这个系统的模型描述。 遗传算法运算规则在这个研究中,应用了一个比较稳定的遗传算法运算规则。对于每一代，父母代都是从库里挑选出来的，下一代则是由他们的作用交叉而产生的代替了现有库中的成员。作用交叉的数量是和库的总类相等的，也就是说交叉率是百分之百。交叉运算法则是一种限定了作为结果的树的深度的子树交叉法。遗传算法参数比如转换率和群体大小要依据应用而改变。更难的问题在于期望的模型结构是联合体或者数据是聒噪的，这时通常需要更大的群体大小

38、。在这个研究中转换率不会出现对系统调查很明显的影响。通常只有2的受到影响。函数库根据应用率和可能在这个系统辨识中期望的非线性模型的类型而改变。处理线性系统的核心方法经常是非常有用的。结果发现，具体的非线性系统比如查表，如果非线性存在于动态系统中，那么其中所代表的物理现象只有被遗传算法运算法则所选定。这将允许系统，以测试具体的非线性系统。程序模型结构辨识遗传算法的库中的每个成员代表这个系统的候选人模型。评估每个模型并给定它一些合适的价值是必要的。每名候选人是综合采用数值积分例行制作时间响应。这个仿真时间响应，是比较实验数据为这个模型以提供一个合适的价值。在这个论文中平方误差函数的和（等式（1）是用来描述所有工作的，虽然可以用很多其他的合适的函数来描述。仿真例子必须鲜明有力。无可避免地，有些候选模式会不稳定，因此，仿真程序必须防止溢出的错误。此外,如果