1、鄭州航空工業管理學院英 文 翻 譯 2011 屆 電氣工程及其自動化 專業 0706073 班級題 目 遺傳算法在非線性模型中的應用 姓 名 學號 指導教師 職稱 副教授 二一 一 年 三 月 三十 日英語原文：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”中文翻譯：遺傳算法在非線性模型中的應用導言：非線性模型的辨識，至少是部分基于真實系統的基層物理學，自從可能需要同時決定模型的結構和參數以來，就出現了很多問題。盡管從測量的響應數據來估計模型參數有很多方法，但是結構的辨識卻更為棘手。選擇模型通常是通過專家知識和實驗研究結合的試驗和誤差逼近法從大量的候選模型中去選擇的。可能的模型結構是從系統的工程知識演繹出來的，而這些模型的參數是從現有的實驗數據得來的。這樣的

35、方法是如此耗時卻未達到最佳標準，可能只有這個過程的自動控制才能更快地從更大范圍的可能模型結構中去研究。遺傳算法（gp）是一種最優化的方法，它可以通過從數據庫自動選擇模型結構元件用來使動態系統的非線性結構及元件之間的結合最優化，然后形成一個完善的數學模型。遺傳算法是通過效仿自然界的進化去產生一個使一些目標函數最大化（或最小化）的模型結構，這些目標函數包括模型和系統響應之間的協調水平的適當測量。一些模型結構通過很多代向著一種解決方案而發展,這種方案是利用可靠的進化操作者和“適者生存”的選擇規則進行。這些模型的參數可能通過被分離和更多完全的辨識過程的傳統狀態而估計出來。應用： 遺傳算法是一種早已投入

36、使用的技術，這種技術已經在一些包括信號處理運算規則和化學加工辨識在內的非線性建模任務中得到應用。在連續時間系統模型的辨識中，瑪倫巴赫、貝特哈慈和格雷研究了應用方框圖導向仿真以達到遺傳算法最優化問題，另外關于遺傳算法在非線性系統辨識中的應用問題在格雷的另一片論文中得以討論。在這篇文章中，遺傳算法是應用在從實驗數據得來的模型結構的辨識中，其中被研究的系統是用來代表非線性連續時域動態模型的。這些模型結構逐漸發展成為遺傳算法運算規則，使得包括模型和系統響應之間的協調水平的適當測量在內的目標函數最小化。舉例說明： （1）在此式子中，是指n次數據點中每一次模型輸出和實驗數據之間的誤差。遺傳算法運算規則是在

37、函數庫的基礎上實現構造和重建的，那種模型的單一和模仿的及恰當的退火方法是用來估計一個合適的函數如同方程（1）所示。通常遺傳算法是在不斷的完善，直到這個遺傳算法最后匯聚到這個系統的模型描述。 遺傳算法運算規則在這個研究中,應用了一個比較穩定的遺傳算法運算規則。對于每一代，父母代都是從庫里挑選出來的，下一代則是由他們的作用交叉而產生的代替了現有庫中的成員。作用交叉的數量是和庫的總類相等的，也就是說交叉率是百分之百。交叉運算法則是一種限定了作為結果的樹的深度的子樹交叉法。遺傳算法參數比如轉換率和群體大小要依據應用而改變。更難的問題在于期望的模型結構是聯合體或者數據是聒噪的，這時通常需要更大的群體大小

38、。在這個研究中轉換率不會出現對系統調查很明顯的影響。通常只有2的受到影響。函數庫根據應用率和可能在這個系統辨識中期望的非線性模型的類型而改變。處理線性系統的核心方法經常是非常有用的。結果發現，具體的非線性系統比如查表，如果非線性存在于動態系統中，那么其中所代表的物理現象只有被遺傳算法運算法則所選定。這將允許系統，以測試具體的非線性系統。程序模型結構辨識遺傳算法的庫中的每個成員代表這個系統的候選人模型。評估每個模型并給定它一些合適的價值是必要的。每名候選人是綜合采用數值積分例行制作時間響應。這個仿真時間響應，是比較實驗數據為這個模型以提供一個合適的價值。在這個論文中平方誤差函數的和（等式（1）是用來描述所有工作的，雖然可以用很多其他的合適的函數來描述。仿真例子必須鮮明有力。無可避免地，有些候選模式會不穩定，因此，仿真程序必須防止溢出的錯誤。此外,如果