外文翻譯---遺傳算法在非線性模型中的應(yīng)用

1、<p><b>　　英 文 翻 譯</b></p><p>　　2011 屆 電氣工程及其自動化 專業(yè) 0706073 班級</p><p>　　題 目 遺傳算法在非線性模型中的應(yīng)用 </p><p>　　姓 名 學(xué)號 070607313

2、 </p><p><b>　　英語原文：</b></p><p>　　Application of Genetic Programming to Nonlinear Modeling</p><p>　　Introduction</p><p>　　Identification of nonlinear mode

3、ls which are based in part at least on the underlying physics of the real system presents many problems since both the structure and parameters of the model may need to be determined. Many methods exist for the estimatio

4、n 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 experimental investigation is adopted to choos

5、e between a number of candid</p><p>　　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 e

6、lements from 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 object

7、ive function involving an appropriate measure of the level of agreement between the model and system response. </p><p>　　Application</p><p>　　Genetic programming is an established technique whic

8、h 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, the a

9、pplication 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 dis

10、cussed i</p><p>　　The model structure evolves as the GP algorithm minimizes some objective function involving an appropriate measure of the level of agreement between the model and system responses. One exam

11、ples is </p><p>　　(1) </p><p>　　Where is the error between model output and experimental data for each of N data points. The GP algorithm constructs and reconstructs model structures

12、from the function library. Simplex and simulated annealing method and the fitness 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 ev

13、entually converges to a model description of the system.</p><p>　　The Genetic programming algorithm</p><p>　　For this research, a steady-state Genetic-programming algorithm was used. At each gen

14、eration, 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

15、of the population i.e. the crossover rate is 100℅. The crossover algorithm used was a subtree crossover with a limit on the depth of the resulting tree.</p><p>　　Genetic programming parameters such as mutati

16、on 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 generally require larger population sizes. Mutation rate

17、did not appear to have a significant effect for the systems investigated during this research. Typically, a value of about 2℅ was chosen.</p><p>　　The function library varied according to application rate an

18、d what type of nonlinearity might be expected in 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 phen

19、omenon would only be selected by the Genetic Programming algorithm if that nonlinearity actually existed in the dynamic system.</p><p>　　This allows the system to be tested for specific nonlinearities.</p

20、><p>　　Programming model structure identification</p><p>　　Each member of the Genetic Programming population represents a candidate model for the system. It is necessary to evaluate each model and

21、assign to it some fitness value. Each candidate is integrated 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

22、 that model. A sum of squared error function (Eq.(1)) is used in all the work described in this paper, although many other fitness functions c</p><p>　　The simulation routine must be robust. Inevitably, some

23、 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 syst

24、ems are unstable.</p><p>　　Parameter estimation</p><p>　　Many of the nodes of the GP trees contain numerical parameters. These could be the coefficients of the transfer functions, a gain value o

25、r in the case of a time delay, the delay itself. It is necessary to identify the numerical parameters of each nonlinear model before evaluating its fitness. The models are randomly generated and can therefore contain lin

26、early dependent parameters and parameters which have no effect on the output. Because of this, gradient based methods cannot be used. Genetic P</p><p>　　One such combination is simulated annealing with Nelde

27、r-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 annealing adds a random componen

28、t and the temperature scheduling to the simplex algorithm thus improving the robustness of the method .</p><p>　　This has been found to be a robust and reasonably efficient numerical optimization algorithm.

29、The parameter estimation phase can also be used to identify other numerical parameters in part of the model where the structure is known but where there are uncertainties about parameter values.</p><p>　　Rep

30、resentation of a GP candidate model</p><p>　　Nonlinear time domain continuous dynamic models can take a number of different forms. Two common representations involve sets of differential equations or block d

31、iagrams. 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

32、and equation based representations are considered in this paper along with a third hybrid representation incorporating</p><p>　　Choice of experimental data set——experimental design</p><p>　　The

33、identification of nonlinear systems presents particular problems regarding experimental design. The system must be excited across the frequency range of interest as with a linear system, but it must also cover the range

34、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 of the system state space.&

35、lt;/p><p>　　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

36、 quantity of data. A recommendation on how to select efficient step and PRBS signals to cover the entire frequency rage of interest may be found in Godfrey and Ljung’s texts.</p><p>　　Model validation</p&

37、gt;<p>　　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 techniques for vali

38、dation 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 refin

39、e the Genetic Programming algorithm as part of an iterative model developmen</p><p>　　Selected from “Control Engineering Practice, Elsevier Science Ltd. ,1998”</p><p><b>　　中文翻譯：</b>

40、</p><p>　　遺傳算法在非線性模型中的應(yīng)用</p><p><b>　　導(dǎo)言：</b></p><p>　　非線性模型的辨識，至少是部分基于真實(shí)系統(tǒng)的基層物理學(xué)，自從可能需要同時(shí)決定模型的結(jié)構(gòu)和參數(shù)以來，就出現(xiàn)了很多問題。盡管從測量的響應(yīng)數(shù)據(jù)來估計(jì)模型參數(shù)有很多方法，但是結(jié)構(gòu)的辨識卻更為棘手。選擇模型通常是通過專家知識和實(shí)驗(yàn)研究結(jié)合的試

41、驗(yàn)和誤差逼近法從大量的候選模型中去選擇的?？赡艿哪Ｐ徒Y(jié)構(gòu)是從系統(tǒng)的工程知識演繹出來的，而這些模型的參數(shù)是從現(xiàn)有的實(shí)驗(yàn)數(shù)據(jù)得來的。這樣的方法是如此耗時(shí)卻未達(dá)到最佳標(biāo)準(zhǔn)，可能只有這個(gè)過程的自動控制才能更快地從更大范圍的可能模型結(jié)構(gòu)中去研究。</p><p>　　遺傳算法（GP）是一種最優(yōu)化的方法，它可以通過從數(shù)據(jù)庫自動選擇模型結(jié)構(gòu)元件用來使動態(tài)系統(tǒng)的非線性結(jié)構(gòu)及元件之間的結(jié)合最優(yōu)化，然后形成一個(gè)完善的數(shù)學(xué)模型。遺傳算

42、法是通過效仿自然界的進(jìn)化去產(chǎn)生一個(gè)使一些目標(biāo)函數(shù)最大化（或最小化）的模型結(jié)構(gòu)，這些目標(biāo)函數(shù)包括模型和系統(tǒng)響應(yīng)之間的協(xié)調(diào)水平的適當(dāng)測量。一些模型結(jié)構(gòu)通過很多代向著一種解決方案而發(fā)展,這種方案是利用可靠的進(jìn)化操作者和“適者生存”的選擇規(guī)則進(jìn)行。這些模型的參數(shù)可能通過被分離和更多完全的辨識過程的傳統(tǒng)狀態(tài)而估計(jì)出來。</p><p><b>　　應(yīng)用：</b></p><p>

43、;　　遺傳算法是一種早已投入使用的技術(shù)，這種技術(shù)已經(jīng)在一些包括信號處理運(yùn)算規(guī)則和化學(xué)加工辨識在內(nèi)的非線性建模任務(wù)中得到應(yīng)用。在連續(xù)時(shí)間系統(tǒng)模型的辨識中，瑪倫巴赫、貝特哈慈和格雷研究了應(yīng)用方框圖導(dǎo)向仿真以達(dá)到遺傳算法最優(yōu)化問題，另外關(guān)于遺傳算法在非線性系統(tǒng)辨識中的應(yīng)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(yīng)用在從實(shí)驗(yàn)數(shù)據(jù)得來的模型結(jié)構(gòu)的辨識中，其中被研究的系統(tǒng)是用來代表非線性連續(xù)時(shí)域動態(tài)模型的。</p>

44、<p>　　這些模型結(jié)構(gòu)逐漸發(fā)展成為遺傳算法運(yùn)算規(guī)則，使得包括模型和系統(tǒng)響應(yīng)之間的協(xié)調(diào)水平的適當(dāng)測量在內(nèi)的目標(biāo)函數(shù)最小化。舉例說明：</p><p><b>　?。?）</b></p><p>　　在此式子中，是指N次數(shù)據(jù)點(diǎn)中每一次模型輸出和實(shí)驗(yàn)數(shù)據(jù)之間的誤差。遺傳算法運(yùn)算規(guī)則是在函數(shù)庫的基礎(chǔ)上實(shí)現(xiàn)構(gòu)造和重建的，那種模型的單一和模仿的及恰當(dāng)?shù)耐嘶鸱椒ㄊ怯脕砉?/p>

45、計(jì)一個(gè)合適的函數(shù)如同方程（1）所示。通常遺傳算法是在不斷的完善，直到這個(gè)遺傳算法最后匯聚到這個(gè)系統(tǒng)的模型描述。</p><p><b>　　遺傳算法運(yùn)算規(guī)則</b></p><p>　　在這個(gè)研究中,應(yīng)用了一個(gè)比較穩(wěn)定的遺傳算法運(yùn)算規(guī)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(chǎn)生的代替了現(xiàn)有庫中的成員。作用交叉的數(shù)量是和庫的總類相等的，也

46、就是說交叉率是百分之百。交叉運(yùn)算法則是一種限定了作為結(jié)果的樹的深度的子樹交叉法。</p><p>　　遺傳算法參數(shù)比如轉(zhuǎn)換率和群體大小要依據(jù)應(yīng)用而改變。更難的問題在于期望的模型結(jié)構(gòu)是聯(lián)合體或者數(shù)據(jù)是聒噪的，這時(shí)通常需要更大的群體大小。在這個(gè)研究中轉(zhuǎn)換率不會出現(xiàn)對系統(tǒng)調(diào)查很明顯的影響。通常只有2℅的受到影響。</p><p>　　函數(shù)庫根據(jù)應(yīng)用率和可能在這個(gè)系統(tǒng)辨識中期望的非線性模型的類型而

47、改變。處理線性系統(tǒng)的核心方法經(jīng)常是非常有用的。結(jié)果發(fā)現(xiàn)，具體的非線性系統(tǒng)比如查表，如果非線性存在于動態(tài)系統(tǒng)中，那么其中所代表的物理現(xiàn)象只有被遺傳算法運(yùn)算法則所選定。</p><p>　　這將允許系統(tǒng)，以測試具體的非線性系統(tǒng)。</p><p><b>　　程序模型結(jié)構(gòu)辨識</b></p><p>　　遺傳算法的庫中的每個(gè)成員代表這個(gè)系統(tǒng)的候選人模

48、型。評估每個(gè)模型并給定它一些合適的價(jià)值是必要的。每名候選人是綜合采用數(shù)值積分例行制作時(shí)間響應(yīng)。這個(gè)仿真時(shí)間響應(yīng)，是比較實(shí)驗(yàn)數(shù)據(jù)為這個(gè)模型以提供一個(gè)合適的價(jià)值。在這個(gè)論文中平方誤差函數(shù)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(shù)來描述。</p><p>　　仿真例子必須鮮明有力。無可避免地，有些候選模式會不穩(wěn)定，因此，仿真程序必須防止溢出的錯(cuò)誤。此外,如果GP算法能正常工作，即使這些系統(tǒng)是

49、不穩(wěn)定的，所有系統(tǒng)也必須返回一個(gè)合適的價(jià)值。</p><p><b>　　參數(shù)估計(jì)</b></p><p>　　許多遺傳算法樹的節(jié)點(diǎn)包含有數(shù)值參數(shù)。這些傳遞函數(shù)的系數(shù)、增益值或是在時(shí)間延遲的情況下，將會使自身延遲。在評估它的適當(dāng)?shù)膬r(jià)值前，有必要查明每一個(gè)非線性模型的數(shù)值參數(shù)。模型是隨機(jī)產(chǎn)生的，因此，可以線性地包含相關(guān)參數(shù)和參數(shù)，并不會影響產(chǎn)量。正因?yàn)槿绱?，基于梯度的?/p>

50、法也就不能使用了。雖然遺傳算法可以用于識別數(shù)值參數(shù)，但比起其他方法它的效率較低。而選定的做法是Nelder-Simplex和模擬退火方法的聯(lián)合，模擬退火的最優(yōu)化方法是類似于金屬冷卻的過程。作為金屬冷卻過程，原子組織起來形成一個(gè)有序的最低能源結(jié)構(gòu)，而數(shù)額振動或運(yùn)動中的原子是依賴于溫度的。隨著溫度的降低，運(yùn)動雖然是任意的，成為較少的振幅，并且只要溫度足夠慢地緩慢減少，原子就能使自己向最低的能源結(jié)構(gòu)運(yùn)動。在模擬退火過程中，參數(shù)估計(jì)是從一些隨機(jī)

51、值中開始的，并讓他們改變他們的價(jià)值，這個(gè)搜索空間是由一個(gè)金額于數(shù)量界定為系統(tǒng)的“溫度”。如果一個(gè)參數(shù)變化，全面提升性能，它是能被接受的，如果它降低了性能，也是有一定概率的被接受的。溫度下降根據(jù)一些預(yù)定的“冷卻”附表，參數(shù)值也應(yīng)隨著溫度的降低收斂到一些解決方法。當(dāng)其他的數(shù)字優(yōu)化技術(shù)結(jié)合起來時(shí)，模擬退火方</p><p>　　這樣一個(gè)模擬退火技術(shù)和Nelder-Simplex技術(shù)的組合是（n+1）的空間形狀，其中n是

52、參數(shù)的數(shù)量。這個(gè)簡單的探討搜索空間慢慢改變其形狀靠近了最佳的解決方案。模擬退火以單純的算法增加了隨機(jī)性成分和溫度調(diào)度，提高了方法的可靠性。</p><p>　　這已經(jīng)被發(fā)現(xiàn)是一個(gè)穩(wěn)健而合理的有效率的數(shù)值優(yōu)化算法，參數(shù)估計(jì)階段可以被用來確定模型的其他部分的數(shù)值參數(shù)。該模式的結(jié)構(gòu)是眾所周知的，但有不確定性參數(shù)值。</p><p>　　遺傳算法候選模型的代表性</p><p&

53、gt;　　非線性連續(xù)時(shí)域動態(tài)模型可以采取一些不同的形式。微分方程和方框圖是兩種普通代表，這兩種形式的模型是眾所周知的，并且是比較容易模擬的，對于仿真、可視化和在遺傳算法運(yùn)算規(guī)則的施行各有其優(yōu)缺點(diǎn)。方框圖和基于表示法的方程在本文中被考慮隨著第三種混合表示法納入微分和差分算子成為一個(gè)基于代表性的方程式。</p><p>　　實(shí)驗(yàn)數(shù)據(jù)集的選擇——實(shí)驗(yàn)設(shè)計(jì)</p><p>　　非線性系統(tǒng)辨識提出了

54、關(guān)于實(shí)驗(yàn)設(shè)計(jì)的特殊問題。該系統(tǒng)必須對于線性系統(tǒng)在整個(gè)頻率范圍內(nèi)被激勵(lì)，但是它也一定要涵蓋系統(tǒng)中的任何非線性范圍。這可能意味著，輸入形式充分的多樣化刺激著系統(tǒng)的不同模態(tài)并且數(shù)據(jù)覆蓋了系統(tǒng)狀態(tài)空間的運(yùn)作范圍。</p><p>　　識別一個(gè)準(zhǔn)確的模型需要打的訓(xùn)練數(shù)據(jù)集。然而仿真時(shí)間將會和數(shù)據(jù)點(diǎn)的數(shù)量成正比，因而最優(yōu)時(shí)間必須兼顧數(shù)據(jù)的數(shù)量。一項(xiàng)建議，就如何選擇有效的步驟和 PRBS信號以覆蓋整個(gè)頻率范圍，這個(gè)方法可能在高

55、德費(fèi)和劉佳的論文中有所體現(xiàn)。</p><p><b>　　模型驗(yàn)證</b></p><p>　　任何建模程序的一個(gè)重要組成部分是模型驗(yàn)證。新的模型結(jié)構(gòu)必須同不同的數(shù)據(jù)集予以審定，從而用于優(yōu)化過程。有許多非線性模型驗(yàn)證的技術(shù)，其中最簡單的就是模擬匹配模型的時(shí)間響應(yīng)和從實(shí)際系統(tǒng)中來的現(xiàn)有響應(yīng)數(shù)據(jù)相比較的技術(shù)。該模型驗(yàn)證的結(jié)果可以用來改進(jìn)作為反復(fù)的模型發(fā)展過程的一部分的遺傳