電氣工程及其自動化畢業(yè)設(shè)計英語翻譯--遺傳算法在非線性模型中的應(yīng)用

1、<p><b>　　英語原文：</b></p><p>　　Application of Genetic Programming to Nonlinear Modeling</p><p>　　Introduction</p><p>　　Identification of nonlinear models which are bas

2、ed 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 estimation of parameters

3、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 choose between a numb

4、er 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 elements from a d

5、atabase 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 inv

6、olving 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 which has been appli

7、ed 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 application of a

8、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 i</p&g

9、t;<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 examples is </p&g

10、t;<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 from the functio

11、n 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 eventually converg

12、es 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 generation, two par

13、ents 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 populatio

14、n 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 mutation rate and popu

15、lation 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 did not appear t

16、o 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 and what type of n

17、onlinearity 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 phenomenon would onl

18、y 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><p>　

19、　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 assign to it som

20、e 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 that model. A s

21、um 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 of the candidat

22、e 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 are unstable

23、.</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 or in the case of

24、 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 linearly dependent

25、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 Nelder-simplex is an

26、(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 component and the temper

27、ature 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.The parameter es

28、timation 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>　　Representation of a

29、 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 diagrams. Both th

30、ese 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 bas

31、ed 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 identification o

32、f 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 of any nonlinear

33、ities 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.</p><p

34、>　　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 dat

35、a. 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><p>　　

36、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 validation of nonlin

37、ear 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 Pr

38、ogramming 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></p><

39、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)合的試驗(yàn)和誤差逼近法從大量的候選模型中

40、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卻未達(dá)到最佳標(biāo)準(zhǔn)，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(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，然后形成一個完善的數(shù)學(xué)模型。遺傳算法是通過效仿自然界的進(jìn)化去產(chǎn)生一

41、個使一些目標(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)而估計出來。</p><p><b>　　應(yīng)用：</b></p><p>　　遺傳算法是一種早已投入使用

42、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)時域動態(tài)模型的。</p><p>　　這些模型結(jié)

43、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>　　（1）</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怯脕砉烙嬕粋€合適的函數(shù)如同方程（1）所

44、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(tǒng)的模型描述。</p><p><b>　　遺傳算法運(yùn)算規(guī)則</b></p><p>　　在這個研究中,應(yīng)用了一個比較穩(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，也就是說交叉率是百分之百。交叉運(yùn)算

45、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，這時通常需要更大的群體大小。在這個研究中轉(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)用率和可能在這個系統(tǒng)辨識中期望的非線性模型的類型而改變。處理線性系統(tǒng)的核心方法經(jīng)常

46、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成員代表這個系統(tǒng)的候選人模型。評估每個模型并給定它一些合適

47、的價值是必要的。每名候選人是綜合采用數(shù)值積分例行制作時間響應(yīng)。這個仿真時間響應(yīng)，是比較實(shí)驗(yàn)數(shù)據(jù)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(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誤。此外,如果GP算法能正常工作，即使這些系統(tǒng)是不穩(wěn)定的，所有系統(tǒng)也必須返回一個

48、合適的價值。</p><p><b>　　參數(shù)估計</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值前，有必要查明每一個非線性模型的數(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?，基于梯度的方法也就不能使用了。雖然遺傳算法可

49、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)估計是從一些隨機(jī)值中開始的，并讓他們改變他們的價

50、值，這個搜索空間是由一個金額于數(shù)量界定為系統(tǒng)的“溫度”。如果一個參數(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，模擬退火方</p><p>　　這樣一個模擬退火技術(shù)和Nelder-Simplex技術(shù)的組合是（n+1）的空間形狀，其中n是參數(shù)的數(shù)量。這個簡單的探討搜索空

51、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)是一個穩(wěn)健而合理的有效率的數(shù)值優(yōu)化算法，參數(shù)估計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>　　非線性連續(xù)時域動態(tài)模型

52、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</p><p>　　非線性系統(tǒng)辨識提出了關(guān)于實(shí)驗(yàn)設(shè)計的特殊問題。該系統(tǒng)必

53、須對于線性系統(tǒng)在整個頻率范圍內(nèi)被激勵，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>　　識別一個準(zhǔn)確的模型需要打的訓(xùn)練數(shù)據(jù)集。然而仿真時間將會和數(shù)據(jù)點(diǎn)的數(shù)量成正比，因而最優(yōu)時間必須兼顧數(shù)據(jù)的數(shù)量。一項建議，就如何選擇有效的步驟和 PRBS信號以覆蓋整個頻率范圍，這個方法可能在高德費(fèi)和劉佳的論文中有所體現(xiàn)。&l