使用rbf神經(jīng)網(wǎng)絡(luò)進(jìn)行優(yōu)化冷藏庫(kù)的控制外文文獻(xiàn)翻譯

1、<p>　　使用RBF神經(jīng)網(wǎng)絡(luò)進(jìn)行優(yōu)化冷藏庫(kù)的控制</p><p>　　施正榮,成國(guó)棟,王琦鴻,徐燕和薛國(guó)信</p><p>　　213016年常州江蘇機(jī)構(gòu)Petrochemical Technology,代為辦理1999年11月26日(收到)</p><p>　　文摘:近年來,先進(jìn)控制技術(shù)最優(yōu)控制冷藏。但仍有許多缺點(diǎn)。的一個(gè)主要問題是,傳統(tǒng)方法不能實(shí)現(xiàn)

2、在線預(yù)測(cè)最優(yōu)控制制冷系統(tǒng)的簡(jiǎn)單而有效的算法。一個(gè)RBF神經(jīng)網(wǎng)絡(luò)有很強(qiáng)的非線性映射能力,一個(gè)好的插值性能,價(jià)值和更高的訓(xùn)練速度。因此本文提出了一種兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)。將測(cè)量值與預(yù)測(cè)值,兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)用于在線預(yù)測(cè)最優(yōu)控制的冷藏溫度。新方法的應(yīng)用效果顯示一個(gè)巨大的成功。</p><p>　　關(guān)鍵詞:RBF神經(jīng)網(wǎng)絡(luò)、冷藏、在線預(yù)測(cè)最優(yōu)控制。</p><p><b>　　介紹</

3、b></p><p>　　冷庫(kù)溫度的預(yù)測(cè)最優(yōu)控制找到了廣泛應(yīng)用在農(nóng)業(yè)工程,特別是冷藏的水果和蔬菜保鮮的。所有的currently-used溫度控制單元面臨如何選擇最適溫度為控制對(duì)象的問題，如何進(jìn)行冷藏庫(kù)溫度的變化，和如何實(shí)現(xiàn)最優(yōu)控制。大量的工作研究了前面的方法是基于泰勒級(jí)數(shù)理論和PID控制算法[1,5]。后來,毛皮商的轉(zhuǎn)換方法,切比雪夫的理論和一些基礎(chǔ)知識(shí)的系統(tǒng)我們得到了并且使用了更好的結(jié)論(2、3)。近年

4、來,英國(guó)石油公司將神經(jīng)網(wǎng)絡(luò)用于冷庫(kù)溫度的最優(yōu)控制。BP神經(jīng)網(wǎng)絡(luò)具有良好的非線性映射的性能,但它有太多的地方并不是那么理想,通常是其訓(xùn)練速度太慢了(2、5)。因此它不能方便地用于在線控制計(jì)算。后來也提出了一種兩階段RBF神經(jīng)網(wǎng)絡(luò)實(shí)現(xiàn)在線最優(yōu)控制的冷藏溫度。在第一階段的使用過程中確定當(dāng)前最佳制冷系統(tǒng)的溫度,和第二個(gè)階段是用于在未來時(shí)間點(diǎn)進(jìn)行確定溫度的值。此外, 他的解決方案是用于制冷系統(tǒng)的直接行動(dòng)，一個(gè)最難的問題是解決了。</p>

5、;<p>　　采用RBF神經(jīng)網(wǎng)絡(luò)分為兩個(gè)階段。第一階段是用來確定最佳值的冷藏溫度, 而第二個(gè)是用來預(yù)測(cè)溫度。一般來說,假設(shè)n 個(gè)輸入變量,…, 和m 個(gè)輸出變量,…, .則：</p><p><b>　　(1)</b></p><p><b>　　(2)</b></p><p>　　使用RBF神經(jīng)網(wǎng)絡(luò)最優(yōu)控制

6、冷藏，代表一個(gè)點(diǎn)的n維輸入空間,而代表一個(gè)點(diǎn)的m維輸出空間,假設(shè)隱藏的單位的數(shù)量是H。每個(gè)隱單元使用了兩個(gè)參數(shù),一個(gè)是標(biāo)量,另一個(gè)是矢量。假設(shè)的訓(xùn)練樣本集是。一般來說,應(yīng)該滿足。RBF神經(jīng)網(wǎng)絡(luò)是基于插值radius-based功能的性能。為了改善性能,使用下列方程計(jì)算出RBF神經(jīng)網(wǎng)絡(luò)的輸出。</p><p><b>　　(3)</b></p><p>　　在這里,分子

7、是一種傳統(tǒng)的RBF插值算法表達(dá)式,而分母不變的插值表達(dá)式（1）通過這種分母,衰減指數(shù)函數(shù)的分子是取消了極大的分母。通過這種方式,改進(jìn)的RBF神經(jīng)網(wǎng)絡(luò)具有更好的性能。</p><p>　　3、在線計(jì)算的冷藏溫度</p><p>　　選擇的目標(biāo)價(jià)值冷藏溫度,需要綜合考慮所有的因素。為了合理地使用能源,制冷過程中應(yīng)該有一個(gè)高性能系數(shù)，而和制冷量子與所需的能源的關(guān)系應(yīng)該滿足公式</p>

8、<p><b>　　(4)</b></p><p>　　研究結(jié)果表明, 隨蒸發(fā)溫度和冷凝溫度的下降而增加，而且一個(gè)更高的蒸發(fā)溫度和冷凝溫度較低有利于保持新鮮的水果和蔬菜。因此,制冷系統(tǒng)應(yīng)該運(yùn)行在更高的蒸發(fā)溫度和冷凝溫度較低的環(huán)境中。然而,蒸發(fā)溫度顯然是在冷藏條件下的溫度對(duì)象的限制。</p><p>　　為一種特殊的水果或蔬菜就進(jìn)入冷藏，它的最佳儲(chǔ)存溫度可

9、以得到正交實(shí)驗(yàn)方法。最佳儲(chǔ)存溫度隨著儲(chǔ)存時(shí)間的增加而減小。單位水果或者蔬菜的損失滿足公式</p><p><b>　　(5)</b></p><p>　　式中是由水果或蔬菜被凍傷造成的，而是由于時(shí)間關(guān)系而日益惡化造成的。當(dāng)環(huán)境溫度升高了，降低但是會(huì)升高。這兩個(gè)數(shù)據(jù)都和存儲(chǔ)時(shí)間相關(guān)。因此，</p><p><b>　　(6)</b

10、></p><p>　　在這個(gè)式子中，會(huì)隨著溫度的升高而降低，但是會(huì)升高。表示進(jìn)入存儲(chǔ)的時(shí)間，則表示表示存儲(chǔ)時(shí)間,然后我們有</p><p><b>　　(7)</b></p><p>　　對(duì)于水果或者蔬菜來說，其最佳儲(chǔ)存溫度應(yīng)該滿足以下方程</p><p><b>　　(8)</b><

11、/p><p>　　設(shè)水果或蔬菜的重力是，其存儲(chǔ)損失為，則在單位時(shí)間間隔內(nèi)總存儲(chǔ)損失為</p><p><b>　　(9)</b></p><p>　　設(shè)表示最佳儲(chǔ)存溫度。它應(yīng)該滿足</p><p><b>　　(10)</b></p><p><b>　　就是</

12、b></p><p><b>　　(11)</b></p><p>　　用上面?zhèn)鹘y(tǒng)的方法計(jì)算是比較費(fèi)時(shí)間的，因此我們使用RBF神經(jīng)網(wǎng)絡(luò)實(shí)現(xiàn)的解決方案。這種RBF神經(jīng)網(wǎng)絡(luò)的第一部分提出兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)。這種網(wǎng)絡(luò)只有一個(gè)輸出，，，并且有2n個(gè)輸入，即, 和 ,。在這里作為隱藏的單位使用，方程（11）用于產(chǎn)生足夠的訓(xùn)練樣本。</p><p>

13、　　4、冷庫(kù)溫度的在線預(yù)測(cè)</p><p>　　最優(yōu)控制的關(guān)鍵問題之一的存儲(chǔ)溫度是如何準(zhǔn)確預(yù)測(cè)溫度。因?yàn)樗麄兊聂敯粜?基于神經(jīng)網(wǎng)絡(luò)的預(yù)測(cè)方法吸引了越來越多的關(guān)注。BP神經(jīng)網(wǎng)絡(luò)是一種早期的神經(jīng)網(wǎng)絡(luò)用于這一目的。但它的訓(xùn)練時(shí)間通常是太長(zhǎng),和它有很多局部最小值點(diǎn)。因此,RBF神經(jīng)網(wǎng)絡(luò)由于其較高的訓(xùn)練速度吸引了越來越多的關(guān)注。本文采用兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)預(yù)測(cè)存儲(chǔ)溫度。在預(yù)測(cè)過程中,溫度和濕度之間的耦合關(guān)系應(yīng)該考慮。本文選擇

14、輸出變量, 在同一時(shí)間內(nèi)設(shè)置包括溫度變量和濕度變量。輸入變量的選擇考慮是否有執(zhí)行控制,涉及以下兩種不同的情況:</p><p>　　案例l:自動(dòng)控制系統(tǒng)</p><p>　　假設(shè)有R個(gè)冷藏的操作變量和S個(gè)狀態(tài)變量?？紤]一個(gè)時(shí)間窗口組成的個(gè)時(shí)間點(diǎn),</p><p><b>　　(12)</b></p><p>　　分別用和

15、表示和 在時(shí)的值，令</p><p><b>　　(13)</b></p><p><b>　　(14) </b></p><p>　　式中，這些預(yù)測(cè)的作用是根據(jù)（13）式中的向量確定（14）式中的，在當(dāng)前時(shí)間，所有的測(cè)量結(jié)果可以用來構(gòu)造預(yù)測(cè)網(wǎng)絡(luò)的輸入。假設(shè)所有的操作變量和狀態(tài)變量可以被測(cè)量，但是在以后他們的值都是未知的。

16、為了構(gòu)建一個(gè)預(yù)測(cè)樣本，相關(guān)的時(shí)間 應(yīng)該滿足公式 。否則,未知值將包含在示例將是不合理的。</p><p>　　假設(shè)已經(jīng)得到了足夠多的樣品，首先,計(jì)算隱藏單位的參數(shù),然后計(jì)算存儲(chǔ)溫度的預(yù)測(cè)價(jià)值。</p><p><b>　　例2:自動(dòng)控制系統(tǒng)</b></p><p>　　此時(shí),輸入變量的設(shè)置只包含環(huán)境溫度、濕度和量子存儲(chǔ)的水果和蔬菜,等等。任何

17、輸入變量不出現(xiàn)在控制算法,而預(yù)測(cè)變量是穩(wěn)定狀態(tài)變量的值。RBF神經(jīng)網(wǎng)絡(luò)的非線性映射函數(shù)是用來設(shè)計(jì)穩(wěn)定模型。當(dāng)狀態(tài)變量的穩(wěn)定值,控制算法用于計(jì)算倉(cāng)庫(kù)的溫度, 因此預(yù)測(cè)變量的集合不包含任何變量控制。這就是為什么預(yù)例2中設(shè)置預(yù)測(cè)變量和控制變量與例1的不同之處。</p><p>　　5、在線最優(yōu)控制的冷藏溫度</p><p>　　普通PID控制算法的一個(gè)變量單位需要以下公式</p>

18、<p><b>　?。?5）</b></p><p>　　和分別是初始值和控制變量的當(dāng)前值。是分配值和控制對(duì)象的實(shí)際價(jià)值的區(qū)別,即</p><p><b>　?。?6）</b></p><p>　　和分別是時(shí)間點(diǎn)處的實(shí)際值和分配的控制對(duì)象的值，寫出方程(15)的增量形式,然后我們可以得到</p>&

19、lt;p><b>　?。?7）</b></p><p>　　式子中 是積分系數(shù), 是微分系數(shù)。用另一種形式寫上面的方程,我們可以得到</p><p><b>　?。?8）</b></p><p>　　在得到控制變量的預(yù)測(cè)值的情況下，式(17)和（18）就會(huì)發(fā)生改變。表示當(dāng)前時(shí)間，并且設(shè)在和 時(shí)刻變量的預(yù)測(cè)的值分別是

20、和，令</p><p><b>　?。?9）</b></p><p>　　結(jié)合歷史值和變量的預(yù)測(cè)值計(jì)算方程 (18) 的右邊。令</p><p><b>　?。?0）</b></p><p><b>　　（21）</b></p><p><b>

21、;　?。?2） </b></p><p>　　用這個(gè)方法，方程（18）可以變成一下格式</p><p><b>　?。?3）</b></p><p><b>　　上式中的值應(yīng)該滿足</b></p><p>　　， ， （24）</p><p>　　因

22、此系統(tǒng)中只有6獨(dú)立系數(shù)待定。選擇這些系數(shù)作為條件來確保他們能夠讓的數(shù)學(xué)期望最小,也就是說,我們有以下方程</p><p><b>　?。?5）</b></p><p><b>　　與下面的約束條件</b></p><p>　　所有的的初始值可以被選為。</p><p><b>　　6、應(yīng)用

23、程序</b></p><p>　　本文提出的方法已被用于最優(yōu)控制溫度冷藏的水果和蔬菜。表1列出了水果和蔬菜的日常存儲(chǔ)損失之前和之后使用本文提出的方法。對(duì)于一種特殊的水果或蔬菜來說,其日常損失率是指 </p><p>　　式中表示水果和蔬菜的種類的數(shù)量, 和 分別表示每天入口的特殊水果或蔬菜的損失和市場(chǎng)價(jià)格，。只是損失不包括水果或蔬菜腐爛而被丟棄的部分, 而且也存在越來越不新

24、鮮了而造成的價(jià)格降低，假設(shè)水果或蔬菜的市場(chǎng)價(jià)值是基于其存儲(chǔ)容量，。每天總損失率可以根據(jù)以下公式計(jì)算。</p><p>　　從表,我們可以看到,通過使用本文提出的控制方法,保鮮效果已經(jīng)大大提高,系統(tǒng)運(yùn)行更穩(wěn)定</p><p><b>　　7.結(jié)論</b></p><p>　　本文提出了一種兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)計(jì)算的最佳冷藏溫度和溫度的預(yù)測(cè)。在此基礎(chǔ)

25、上,修改后的PID控制算法。以這種方式實(shí)現(xiàn)溫度的在線優(yōu)化控制,并得到了滿意的結(jié)果。兩級(jí)RBF神經(jīng)網(wǎng)絡(luò)具有強(qiáng)大的非線性映射能力和插值的一個(gè)很好的性能值，它也有一個(gè)更高的訓(xùn)練速度。本文提出的方法可用于其它控制問題在農(nóng)業(yè)工程與一個(gè)偉大的前景。</p><p>　　Using RBF Neural Network for Optimum</p><p>　　Control of a Cold St

26、orage</p><p>　　Shi Guodong, Wang Qihong , Xu Yan & Xue Guoxin</p><p>　　Jiangsu Institution of Petrochemical Technology, Changzhou 213016, P.R.China</p><p>　　(Received November 2

27、6, 1999)</p><p>　　Abstract :In recent years ,advanced control technologies have been for the optimum control of a cold storage. But there are still a lot of shortcomings. One of the main problems is that the

28、 traditional methods can’t realize the on-line predictive optimum control of a refrigerating system with simple and valid algorithms. An RBF neural network has a strong ability in nonlinear mapping, a good interpolating

29、value performance, and a higher training speed. Thus a two-stage RBF neural network is prop</p><p>　　Keywords: RBF neural network, Cold storage, On-line prediction, optimum control.</p><p>　　1.

30、INTRODUCTION</p><p>　　The predictive optimum control of cold storage temperature has found a wide application in a agricultural engineering, especially for keeping fruits and vegetables fresh by cold storage

31、. All of the currently-used temperature control units face the problems on how to choose the optimum temperature as the controlled object, how to predict the temperature variation of the refrigerating storehouse and how

32、to realize the optimum control. A lot of study efforts have been made. The earlier methods wer</p><p>　　2. A TWO- STAGE RBF NEURAL NETWORK</p><p>　　A two-stage RBF neural network is adopted.

33、The first stage is used to determine the optimum value of the cold storage temperature, and the second is used to predict the temperature. Generally, suppose that there are input variables ,…, and output variables ,…,

34、 . Let</p><p><b>　　(1)</b></p><p><b>　　(2)</b></p><p>　　Using RBF Neural Network for Optimum control of a Cold Storage where denotes a point in the -dimen

35、sional input space ,while denotes a point in the dimensional output space ,Suppose that the number of the hidden units is .Every hidden unit uses two parameters, one is scalar quantity ,the other is vector .Suppose th

36、at the set of the training samples is .Generally, should be satisfied. RBF neural networks are based on the interpolating value performance of radius-based functions. To improve t</p><p><b>　　(3)</b

37、></p><p>　　Here, the numerator is a traditional RBF interpolating algorithm expression, and the denominator is the interpolating expression of constant 1.With this denominator, the attenuation of exponent

38、 functions in the numerator is canceled out greatly by that of the denominator. In this way ,the improved RBF neural network has a better performance.</p><p>　　3. THE ON-LINE CALCULATION OF THE COLD STORAG

39、E TEMPERATURE</p><p>　　To choose the target value of the cold storage temperature, it is needed to take overall considerations about all factors. In order to use energy reasonably, the refrigeration proces

40、s should have a high performance coefficient which is the ratio of the refrigeration quantum to the needed energy satisfying </p><p><b>　　(4)</b></p><p>　　Research results show th

41、at increases as the evaporation temperature increases or the condensation temperature decreases [4,6],and a higher evaporation temperature and a lower condensation temperature are beneficial to keep fruits and vegeta

42、ble fresh . Thus the refrigeration system should run under a higher evaporation temperature and a lower condensation temperature. However the evaporation temperature is apparently limited by the temperature of the object

43、 under refrigeration.</p><p>　　For a special kind of fruit or vegetable just entering the cold storage, its optimum storage temperature can be got with the orthogonal experimental method. The optimum storage

44、 temperature decreases with the increasing of the storage time. The loss of per unit of fruit or vegetable is</p><p><b>　　(5)</b></p><p>　　where is produced by frostbiting, while

45、 by deteriorating .When temperature increases , decreases and increases .Both of them are related to the storage time , thus </p><p><b>　　(6)</b></p><p>　　where decreases and in

46、creases respectively when the temperature increases , denotes the time of entering the storage, while denotes the storage time, then we have</p><p><b>　　(7)</b></p><p>　　For fr

47、uit or vegetable, its optimum storage temperature should satisfy the following equation</p><p><b>　　(8)</b></p><p>　　Let the gravity of fruit or vegetable be ,its storage loss ,

48、then the total storage loss in a unit time interval is </p><p><b>　　(9)</b></p><p>　　Let denote the optimum storage temperature in general .It should satisfy</p><p><

49、;b>　　(10)</b></p><p><b>　　that is,</b></p><p><b>　　(11)</b></p><p>　　The calculation of in above formulae with traditional methods is time consumin

50、g. Hence we use an RBF neural network to accomplish the solution of . This RBF neural network is the first part of the two-stage RBF neural network proposed in the paper .It has only one output , ,,and inputs, that is ,

51、 and ,.hidden units are used here .Equation(11) is used to produce enough training samples.</p><p>　　4、THE ON-LINE PREDICTION OF THE COLD STORAGE TEMPERATURE</p><p>　　One of the key problems of

52、the optimum control over the storage temperature is how to predict the temperature accurately. Because of their robustness ,the prediction methods based on neural networks have attracted more and more attentions. BP neur

53、al network is a kind of earlier used neural network for this purpose .But its training time is usually too long, and it has many local minimum points. Thus the RBF neural network has attracted more and more attention tha

54、nks to its higher training speed.</p><p>　　Case l: Automatic control system is off</p><p>　　Suppose that there are R operating variables of the cold storage and state variables .Consider a tim

55、e window composed of time points,</p><p><b>　　(12)</b></p><p>　　Use and to denote the values of and at time point respectively . Let</p><p><b>　　(13)</b>&

56、lt;/p><p><b>　　(14)</b></p><p>　　Where . The task of the prediction is to determine of (14)according to the vector of (13) .For the current time ,all of the measured results can be u

57、sed to construct the inputs of the prediction network. Suppose that all of the operating variables and state variables can be got by measuring ,and their values in the future are unknown. To construct a prediction sample

58、 ,the related time should satisfy .Otherwise, unknown values would be contained in the sample which would be unreasonable.</p><p>　　Suppose that enough samples have been got .First, calculate the paramete

59、rs of the hidden units, then calculate the prediction value of the storage temperature.</p><p>　　Case2 :Automatic control system is on</p><p>　　At this time, the set of the input variables only

60、contains the environmental temperature, humidity and quantum of the stored fruits and vegetables ,etc. Any of the input variables doesn’t appear in the control algorithm ,while the prediction variables are the stable val

61、ues of the state variables. The nonlinear mapping function of the RBF neural network is used to design the stable models. When the stable values of the state variables have been obtained, the control algorithm is used to

62、 calculate</p><p>　　5.THE ON-LINE OPTIMUM CONTROL OF THE COLD STORAGE TEMPERATURE</p><p>　　The common PID control algorithm of a variable unit takes the following form</p><p><b&

63、gt;　?。?5）</b></p><p>　　Where and are the initial value and the current value of the controlled variable respectively . is the difference between the assigned value and the real value of the control ob

64、ject, that is</p><p><b>　?。?6）</b></p><p>　　where and are the real value at time point and the assigned value of the control object respectively. Write equation (15) in the increme

65、ntal form ,then we have</p><p><b>　?。?7）</b></p><p>　　Where is the integral coefficient, is the differential coefficient .Write the above equations in another form, then we have<

66、/p><p><b>　?。?8）</b></p><p>　　Under the case of having got the predicted value of the controlled variable ,equations(17)and(18)should be changed .Let denote the current time ,and suppos

67、e that the predicted values at the instants and of variable with RBF neural network are and respectively ，Let</p><p><b>　?。?9）</b></p><p>　　Combine the historic values with the pre

68、dicted values of the variable to calculate the right side of equation(18).Let</p><p><b>　?。?0）</b></p><p><b>　?。?1）</b></p><p><b>　?。?2） </b>

69、</p><p>　　In this way ,equation (18) is changed into the following form</p><p><b>　?。?3）</b></p><p>　　The values of in above equations should satisfy</p><p>

70、;　　， ， （24）</p><p>　　Hence there are only 6 independent coefficients to be determined. Choose them as the condition to determine them is that they should let the mathematical expectation of get its minimu

71、m, that is ,we have the following equation</p><p><b>　　（25）</b></p><p>　　with the following constraint condition</p><p>　　All of the initial values of can be chosen as .

72、</p><p>　　6. APPLICATION</p><p>　　The methods proposed in the paper have been used for the optimum control over the temperature of a cold storage for fruits and vegetables. Table 1 lists the dai

73、ly storing losses of the fruits and vegetables before and after the methods proposed in the paper are used. For a special kind of fruit or vegetable, its daily loss rate is defined as</p><p>　　Where is the n

74、umber of the kinds of fruits and vegetables, and are the loss and the market price of daily entry volume of special kind fruit or vegetable respectively,.The loss does not only include the discarded part caused by dete

75、riorating, but also the price decrease caused by the decreasing of the freshness .Suppose that the market value of fruit or vegetable based on its storing volume is ,define </p><p>　　The total daily loss ra

76、te can be calculated according to the following equation </p><p>　　From Table l, we can see that by using the control methods proposed in the paper ,the fresh-keeping result has been improved greatly and th

77、e system runs more stably </p><p>　　7.CONCLUSION</p><p>　　The paper proposes a two-stage RBF neural network for the calculation of the optimum cold storage temperature and the prediction of the

78、temperature .Based on it, a modified PID control algorithm is proposed .In this way the on-line optimum control of the temperature is realized ,and satisfactory results are got .The two-stage RBF neural network has a str

79、ong ability of nonlinear mapping and a good performance of interpolating value .It also has a higher training speed. The methods proposed in the</p><p>　　REFERENCES</p><p>　　[1]Foster W R ,Collo

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84、nite Difference Approach. International Journal of Refrigeration, 1997,20(7):470-482.</p><p>　　Shi Guodong was born in Changzhou in 1956. He is currently a professor of Department of Computer Science and Eng

85、ineering at Jiangsu Institute of Petrochemical Technology. His research interests are in neural network and control , electrical technology.</p><p>　　Wang Qihong was born in Beijing in 1956. She graduated fr

86、om Department of Automation of Tianjin University in 1986. She is currently a associate professor of Department of Computer Science and Engineering at Jiangsu Institute of Petrochemical Technology</p><p>