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3 Pages

### zhang_zhefeng

Course: PTE 586, Fall 2010
School: USC
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Word Count: 506

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Assignment PTE586 3 Zhefeng, Zhang Sep, 15 2010 1.Explain how would you design and train an artificial neural network to forecast the Gas rate Because of the known values, an ANN can be designed in the following manner: its consist of 3 layers, the input layer, the hidden layer and the output layer. There are 4 neurons (gas flow rate, water flow rate, well head pressure, well head temperature)...

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Assignment PTE586 3 Zhefeng, Zhang Sep, 15 2010 1.Explain how would you design and train an artificial neural network to forecast the Gas rate Because of the known values, an ANN can be designed in the following manner: its consist of 3 layers, the input layer, the hidden layer and the output layer. There are 4 neurons (gas flow rate, water flow rate, well head pressure, well head temperature) in the input layer, and 2 in the hidden layer, 1 in the output layer (gas rate). The structure is 421. Using 70% of the data for training ANN, the left 30% for testing the training result. Pre-input: using the non-linear sigmoid function f(x)=1/(1 + e- x), if the data does not fall into [0,1] Using x = (x1 - x1min)/(x1max - x1min) From the input layer node X to hidden layer node: The equation for input layer to hidden layer is hni1 = Mhn11 x1 + Mhn12 x2 + Mhn13 x3 + Mhn14x4 hni2 = Mhn21 x1 + Mhn22 x2 + Mhn23 x3 + Mhn24x4 In which, Mhn is the hidden layer nodes matrix, 2 lines 4 columns. Hni is the input data to hidden layer nodes. The equation for output data from the hidden layer node: hno1 = f(hni1)=1/(1+exp(- hni1)) hno2 = f(hni2)=1/(1+exp(- hni2)) From the hidden layer to the output layer oni1 = Mon1,1hno1 +Mon1,2 hno2 + Mon1,3hno3 +Mon1,4hno4 In which, Mon is the output node matrix, 1 line, 2 columns. Oni is the output data from output layer. 2. Present a graph of the ANN and show clearly what are the inputs and outputs of ANN the 3. What conventional statistical method is needed to use before applying the ANN Before applying ANN, conventional extrapolate method is needed, since the data from 8.am to 10.am and Sunday is missing. The data can be extrapolated from the data prior to 8am and after 10am. The average of 2 hours prior to 8am and after 10am can work as a substitute data. And the missing Sunday data can be extrapolated and substituted by the average of Saturday and Friday whole days data. 4. What other soft computing should be used in conjunction with ANN and incorporate the qualifiers in the solution. Fuzzy logic should be used along side the ANN. The fuzzy qualifier much higher is also one of the fuzzy sets represents the output of the prior daily average rate. Define 5 fuzzy sets on X as much lower, lower, equal, higher, much higher. These sets are drawn into curve function in X. Let Y represents the methods of preprocessing the data. If X is much higher, the method is calculating the daily average rate by daily water flow deducted by 24 hours. When the hourly temperature is near or above the top quartile, Fuzzy sets should be set up as below the lower quartile, near the 2nd quartile, near the 3rd quartile, and near or above the top quartile, using trapezoidal membership functions. Then near or above the top represents a 2 to 3 times growth in gfr. Also adding the limit that the temperature does not exceed the boiling point temperature.
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~&quot;'&quot;Lcfw_(.\Mu.Th('0&quot;\( \/- ~)eJd '. Pr-,e,\ -:&quot;-.L.2,(S)~'L = \'Y\&amp; ,C =(LI,o,r=(1:)-t-\-+-'-f&quot;2--_~)'L.i,-=-]:2'1L.f\-(~7f'~~\ ~fi&quot;L/--I-I-c: I. ~. \j2.0r---i:.:&gt;'S,c-)-~j'2~W~S- Y)-iTq' -:0-3-20
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C_=c.\t(~)~rc.~W _ =_3t:.!-,\2 '._X 2.C-.=(.p t':&gt; ')).~\.\c.0\.u\~ ll.\\-e:.'I'()(\':\)~(\1-\)(x+)Xi-.k).,,~-. ---. x= ~ .G)t(:.--\-V)L w)I,z:.).',Q'j.'~v-)~z:~Q)uoh_._-_.n~.lr.,&quot;\-:2 \'W.'1) -? (I 1-l ')ujx
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rl~\\y'rl 0-\t. 4 ~G\J\=t:x'LJ, \.~ _2\2.+CDy.=0 &quot;~(t'Z._:&gt; ') '2. .= es-\-(6-( '1 -&quot;')~) 1--3':zs(1- -~)?r&quot;&quot;'~ + 4 &quot;'~/(t'- - t'X'2.~:t-.:-O .,-t- ('-t _ -z.'))( '2.+ (:')(2'2.2.2-S2.:-=- 21+- g =-_-z.,)2.:.l~&lt;:. = (D
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r-~-~-=-'~-\r .~c'i:-cfw_1~-~-S=-. \ ~t_\5',I+ 2.0-'-&quot;-~7, -&quot;&gt;-=-'-&quot;'~-~-tt-\~4J-~\~O~-~\$g=II _.-) 9 ,.;.toi11-01--~l ;2~-~\~-~l1\i=I-T.=O=~=~\~2~b~--H-&quot;'!'S-.:.'X.L.:V.:)I--~,-~-~0-.31+ 5'e.=-0-+-I-=~-=-')_L.-z.)=. 3
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Math 4A - CastrocondeQuiz SA (15.1)Name:I.D.#:~Q._~Start you work after the last question. Attach more paper to this page, if needed.J= x-1.Find the domain and range of the function ft, y)2.Describe the level curves of the function I(x, y)3.I
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k:.~Name:I.D.#:Math 4A - CastrocondeQuiz 5B (15.1)Start you work after the last question. Attach more paper to this page, if needed.= In(x- y2).1.Find the domain and range of the function f(x,y)domain.2.Describe the level curves of the function
Irvine Valley College - MATH - 4A
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1-/I-+-~)~=--'&lt;,.~ :.-0',2.~z:&gt; ~\=_Y'\:.Y-+-' &quot;,',_x; 2- -=t-~ ~&lt;:,.('I.)-\-02~2 kV\ l)(S'I'-C&quot;-J .J. 2.jr(IL~x.:,~.\.- (0 l D/-o-l'r~\)-\'&gt;l')','Y\:'sd ~')~~&quot;,2.c&gt;&lt;)=-~L.;2.)&lt; ~ '2.-~ - \. 1 :-l')Z.J=-_t.)(+2.,\-