电力负荷预测毕业论文中英文资料外文翻译文献(6)

The paper is organized as follows: section 2 proposes the grey forecasting model GM(1,1): section 3 presents Estimate ? with improved genetic algorithm:section 4 puts forward a short-term daily load forecasting realized by GM(1,1)-IGA and finally, a conclusion is drawn in section 5.

2. Grey prediction model GM (1,1)

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中英文资料

This section reviews the operation of grey forecasting in details. The grey model GM(1,1) is a time series forecasting model. It has three basic operations: (1) accumulated generation, (2) inverse accumulated generation, and (3) grey modeling. The grey forecasting model uses the operations of accumulated to construct differential equations.Intrinsically speaking, it has the characteristics of requiring less data.

The grey model GM(1,1), i.e., a single variable first-order grey model, is summarized as follows:

Step1: Denote the initial time sequence by

0000 x?0?=x???1?,x???2?,x???3?,...,x???n?

??x(0) is the given discrete n-th-dimensional sequence.x(0)(m) is the time series data at time m , n must be equal to or larger than 4. On the basis of the initial sequence x(0) , a new sequence x(1) is set up through the accumulated generating operation in order to provide the middle message of building a model and to weaken the variation tendency, so x(1) is defined as:

x?1??x?1??1?,x?1??2?,x?1??3?,...x?1??n?

??Where x?1??1??x?0??1?， and x?1??k???x?0??m?,k?2,3?n and

m?1kx?r??x?r??1?,x?r??2?,x?r??3?,...x?r??n?is the r

??times accumulated series.

Step2: To set the ? value to fine z(1)(k)

According to GM (1, 1), we can form the following first-order grey differential equation:

dx???ax?1??b dt1And its difference equation isx?0??k??az?1??k??b.Where a was called the developing coefficient of GM,and b was called the control variable.

Denoting the differential coefficient subentry in the form of difference, we can get:

????dx?1?x?k?1??x?k?11 ??x???k?1??x???k?

dtk?1?k11Before a grey GM (1, 1) model was set up, a proper ? value needed to be assigned for a better background value z(1)(k). The sequence of background values was defined as:

z?1??z?1??1?,z?1??2?,??z?1??n?

??1Among them

z???k???*x???k???1???*x???k?1?,k?2,3?n,0???1

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中英文资料

For convenience, the ? value was often set to 0.5,the z(1)(k) was derived as:

?x?1??k??x?1??k?1??1? z???k???2However, this constant ? might not be optimal because the different questions might need different ? value. And, both developing coefficient a and control variable b were determined by the z(1)(k). The process of the original grey information for whitening may be suppressed resulted from the coefficient ? was constant. Hence, the accuracy of prediction value x?(0)(k) in GM (1, 1) model would seriously be decreased. In order to correct the defect, the coefficient ? must be a variable based on the feature of problems,so we estimate ? by genetic algorithms.

Step3: To construct accumulated matrix B and coefficient vector X n . Applying the Ordinary Least Square (OLS) method obtains the developing coefficient a , b was as follows:

??z?1??2???1???z?3?B??????z?1??n??1??1? ???1??T?0??0???0and xn??x2,x3?,,x???n ?????T?????BT*B??1*BT*X ?,bSo ?an??Step4: To obtain the discrete form of first-order grey differential equation, as follows:

The solution of x(1) is

???ak???0?bb???k?1???x?1???*e? x????aa???1?And the solution of x(0) is

???ak??0?b??k?1??x??k?1??x??k???e?1?*?x?1???*e? x???a???0??1??1??a

3. Estimate ? with improved GA

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中英文资料

In order to estimate the accuracy of grey mode GM(1, 1), the residual error test was essential. Therefore,the objective function of the proposed method in this paper was to ensure that the forecasting value errors were minimum. The objective function was defined as mean absolute percentage error (MAPE) minimization as follows:

minMAPE??e?k?

k?1n Where，e?k????0??k??x?0??k?xx?0??k??100%

??0??k?is forecasting value,n is the number of sequence data. x(0)(k) is original data,xHowever, from the above description of the establishment of GM (1, 1), we can get: In GM (1, 1), the value of parameter ? can determine z(1) , and, both developing coefficient a and control variable b were determined by the z(1)(k).What is more, the solution of x(0) was determined by a and b,so the key part of the whole model selecting process was the value of ? .There is kind of complicated nonlinear relationship between ? and residual errors,and this nonlinearity was hard to solve by resolution, so the optimal selection of ? was the difficult point of GM（1,1）.

Genetic algorithm is a random search algorithm that simulates natural selection and evolution. It is finding widespread application as a consequence of two fundamental aspects: the computational code is very simple and yet provides a powerful search mechanism.They are function independent which means they are not limited by the properties of the function such as continuity, existence of derivatives, etc. Although the binary representation was usually applied to many optimization problems, in this paper, we used the improved decimal-code representation scheme for solution. The improved decimal-code representation in the GA offers a number of advantages in numerical function optimization over binary encoding. The advantages can be briefly described as follows:

Step1:Efficiency of GA is increased as there is no need to convert chromosomes to the binary type,

Step2:Less memory is required as efficient floating-point internal computer representations can be used directly,

Step3:There is no loss in precision by discrimination to binary or other values, and there is greater freedom to use different genetic operators …… 此处隐藏：3888字，全部文档内容请下载后查看。喜欢就下载吧 ……