灰度预测法

Posted 2020-10-17

灰色预测法是一种对含有不确定因素的系统进行预测的方法。灰色系统是介于白色系统和黑色系统之间的一种系统。

　　白色系统是指一个系统的内部特征是完全已知的，即系统的信息是完全充分的。而黑色系统是指一个系统的内部信息对外界来说是一无所知的，只能通过它与外界的联系来加以观测研究。灰色系统内的一部分信息是已知的，另一部分信息时未知的，系统内各因素间具有不确定的关系。

　　灰色预测通过鉴别系统因素之间发展趋势的相异程度，即进行关联分析，并对原始数据进行生成处理来寻找系统变动的规律，生成有较强规律性的数据序列，然后建立相应的微分方程模型，从而预测事物未来发展趋势的状况。其用等时距观测到的反应预测对象特征的一系列数量值构造灰色预测模型，预测未来某一时刻的特征量，或达到某一特征量的时间。

 

 

  1 # -*- coding: utf-8 -*-
  2 """
  3 Spyder Editor
  4 
  5 This is a temporary script file.
  6 """
  7 import numpy as np
  8 import math
  9 
 10 raw_data = [413.05,416.51,420.47,410.01,411.87,415.91,415.5,417.28,418.75,407.86,408.68,411.25,411.88,417.7,418.12,415.3,416,416.71,427.36,424.06,416,413.12,416.02,417.9,420.3,420.6,420.46,423.75,422.57,422.28,418.5,418.47,421.32,423.74,426.59,424.75,426.01,431.48,432.04,428.51,430.03,437.76,443.85,452.26,447.8,453.69,463.02,461.77,468.14,444.85,450.46,455.32,446.6,451.11,443.73,450.39,447.38,448.4,461.18,460.2,459.87,461.56,450.7,452.28,455.01,455.76,455.8,457.89,453.01,453.24,453.52,434.55,441.57,440.81,437.48,443.51,445.03,449.09,453.95,472.01,526.02,531,532.89,530.69,536.79,538.8,570.87,572.87,574.02,585.34,576.88,583.05,575.52,580.09,614.51,672,705.87,684.5,696.99,769.5,747.95,757.6,767.3,743.9,668.6,605.85,625.8,665.5,664.87,627.42,662.33,646.61,640,674.74,674.75,705.99,659.29,681.34,667.8,677.04,640.51,664.8,648.11,649.72,647.95,667.19,653.7,659.78,665.5,665.33,683.2,674.3,675,665.85,665.01,648.04,654.03,661.82,654.17,648.47,655.51,655.93,658.34,654.99,622.83,608.29,604.1,590.28,591.27,585.5,583.73,569.41,564.64,574.17,571.83,572.21,573.51,582.1,581.42,588.01,583.54,580.32,577.2,578.02,568.55,574.17,574.78,579.49,576.15,572.73,579.85,609.89,614.52,611.5,615.23,619.75,631.73,626.25,628,612.08,611.62,614.23,613.88,611.81,610.01,607.69,613.03,609.79,600.14,597.43,597.08,603.29,602.55,600.36,609.14,605.53,603.76,604.6,611.1,614.09,609.09,612.67,610.98,614.09,613.51,620.13,620.5,616.56,618.87,641.87,637.63,637.01,643,640.2,644.18,639.79,638.68,631.77,632.46,636.73,664.99,659.03,654.65,659.52,678.7,688.67,693.47,714.51,702.55,701.02,734.6,750.85,692.51,707.62,708.89,713.95,705.55,711.99,724.54,714.87,716.22,703.57,703.64,707.43,712.17,744.98,740.67,753.97,752.9,729.67,738.99,749.85,742,737.61,740.36,731.19,724.9,731.52,731.05,739,755.36,774.88,765.46,768.5,750.62,757.36,765.01,765.01,770.5,772.9,770.21,777.99,775,774.49,777.43,784.17,790.99,790.21,790.59,797.99,829.34,859.2,918.99,895.24,898,906.4,936.43,981.7,974.74,959.26,966.58,998.99,1019.3,1037.5,1139.6,1003.2,898.5,908,915.9,903,905.76,779.54,804.58,828.12,815.3,820.74,830.1,903.99,887.46,900.29,895.74,924.02,923.72,908.52,886.1,893.35,915.12,916.7,919.43,912.55,917.35,966.19,983.73,1007,1015.7,1031.1,1006.6,1022.6,1052.1,1048.8,984.97,992,1000.1,996.01,996.5,1013.3,1013.9,1038.5,1056.2,1059.7,1056.2,1091.2,1129.6,1125.5,1189.8,1185.4,1153,1178.3,1195.5,1189.1,1233.2,1258,1289.2,1267.8,1278.4,1279.2,1232.4,1150,1190.4,1115.4,1172.4,1224.4,1238.5,1245,1256.2,1168.6,1070.4,971.51,1016.5,1040.5,1115.9,1039.1,1032.7,942.13,972.17,968.9,1042.7,1044.7,1041.8,1041.2,1081.5,1093.5,1107.5,1150.1,1145.8,1140.4,1191.5,1196.6,1188.1,1215.9,1220.3,1235.6,1227.4,1186.9,1206.8,1193.3,1212,1240,1265.4,1260.5,1308.5,1327,1346.4,1355.2,1345,1371.1,1400,1440.3,1415.6,1423.6,1435,1533,1558.5,1619,1607.1,1545.1,1597,1619.9,1703.5,1760,1796.9,1853.9,1735,1819.5,1827.3,1772,1786.2,1870,1941.5,1966.5,2059.3,2026.6,2087.3,2249.6,2395.5,2268.1,2125.9,1980.2,2056.9,2207.4,2146.7,2191.8,2312,2405.9,2461,2488.2,2636.9,2844.6,2644,2781.5,2809,2806,2941.8,2569.6,2677.1,2394.3,2377.5,2437.5,2610.1,2491.4,2582,2714.5,2624.4,2672.8,2674.9,2502.6,2483.3,2393.6,2521.2,2518.2,2472.4,2420.6,2346.2,2445.1,2524,2579.9,2598.6,2593.2,2479.3,2542,2477.9,2318.3,2283.8,2375.6,2330.1,2206.5,1978.6,1925,2220,2302.8,2253.4,2865.1,2659,2844.7,2750.1,2769.7,2560.9,2527.7381,2664.6,2784.8,2713.1,2748.2,2854.3,2731.3,2702,2790.3,2860,3252.3,3232.1,3396,3415,3340.4,3405,3643.4,3866.2,4061.6,4320.8,4151.8,4386.4,4263,4090.1,4145,4063.1,3998.2,4081.9,4130.2,4322.1,4351.5,4340.4,4332.8,4385.1,4587.1,4568,4718.3,4907.7,4532.3,4598.5,4205,4375,4595.8,4613.7,4304,4315.9,4233.9,4198.7,4149.4,3849.7,3235.3,3697.1,3681.5,3666.6,4084.4,3892.2,3872.4,3596.7,3602.3,3779.6,3654.7,3930.1,3881.5,4209.7,4190,4168,4367.1,4404.3,4400.2,4310.6,4215.9,4312,4370,4435.6,4611.9,4782.3,4777.7,4824.9,5440,5636.8,5833.5,5713.9,5764.8,5597.1,5567,5694.2,5983.8,6005.1,5981.3,5907.3,5510,5724.1,5890,5759.7,5720.3,6150,6130,6455.1]
 11 
 12 # n = len(raw_data)
 13 # print(n)
 14 # # 7446.1 
 15 
 16 min = 7
 17 max = len(raw_data)
 18 
 19 for i in range(max, (max - 61), -1):
 20     if (i > (max - min)):
 21         continue;
 22     # print(raw_data[i:998])
 23     history_data = raw_data[i:max]
 24 
 25     n = len(history_data)
 26     # print(n)
 27     X0 = np.array(history_data)
 28 
 29     #累加生成
 30     history_data_agg = [sum(history_data[0:i+1]) for i in range(n)]
 31     X1 = np.array(history_data_agg)
 32 
 33     #计算数据矩阵B和数据向量Y
 34     B = np.zeros([n-1,2])
 35     Y = np.zeros([n-1,1])
 36     for i in range(0,n-1):
 37         B[i][0] = -0.5*(X1[i] + X1[i+1])
 38         B[i][1] = 1
 39         Y[i][0] = X0[i+1]
 40 
 41     #计算GM(1,1)微分方程的参数a和u
 42     #A = np.zeros([2,1])
 43     A = np.linalg.inv(B.T.dot(B)).dot(B.T).dot(Y)
 44     a = A[0][0]
 45     u = A[1][0]
 46 
 47     #建立灰色预测模型
 48     XX0 = np.zeros(n)
 49     XX0[0] = X0[0]
 50     for i in range(1,n):
 51         XX0[i] = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(i));
 52 
 53 
 54     #模型精度的后验差检验
 55     e = 0      #求残差平均值
 56     for i in range(0,n):
 57         e += (X0[i] - XX0[i])
 58     e /= n
 59 
 60     #求历史数据平均值
 61     aver = 0;     
 62     for i in range(0,n):
 63         aver += X0[i]
 64     aver /= n
 65 
 66     #求历史数据方差
 67     s12 = 0;     
 68     for i in range(0,n):
 69         s12 += (X0[i]-aver)**2;
 70     s12 /= n
 71 
 72     #求残差方差
 73     s22 = 0;       
 74     for i in range(0,n):
 75         s22 += ((X0[i] - XX0[i]) - e)**2;
 76     s22 /= n
 77 
 78     #求后验差比值
 79     C = s22 / s12   
 80     # print(C)
 81 
 82     #求小误差概率
 83     cout = 0
 84     for i in range(0,n):
 85         if abs((X0[i] - XX0[i]) - e) < 0.6754*math.sqrt(s12):
 86             cout = cout+1
 87         else:
 88             cout = cout
 89     P = cout / n
 90     # print(P)
 91 
 92     if (C < 0.35 and P > 0.95):
 93         #预测精度为一级
 94         f = np.zeros(1)
 95         value = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(n)) 
 96         level = "好好"
 97         # m = 1   #请输入需要预测的年数
 98         # f = np.zeros(m)
 99         # print(‘往后m各年负荷为：‘)
100         # f = np.zeros(m)
101         # for i in range(0,m):
102             # f[i] = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(i+n))  
103             # result = f[i]
104     elif(C < 0.45 and P > 0.80):
105         f = np.zeros(1)
106         value = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(n)) 
107         level = "合格"
108     elif(C < 0.5 and P > 0.7):
109         f = np.zeros(1)
110         value = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(n)) 
111         level = "勉强"
112     else:
113         value = 0.0
114         level = "不合"
115         
116     print("%3s\t%2s\t%10.2f"%(n, level, value))

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