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 %2s %10.2f"%(n, level, value))