预测分析 Python BP神经网络模型 公路运量预测（学习笔记）_bp神经网络铁路客运量预测算法

import numpy as np
import matplotlib.pyplot as plt

#学习函数
def logsig(x):
    return 1/(1+np.exp(-x))

#数据
#人数(单位：万人)
population=[20.55,22.44,25.37,27.13,29.45,30.10,30.96,34.06,36.42,38.09,39.13,39.99,41.93,44.59,47.30,52.89,55.73,56.76,59.17,60.63]
#机动车数(单位：万辆)
vehicle=[0.6,0.75,0.85,0.9,1.05,1.35,1.45,1.6,1.7,1.85,2.15,2.2,2.25,2.35,2.5,2.6,2.7,2.85,2.95,3.1]
#公路面积(单位：万平方公里)
roadarea=[0.09,0.11,0.11,0.14,0.20,0.23,0.23,0.32,0.32,0.34,0.36,0.36,0.38,0.49,0.56,0.59,0.59,0.67,0.69,0.79]
#公路客运量(单位：万人)
passengertraffic=[5126,6217,7730,9145,10460,11387,12353,15750,18304,19836,21024,19490,20433,22598,25107,33442,36836,40548,42927,43462]
#公路货运量(单位：万吨)
freighttraffic=[1237,1379,1385,1399,1663,1714,1834,4322,8132,8936,11099,11203,10524,11115,13320,16762,18673,20724,20803,21804]

#数据转为矩阵
samplein=np.mat([population,vehicle,roadarea])
sampleinminmax=np.array([samplein.min(axis=1).T.tolist()[0],samplein.max(axis=1).T.tolist()[0]]).transpose() #3*2
sampleout=np.mat([passengertraffic,freighttraffic])
sampleoutminmax=np.array([sampleout.min(axis=1).T.tolist()[0],sampleout.max(axis=1).T.tolist()[0]]).transpose() #2*2
#最大最小法归一
sampleinnorm=(2*(np.array(samplein.T)-sampleinminmax.transpose()[0])/(sampleinminmax.transpose()[1]-sampleinminmax.transpose()[0])-1).transpose()
sampleoutnorm=(2*(np.array(sampleout.T)-sampleoutminmax.transpose()[0])/(sampleoutminmax.transpose()[1]-sampleoutminmax.transpose()[0])-1).transpose()

#给输出样本添加噪音
noise=0.03*np.random.rand(sampleoutnorm.shape[0],sampleoutnorm.shape[1])
sampleoutnorm+=noise

#定义模型参数
maxepochs=60000
learnrate=0.035 #学习效率
errorfinal=0.65*10**(-3) #误差阈值
samnum=20 #样本个数
indim=3 #输入变量个数
outdim=2 #输出变量个数
hiddenunitnum=8 #隐藏层神经元个数
#将参数初始化为随机值
w1=0.5*np.random.rand(hiddenunitnum,indim)-0.1 
b1=0.5*np.random.rand(hiddenunitnum,1)-0.1
w2=0.5*np.random.rand(outdim,hiddenunitnum)-0.1
b2=0.5*np.random.rand(outdim,1)-0.1

#训练模型
errhistory=[]
for i in range(maxepochs):
	#正向传播
    hiddenout=logsig((np.dot(w1,sampleinnorm).transpose()+b1.transpose())).transpose() #隐含层结果
    networkout=(np.dot(w2,hiddenout).transpose()+b2.transpose()).transpose() #输出层结果
    err=sampleoutnorm-networkout #误差
    sse=sum(sum(err**2))
    errhistory.append(sse)
    if sse<errorfinal:
        break  
    #反向传播
    delta2=err
    delta1=np.dot(w2.transpose(),delta2)*hiddenout*(1-hiddenout)
    dw2=np.dot(delta2,hiddenout.transpose())
    db2=np.dot(delta2,np.ones((samnum,1)))
    dw1=np.dot(delta1,sampleinnorm.transpose())
    db1=np.dot(delta1,np.ones((samnum,1)))
    w2+=learnrate*dw2
    b2+=learnrate*db2
    w1+=learnrate*dw1
    b1+=learnrate*db1
    
#误差曲线
errhistory10=np.log10(errhistory)
minerr=min(errhistory10)
plt.plot(errhistory10)
plt.plot(range(0,i+1000,1000),[minerr]*len(range(0,i+1000,1000)))
ax=plt.gca() #获得当前对象ax
#自定义刻度标签
ax.set_yticks([-2,-1,0,1,2,minerr])
ax.set_yticklabels([u'$10^{-2}$',u'$10^{-1}$',u'$1$',u'$10^{1}$',u'$10^{2}$',str(('%.4f'%np.power(10,minerr)))])
ax.set_xlabel('iteration')
ax.set_ylabel('error')
ax.set_title('Error History')
#plt.savefig("errorhistory.png",dpi=700) #保存图片
plt.show()
plt.close()
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#仿真输出和实际输出
hiddenout=logsig((np.dot(w1,sampleinnorm).transpose()+b1.transpose())).transpose() #隐含层结果
networkout=(np.dot(w2,hiddenout).transpose()+b2.transpose()).transpose() #输出层结果
diff=sampleoutminmax[:,1]-sampleoutminmax[:,0] #实际输出极差
networkout2=(networkout+1)/2
networkout2[0]=networkout2[0]*diff[0]+sampleoutminmax[0][0] #预测客运量
networkout2[1]=networkout2[1]*diff[1]+sampleoutminmax[1][0] #预测货运量
sampleout=np.array(sampleout) #实际值

fig,axes=plt.subplots(nrows=2,ncols=1,figsize=(12,10))

#客运量曲线
line1,=axes[0].plot(networkout2[0],'k',marker=u'$\circ$')
line2,=axes[0].plot(sampleout[0],'r',markeredgecolor='b',marker=u'$\star$',markersize=9)
#自定义刻度标签
axes[0].legend((line1,line2),('simulation output','real output'),loc='upper left')
yticks=[0,20000,40000,60000]
ytickslabel=[u'$0$',u'$2$',u'$4$',u'$6$']
axes[0].set_yticks(yticks)
axes[0].set_yticklabels(ytickslabel)
axes[0].set_ylabel(u'passenger traffic$(10^4)$')
xticks=range(0,20,2)
xtickslabel=range(1990,2010,2)
axes[0].set_xticks(xticks)
axes[0].set_xticklabels(xtickslabel)
axes[0].set_xlabel(u'year')
axes[0].set_title('Passenger Traffic Simulation')

#货运量曲线
line3,=axes[1].plot(networkout2[1],'k',marker=u'$\circ$')
line4,=axes[1].plot(sampleout[1],'r',markeredgecolor='b',marker=u'$\star$',markersize=9)
#自定义刻度标签
axes[1].legend((line3,line4),('simulation output','real output'),loc='upper left')
yticks=[0,10000,20000,30000]
ytickslabel=[u'$0$',u'$1$',u'$2$',u'$3$']
axes[1].set_yticks(yticks)
axes[1].set_yticklabels(ytickslabel)
axes[1].set_ylabel(u'passenger traffic$(10^4)$')
xticks=range(0,20,2)
xtickslabel=range(1990,2010,2)
axes[1].set_xticks(xticks)
axes[1].set_xticklabels(xtickslabel)
axes[1].set_xlabel(u'year')
axes[1].set_title('Freight Traffic Simulation')
#fig.savefig("simulation.png",dpi=500,bbox_inches='tight')
plt.show()
plt.close()
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