该程序利用一阶局域加权法进行混沌时间序列的预测
- %AOLMM多步预测函数
- function [FChaosPredict] = FunctionChaosPredict(Data,N,mtbp,deltaT,tao,d,MaxStep)
- %Data是一维信号时间序列,N是信号数据长度,mtbp,deltaT,tao,d分别是重构相空间的平均时间序列、采样周期、时延及嵌入维
- roll=Data;%取横摇数据
- M = N - (d - 1)*tao;
- for i = 1 : M
- for j = 1 : d
- MatrixX(i,j) = roll(i + (j - 1)*tao);
- end
- end
- %计算相空间中第M点与各点的距离
- for j = 1 : (M - 1)
- Dis(j) = norm(MatrixX(M,:) - MatrixX(j,:),2);
- end
- %排序计算相空间中第M点的(m+1)个参考邻近点
- for i = 1 : (d + 1)
- NearDis(i) = Dis(i);
- NearPos(i) = i;
- end
- for i = (d + 2) : (M - mtbp)
- for j = 1 : (d + 1)
- if (abs(i-j)>mtbp) %& abs(i-j)<10*mtbp
- if(Dis(i) < NearDis(j))
- NearDis(j) = Dis(i);
- NearPos(j) = i;
- break;
- end
- end
- end
- end
- SortedDis = sort(NearDis);
- MinDis = SortedDis(1);
- %计算第M点的(m+1)个参考邻近点的权P[i]
- SumP = 0;
- for i = 1 : (d + 1)
- P(i) = exp(-NearDis(i)/MinDis);
- SumP = SumP + P(i);
- end
- P = P/SumP;
- %用最小二乘法计算a[],b[]
- for step=1:1:MaxStep
- aCoe1 = 0;
- aCoe2 = d;
- bCoe1 = 0;
- bCoe2 = 0;
- e = 0;
- f = 0;
- for i = 1 : (d + 1)
- aCoe1 = aCoe1 + P(i)*sum(MatrixX(NearPos(i),:));
- bCoe1 = bCoe1 + P(i)*(MatrixX(NearPos(i),:)*MatrixX(NearPos(i),:)');
- e = e + P(i)*(MatrixX(NearPos(i) + step,:)*MatrixX(NearPos(i),:)');
- f = f + P(i)*sum(MatrixX(NearPos(i) + step,:));
- end
- bCoe2 = aCoe1;
- CoeMatrix = [aCoe1,bCoe1;aCoe2,bCoe2];
- ResultMatrix = [e;f];
- abResult = pinv(CoeMatrix)*ResultMatrix;
- a = abResult(1);
- b = abResult(2);
- for j = 1 : d
- % MatrixX(M + step,j) = a + b*MatrixX(M,j); %以历史上相近点的演化规律作为中心点的演化规律以中心点为基准进行预报
-
- MatrixX(M + step,j) = 0;
- for i = 1 : (d + 1)
- MatrixX(M + step,j) = MatrixX(M + step,j) + P(i)*(a + b*MatrixX(NearPos(i),j)); %以历史上相近点的演化加权和直接作为中心点的演化点进行预报
- end
- end
- %误差修正
- if M-tao+step+(d-1)*tao < N+1
- for j=1:d-1
- err(j)=MatrixX(M + step,j)-roll(M+step+(j-1)*tao);
- end
- ppp=1:d-1;ttt=err;neterr=newrbe(ppp,ttt);xxx=2:d;errp=sim(neterr,xxx);
- PredictedData(step) = MatrixX(M + step,d) - errp(d-1);
- roll(N+step)=PredictedData(step);
- else
- PredictedData(step) = MatrixX(M + step,d);
- end% roll(N+k)=PredictedData(k);
- FChaosPredict(step) = PredictedData(step);
- % FChaosPredict(step) = MatrixX(M + step,d);
- end
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