基于隶属度修正的加权马尔可夫链的降水预测

应用Fisher最优分割法将榆林地区1951—2015年的年降水序列划分为9个状态,采用规范化的各阶自相关系数为权重,建立了加权马尔可夫链模型。以属于同一状态的所有降水量的均值作为聚类中心,应用模糊C均值聚类(Fuzzy C-Means,FCM)算法中的隶属函数计算隶属度,以隶属度向量作为预测时的初始状态向量。该模型逐年预测了榆林市2006—2015年的降水状态,结果全部与实际情况一致。基于马尔可夫链的预测结果,采用模糊集中的级别特征值理论分别预测了2006—2015年的降水量,所有预测结果的相对误差都在10%以内,初步表明基于隶属度修正的加权马尔可夫链模型是合理可行的。

Prediction of Annual Precipitation by Weighted Markov Chain Based on Membership Modification

The annual precipitation series of Yulin city from 1951 to 2015 was divided into 9 states by the Fisher optimal partition method.The weighted Markov chain model was established by taking the standardized autocorrelation coefficients as weights.With the mean value of all precipitation in the same state as the cluster center,the membership function of the Fuzzy C-Means was applied to calculate the membership of annual precipitation,and the membership vector was taken as the initial state vector for the time period.The precipitation state from 2006 to 2015 in Yulin city was predicted year by year.All the results agree with the reality.Based on the prediction results of Markov Chain,the precipitation was predicted respectively from 2006 to 2015 by the level characteristics value of Fuzzy Sets,and the relative error of all the prediction results is less than 10％.The preliminary results show that the model of weighted Markov chain based on membership modification is feasible.