多变量时滞计算的最大独立互相关算法

为解决相空间重构中多变量时滞参数难以同时选择的问题,提出一种基于最大独立互相关的时滞计算方法.将响应变量序列分段处理;对各段曲面拟合并将观测变量序列代入拟合函数;迭代运算至互相关最小,得到最优时滞.对最大独立互相关算法与遗传神经网络、互信息法、极大联合熵法进行对比实验,并引入联合递归图与共有近邻比值法作为评价方法,结果表明:最大独立互相关算法克服了传统方法的不足.选取某矿井下进风巷、上隅角、工作面和回风巷4个位置瓦斯浓度的真实数据进行四变量最优时滞选择实验并与互信息法对比,最大独立互相关算法的时滞计算结果为16-3-10-11,共有近邻比为0.58,联合递归密度为0.34%,优于传统方法.提出算法能够应用于实际多变量分析,具有一定实用价值.

A calculation method for multivariate time-delay selection with the maximal independent cross-correlation algorithm

To solve the problem of multivariate time-delay synchronous selection on phase space reconstruction(PSR), a maximal independent cross-correlation(MICC) algorithm was proposed to select multivariate phase space reconstruction time-delays. Firstly, the response variate sequence was segmented, and then, the segment surfaces were fitted and the observational sequences were substituted into the fitting function. At last, the optimal time-delay was computed iteratively when the cross-correlation was minimal. The simulation results of the Lorenz system were used to compare the binary and ternary time-delay selections of MICC algorithm with genetic neural networks, maximal entropy algorithm and mutual information algorithm. Joint recurrence plot(JRP) and mutual nearest neighbor radio(MNNR) were applied to evaluate the selections, and MICC algorithm was superior to the others. Besides, the coal mine gas concentrations of four crucial undermine locations were chosen to be the one real coal mine system coupling variates. The contrast experiments between MICC and mutual information had been done and the time-delays computed using MICC were 16-3-10-11 respectively, meanwhile the MNNR and JRP densities were 0.58 and 0.34%. The results showed that the MICC algorithm had obvious advantages in selecting optimal time-delays of multivariate and could be applied on multivariate analysis in practical issues.