采用信息理论准则的信号源数估计方法及性能对比
Information Criterion-Based Source Number Estimation Methods with Comparison

为了从机械系统观测混合信号中有效评估信号源的数目,以及解决数据点较大时贝叶斯信息准则(BIC)难以计算的问题,在剖析了3种信源数目估计准则(赤池信息准则(AIC)、最小描述长度(MDL)以及贝叶斯信息准则(BIC))的原理和算法的基础上,提出了基于对数函数修正的改进贝叶斯准则(IBIC)。该准则利用对数运算将BIC目标函数中的多参数指数运算转换为乘积运算,在不降低计算精度的条件下,显著改善了BIC准则的计算效率和工程应用性能。仿真实验分析表明:AIC与MDL具有近似的源数估计性能,对非线性调制成分非常敏感;从能量角度分析,提出的新准则容忍非线性调制成分(非线性调制信号能量占观测信号总能量)能量比为5.15％,较AIC(0.07％)与MDL(0.08％)具有更好的鲁棒性能。壳体结构试验台声源数目估计实验表明,3种方法均可有效评估声源数目。本研究对于模态阶数选择、系统复杂度分析以及基于机械系统信号源分离的状态监测与故障诊断具有学术意义和工程应用价值。
To effectively evaluate the source number of mechanical systems from the measured mixed signals, and solve the calculating difficulty of BIC for large data points, three information criterion？？based source number estimation methods, Akaike information criterion (AIC), minimum description length (MDL), and Bayesian information criterion (BIC), are comparatively studied and an improved BIC, named IBIC, is proposed following an exponential function modification, which transforms the multi？？parameter exponential calculating to multiplications. Without decreasing the accuracy, IBIC obviously improves the calculating efficiency and engineering application performances. The numerical case study results show that AIC and MDL obtain the similar performances on source number estimation, and they are both very sensitive to the nonlinear modulation effects. In respect to signal energy ratios, the proposed method has a robustness tolerance on nonlinear modulation effects for 5.15％, which is higher than that of AIC (0.07％) and MDL (0.08％). The results of source number estimation for acoustical signals of a test bed with shell structures show that all the three methods are effective for the given acoustical signals. This work benefits model order selection, complexity analysis of a system, and applications of source separation to mechanical systems for the condition monitoring and fault diagnosis purposes