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Frequency response function estimation techniques and the corresponding coherence functions: A review and update

机译：频率响应函数估计技术与相应的相容函数：评论和更新

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For a structural dynamics engineer assessing a system's vibration characteristics, the frequency response function (FRF) is indispensable, irrespective of whether the setup being tested is experimental, numerical or analytical. This paper outlines the different FRF estimation techniques that have been developed over the years. Algorithms that compute an ordinary least squares (OLS) estimate of the FRF, assuming uncorrelated measurement noise to be present either on the output (H_1) or the input (H_2) signals, have been compared with those that employ total least squares (TLS) equations by making use of an augmented input-output auto and cross power (G_(FFX)/G_(XFF)) matrix at every frequency such as the H_v (using eigenvalue decomposition) and H_(SV D) (using singular value decomposition) algorithms. Another FRF estimation method based upon Cholesky decomposition (H_(CD)) is also discussed. Further discussion has been included of TLS algorithms computing the FRFs for one output at a time, as historically presented in the development of the H,, algorithm, with a case that evaluates the FRF matrix computed for all the outputs simultaneously. The development of the corresponding coherence functions has been presented, highlighting the method dependent paradigms that led to concepts such as virtual coherence and partial coherence while underscoring their equivalence with ordinary and multiple coherence calculations. It has been shown that some of the existing conditioned coherence metrics are inconsistent from an input-output standpoint, for which the corrected interpretations have been subsequently described. This article is unique in that no previous work summarizes all of the previously developed FRF estimation and coherence algorithms and no previous paper explains the inconsistencies in the conditioned coherence functions with respect to multiple coherence.
机译：对于评估系统的振动特性的结构动力学工程师，频率响应函数（FRF）是不可或缺的，无论是否测试的设置是实验性的，数值还是分析。本文概述了多年来开发的不同FRF估计技术。将假设在输出（H_1）或输入（H_2）信号上的不相关测量噪声的普通最小二乘（OLS）估计计算FRF的算法已经被比较了与采用总至少方块（TLS）的输出（H_1）或输入（H_2）信号通过在每个频率下使用增强的输入输出自动和交叉功率（G_（FFX）/ G_（XFF））矩阵，例如H_V（使用特征值分解）和H_（SV D）（使用奇异值分解）算法。还讨论了基于Cholesky分解（H_（CD））的另一FRF估计方法。在历史上呈现一个输出的TLS算法的进一步讨论已经包括在历史上呈现H ,,算法的开发中，其中同时评估为所有输出计算的FRF矩阵。已经提出了相应的相干功能的发展，突出显示了导致诸如虚拟相干性和部分连贯性等概念的方法，同时突出与普通和多个相干性计算的等效相当。已经表明，一些现有的条件连贯度量来自输入输出的角度不一致，随后已经描述了校正解释。本文是独一无二的，因为之前的工作总结了先前开发的FRF估计和一致性算法，并且没有先前的论文解释了调节相干功能的不一致性相对于多次连贯性。

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