模态测试不确定性影响因素分析及传感器布置应用

模态测试结果的准确性会受测试数据采集、数据处理、建模假设和参数估计等不确定性因素的影响. 为研究模态测试中模态参数的不确定性水平及不同影响因素对其的影响规律,本文采用状态空间模型和费希尔信息矩阵的快速模态参数不确定性分析方法,探讨包括振动信号的采样时长、采样频率、采样信噪比和结构的阻尼比等多种因素对模态参数不确定性水平的影响,同时提出利用模态参数不确定性水平来优化传感器布置策略的实用性建议. 结果表明：模态参数的不确定性水平随采样时长、采样频率、信噪比和传感器数量的增加而降低,随结构阻尼比的增大而升高;对于均匀分布结构,多数传感器布置在结构顶部和中上部,少数布置在中下部时,模态参数的整体不确定性水平较低,是一种相对较优的传感器布置方案.

Analysis of Influencing Factors on Uncertainty in Modal Testing and its Application on Sensor Layout Scheme

The accuracy of modal test results is affected by uncertain influencing factors such as data acquisition, data processing, and parameter estimation. To study the uncertainty levels of modal parameters and their behaviors under different influencing factors in modal testing, a fast uncertainty quantification analysis method based on the state space model and Fisher information matrix （FIM） is adopted. The influence of multiple factors including data duration, sampling frequency, signal-to-noise ratio, and damping ratio of vibration signal on the uncertainty levels of modal parameters is discussed, and a practical way for optimizing the sensor layout scheme through uncertainty analysis is proposed. Results show that the uncertainty level of modal parameters decreases with the increase of data duration, sampling frequency, signal-to-noise ratio, and the number of sensors, and increases with the increase of damping ratio; for uniformly distributed structures, the majority of the sensors at the upper and middle region of the structure and only a few at the lower region is a preferred sensor layout scheme with small overall uncertainty of modal parameters.