Application of the bootstrap to the analysis of vibration test data

Structural dynamic testing is concerned with estimation of system properties, including frequency response functions and modal characteristics. These properties are derived from tests on the structure of interest, during which excitations and responses are measured and Fourier techniques are used to reduce the data. The inputs used in a test are frequently radom and excite random responses in the structure of interest. When these random inputs and responses are analyzed they yield estimates of system properties that are random variable and random process realizations. Of course, such estimates of system properties vary randomly from one test to another, but even when deterministic inputs are used to excite a structure, the estimated properties vary from test to test. When test excitations and responses are normally distributed, classical techniques permit us to statistically analyze inputs, responses, and system parameters. However, when the input excitations are non-normal, the system is nonlinear, and/or the property of interest is anything but the simplest, the classical analyses break down. The bootstrap is a technique for the statistical analysis of data that are not necessarily normally distributed. It can be used to statistically analyze any measure of input excitation on response, or any system property, when data are available to make an estimate. It is designed to estimate the standard error, bias, and confidence intervals of parameter estimates. This paper shows how the bootstrap can be applied to the statistical analysis of modal parameters