Nonparametric statistical formulations for structural health monitoring

•Statistical structural health monitoring using nonparametric techniques.•Capacity to utilize both time-domain and frequency-domain data characteristics.•Monitoring damage occurring at multiple locations.•Monitoring the change in the boundary conditions of a structure.•An open-ended structural health monitoring framework facilitating further enrichment. This paper presents a group of nonparametric statistical formulations for structural health monitoring (SHM). Vibration response data are first represented by the coefficients of a series of fitted autoregressive (AR) models in the time domain or by the averages of binned power spectral density (PSD) estimates in the frequency domain. Three types of statistical hypotheses are then formulated and tested by nonparametric techniques to monitor these characteristics. Specifically, two-sample Kolmogorov–Smirnov test, Mann–Whitney test, and Mood test are used in this study. For each type of hypothesis formulation, a function of the resulting P-values is used to define a damage indicator profile (DIP) whereby damage locations are identified. The highlight of these formulations is that, due to their nonparametric nature, they do not require a particular functional form for the probability distribution of the underlying population of an extracted vibration response data characteristic. Two numerically simulated case studies, i.e., a 20-degree-of-freedom system and a hyperbolic paraboloid roof shell, demonstrate the efficacy of the proposed nonparametric SHM formulations. Multiple damage locations are also considered in the case studies.