Statistical moments of autoregressive model residuals for damage localisation

Abstract

Monitoring structural health is a problem with significant importance in the world today. Aging civil infrastructure and aircraft fleets have made non-destructive evaluation an important research topic. Non-destructive techniques based on dynamic signatures have struggled to gain widespread acceptance due to the perceived difficulty in applying these methods, as well as the mixed results they can produce. A simple and reliable method that is useful without in-depth knowledge of the structure is necessary to transition dynamic response-based health monitoring into the industrial mainstream.Modal parameters, including shifting frequencies, damping ratios, and mode shapes have received considerable attention as damage indicators. The results have been mixed and require an expert to carry out the testing and interpretation. Detailed knowledge of the structure before it becomes damaged is required, either in the form of experimental data or an analytical model.A method based on vector autoregressive (ARV) models is proposed. These models accurately capture the predictable dynamics present in the response. They leave the unpredictable portion, including the component resulting from unmeasured input shocks, in the residual.An estimate of the autoregressive model residual series standard deviation provides an accurate diagnosis of damage conditions. Additionally, a repeatable threshold level that separates damaged from undamaged is identified, indicating the possibility of damage identification and localisation without explicit knowledge of the undamaged structure. Similar statistical analysis applied to the raw data necessitates the use of higher-order moments that are more sensitive to disguised outliers, but are also prone to false indications resulting from overemphasising rarely occurring extreme values.Results are included from data collected using an eight-degree of freedom damage simulation test-bed, built and tested at Los Alamos National Laboratory (LANL). Confidence bounds on each moment are computed for the available data sets and are included to illustrate “significant” differences.