Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

Time Series Analysis for Vibration-Based Structural Health Monitoring:A Review

Structural health monitoring(SHM)is a vast,interdisciplinary research field whose literature spans several decades with focusing on condition assessment of different types of structures including aerospace,mechanical and civil structures.The need for quantitative global damage detection methods that can be applied to complex structures has led to vibration-based inspection.Statistical time series methods for SHM form an important and rapidly evolving category within the broader vibration-based methods.In the literature on the structural damage detection,many time series-based methods have been proposed.When a considered time series model approximates the vibration response of a structure and model coefficients or residual error are obtained,any deviations in these coefficients or residual error can be inferred as an indication of a change or damage in the structure.Depending on the technique employed,various damage sensitive features have been proposed to capture the deviations.This paper reviews the application of time series analysis for SHM.The different types of time series analysis are described,and the basic principles are explained in detail.Then,the literature is reviewed based on how a damage sensitive feature is formed.In addition,some investigations that have attempted to modify and/or combine time series analysis with other approaches for better damage identification are presented.

Feature Preserving Mesh Simplification Using Feature Sensitive Metric

We present a new method for feature preserving mesh simplification based on feature sensitive （FS） metric. Previous quadric error based approach is extended to a high-dimensional FS space so as to measure the geometric distance together with normal deviation. As the normal direction of a surface point is uniquely determined by the position in Euclidian space, we employ a two-step linear optimization scheme to efficiently derive the constrained optimal target point. We demonstrate that our algorithm can preserve features more precisely under the global geometric properties, and can naturally retain more triangular patches on the feature regions without special feature detection procedure during the simplification process. Taking the advantage of the blow-up phenomenon in FS space, we design an error weight that can produce more suitable results. We also show that Hausdorff distance is markedly reduced during FS simplification.