Bridge Monitoring with Harmonic Excitation and Principal Component Analysis

Principal Component Analysis is used for damage detection in structures excited by harmonic forces. Time responses are directly analysed by Singular Value Decomposition to deduct two dominant Proper Orthogonal Values corresponding to two Proper Orthogonal Modes. Damage index is defined by the concept of subspace angle that a subspace is built from the two Proper Orthogonal Modes. A subspace angle reflects the coherence between two different structural health states. An example is given through the application on a part of a real prestressed concrete bridge in Luxembourg where different damage states were created by cutting a number of prestressed tendons in four scenarios with increasing levels. Results are better by using excitation frequency close to an eigenfrequency of the structure. The technique is convenient for practical application in operational bridge structures.

Identification of damage-expected members of truss structures using frequency response function

A damaged member in a truss structure leads to a variation in the initial responses of its adjacent members. A flexibility-based approach extracting from the modal data should be implemented as one of the structural damage detection methods. The frequency response function data as dynamic measurements provide more information on the system characteristics compared with modal data. Proper orthogonal modes from the frequency response functions extracted in the given frequency ranges and their modified forms can be utilized as damage indices to detect damages. This study considers damage detection of a truss structure using a frequency response function–based approach transformed to the proper orthogonal modes and a flexibility-based approach using the first few modal data for undamaged and damaged states. The utilization of these two methods is compared through numerical experiments on truss structures. The methods can rarely detect the damaged member accurately, but a group of damage-expected members is detected despite the existence of external noise. It is shown that the frequency response function–based approach can be utilized more explicitly than the flexibility-based approach.

Proper Orthogonal Decomposition of Tapping Microcantilevers in Liquid Atomic Force Microscopy

The modal decomposition of tapping mode atomic force microscopy microcantilevers in liquid environments was studied experimentally. Microcantilevers with different lengths and stiffnesses and two sample surfaces with different elastic moduli were used in the experiment. The response modes of the microcantilevers were extracted as proper orthogonal modes through proper orthogonal decomposition. Smooth orthogonal decomposition was used to estimate the resonance frequency directly. The effects of the tapping setpoint and the elastic modulus of the sample under test were examined in terms of their multi-mode responses with proper orthogonal modes, proper orthogonal values, smooth orthogonal modes and smooth orthogonal values. Regardless of the stiffness of the microcantilever under test, the first mode was dominant in tapping mode atomic force microscopy under normal operating conditions. However, at lower tapping setpoints, the flexible microcantilever showed modal distortion and noise near the tip when tapping on a hard sample. The stiff microcantilever had a higher mode effect on a soft sample at lower tapping setpoints. Modal decomposition for tapping mode atomic force microscopy can thus be used to estimate the characteristics of samples in liquid environments.

Choice of Measurement Locations of Nonlinear Structures Using Proper Orthogonal Modes and Effective Independence Distribution Vector

This paper proposes a methodology to automatically choose the measurement locations of a nonlinear structure/equipment that needs to be monitored while operating. The response of the computational model (or experimental data) is used to construct the proper orthogonal modes applying the proper orthogonal decomposition (POD), and the effective independence distribution vector (EIDV) procedure is employed to eliminate, iteratively, locations that contribute less for the independence of the target proper orthogonal modes.