PSI - Issue 37

Elizabeth K. Ervin et al. / Procedia Structural Integrity 37 (2022) 6–16 Ervin and Zeng / Structural Integrity Procedia 00 (2021) 000 – 000

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i In the second step, the collected time history data from the first step is input to the modal analysis package of the SHE™ program. The package assists the user to identify the structure’s dynamic properties of natural frequencies and mode shapes from frequency response functions. This is independently performed for both states, undamaged or damaged(*). The package then helps the user match modes for the two states of the structure. x ¨ i ( t ) and x ¨ ∗ ( t ) in Figure 1 represent the structure’s measured responses as accelerations in two states, respectively. The third step utilizes dynamic modal properties of the two states to generate DIs. Here, the two mode sets should be matched by carefully comparing mode shapes between states. The comparison of mode shapes is currently subjective, but the uncertainty caused by subjectivity decreases with practice. General mode shape patterns, i.e. bending, torsion, and axial, can assist user to identify the presence of characteristic modes. With the modes matched, the DI calculation package generates the DSFs and then calculates the 51 directional DIs (seventeen in each cardinal direction). Along with the natural frequencies and mode shapes, these uni-axial DIs are used to generate the 24 combined DIs in Table 1. In the fourth step, the GA package of SHE™ uses the normalized resultant DIs along with a binary target vector to optimize the damage detection result. The target vector consists of suspected damage state of each measured location inside the structure, which may be unknown. GA then searches for an optimized combination of weighted DIs until one of the stopping criteria is met. The threshold of effective weight co efficie nt is an open issue so the GA process is repeated three times to check for any lesser but significant DI. Those DIs with weight co efficie nt greater than 0.2 are considered effective DIs. For each GA interaction, DIs with co efficie nt greater than 0.2 are output along with the optimized damage detection result. All remaining non-selected indices are recombined and again input to the GA program for the next iteration. After the three rounds, the GA processing stops, and the co efficie nts of effective DIs are stored. The fifth step visualizes the results for a user. The optimized result in the first iteration is regarded as the best fit of all DIs since it provides the minimum objective function value. Since the weight co efficie nt α i indicates the participation of each DI i , the best-fit result of the optimized damage detection can then be plotted. A sketch of a frame structure with colored nodes is shown in Figure 1, and nodal change is color-coded. Damage location and severity are revealed by high relative values (black and red, darker gradation) in the optimized detection result. status by trying different values for the α i co efficie nts. The residual error of damage localization is | P − T | where T denotes a m × 1 target vector that represents a suspected damage state. Each value of T also ranges from 0 to 1, representing the possibility of damage. The objective function can then be formulated as ( ) ( ) ( ) ( )   ( ) 2 2 1 2 minimize = 1 1 subjective to , , , 0 1 1, 2, 3, , n Objective n n i n      −  + +  −          =   = α ȋ͹Ȍ The GA program herein employs SHE™ with MATLAB ® Global Optimization Toolbox. The GA output is the best-fit weight co efficie nts, which indicates each DI’s effectiveness in damage detection for those specific data sets. The optimized damage detection result will be quantified as severity using Equation (7) along with these best-fit weight co efficie nts. Then the locations are extracted from the m matrix terms. Figure 1 presents the detailed procedure of the optimization methodology for damage detection in any structure. The overall procedure consists of five main steps, titled in boldface and illustrated by dashed boxes. The computational tool is SHE™ program, consisting of three parts: the modal analysis package, DI calculation package, and GA processing package. Each of the three packages is utilized at different steps in the procedure. The first step involves obtaining dynamic responses of a structure, preferably low-frequency civil infrastructure. Measured responses are recommended to be tri-axial, so a structure with m sensor nodes would have 3 m data channels. Time histories of measured responses can be either synchronous or asynchronous since only frequency domain information is mined. Synchronous measurements require the same number of sensors as nodes and is thus inefficient, but asynchronous measurement permits an inspector to install sensor(s) at selected nodes sequentially. As two data sets are compared, the first step should be repeated at least twice to acquire the structure’s responses at different states (e.g. baseline and subsequent inspections, pre- and post-event, as-built and aged).