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

8

3

damage extent. The DIs capture correlations to structural property change by feature recognition and mathematical methods. A comprehensive periodic inspection software package Structural Health Ev aluation™ (SHE™) has been created in the Multi-Function Dynamics Laboratory (MFDL) at the University of Mississippi. This health evaluation software utilizes data from vibration tests on structures. Modal analysis is employed to extract the structure’s modal properties using the time histories of responses; note that no structure modeling is required. Several DSFs are then calculated to compare two states, revealing damage location and severity. The DSFs are further processed to generate multiple DIs for damage localization and severity quantification. The novel GA based scheme presented herein then combines multiple DIs into a single detection vector that is more robust and accurate than individual DIs. Thus, SHE™ provides quantitative results of damage detection while visual inspection can only present qualitative measurements. Since mode shapes are used, health evaluation can provide a global assessment on structural health condition [Worley and Ervin (2017)]. Program inputs can be time history data from experiments or modal data, i.e. mode shapes and modal frequencies, generated by numerical FE software. Two sources are required: (1) a baseline, undamaged, or as-built case and (2) an aged, damaged, or post-event case. With matched mode shapes and modal frequencies, several modal property-based DIs can be calculated. The output are the values of each index as visualized using five colors: green, blue, magenta, red and black which indicate increasing damage severity. Figure 3 shows the color code. Values for a DI greater than 90% of the most damaged value are colored in black (or darkest gradation). Values greater than 70 to 90% of the most damaged value are colored in red. Values greater than 50 to 70% are colored in magenta. Values between 30 to 50% of the most damage point are colored in blue. Finally, values less than 30% are categorized as least damaged and colored in green (or lightest gradation). Note that the selection of thresholds is arbitrary based upon experience. 2.1. Damage sensitive features and damage indices To mathematically define a DSF, consider a structure has m measured sensor nodes and n identified modes. If the ith natural frequency is denoted as ωi , the ith mode shape can be expressed in the vector form as 1 2 , , , 1, 2, i i i im for i n       = =   ȋͳȌ where ϕ ij is the modal displacement at the jth node in the ith mode. The mode shape sets themselves act as a DSF since damage often directly alters deflections. However, more sensitive features are required for cases of noise and small changes. Modal flexibility is a widely accepted damage indicator that utilizes natural frequencies and mode shapes. A proportional flexibility matrix can be determined by the relationship 1 T 2 1 1 n i i i i  − = =   =    F ȋʹȌ where F is the proportional flexibility matrix, Φ = [Φ1 , Φ2 , · · · , Φn ] is the mode shape matrix, and Ω = diag(ω2) is a n × n diagonal frequency matrix in which the ith diagonal term is the square of the ith natural frequency [Moragaspitiya et al. (2013)]. Note that this is not the true flexibility as the stiffness matrix (and its inverse) are unknown. The curvature of a mode shape is its second derivative and has also been widely used as a DSF. When most kinds of damage occur, increased modal curvature is expected due to the loss of stiffness. Modal curvature can be calculated at discrete mode shape points using the central difference approximation as Pandey et al. (1991) used: ( ) ( ) 1 1 1 2 2 ij i j i j ij h h     + − − + = ȋ͵Ȍ