27 Damage Detection Using Derringer’s Function based Weighted Model Updating Method 245 Evaluate error indices Obtain structural dynamic results for updated FE model Use updating parameters to obtain an updated FE model Find updating parameters corresponding to the maximum value of ODF Have all IDFs attained or exceeded their desired value? Locate maximum value of ODF and corresponding values of all IDFs Form ODF by giving equal relative importance to all IDFs Define IDFs using Derringer’s function approach Are RS models adequate? Check adequacy of RS models Develop RS models for all response variables by using regression analysis Develop experimental design matrix and results for response variables Generate initial FE results and SE results Increase relative importance of those IDFs who have not attained desired level Form new ODF Improve RS models No Yes No Yes Fig. 27.1 Algorithm for Derringer’s function based weighted FEMU method 27.2.4 Weighted Model Updating using Derringer’s Function based Updating Method In this paper model updating method of Sehgal and Kumar [20] is used in a damage detection application where all modes of vibration are not equally important. Figure 27.1 shows the algorithm of Derringer’s function based weighted FEMU method. First step in the proposed model updating technique is to generate initial FE and SE results. If experimental set-up is available then SE results can be better replaced by actual experimental results. After that experimental design matrix is formed as per central composite design method. Experimental design matrix is then used to produce corresponding data set for response variables. This data set is then used for developing response surfaces for all response variables such as natural frequencies and Modal Assurance Criterion (MAC) values by regression analysis. Response surface models are then checked for their accuracy and significance by using ANalysis Of VAriance (ANOVA) method. If RS models are not good enough then these are to be modified and checked again for their adequacy. After achieving adequate RS models for all response variables, individual desirability functions are formulated using Derringer’s function approach. Individual desirability functions for natural frequencies and MAC values are of the type “Target” and “Maximum” respectively due to their different nature.
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