Research Papers

Multi-Objective Model Updating Optimization Considering Orthogonality

[+] Author and Article Information
Braden T. Warwick

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: braden.warwick@queensu.ca

Il Yong Kim

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: kimiy@queensu.ca

Chris K. Mechefske

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: chris.mechefske@queensu.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 22, 2018; final manuscript received February 28, 2019; published online April 8, 2019. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 14(6), 061009 (Apr 08, 2019) (11 pages) Paper No: CND-18-1525; doi: 10.1115/1.4043086 History: Received November 22, 2018; Revised February 28, 2019

The coordinate orthogonality check (CORTHOG) and multi-objective optimization considering pseudo-orthogonality as an objective function are introduced to overcome several limitations present in current model updating methods. It was observed that the use of the CORTHOG to remove four inaccurate degrees-of-freedom (DOF) was able to increase the orthogonality between mode shape vectors. The multi-objective model updating process generated a Pareto front with 38 unique optimal solutions. Four critical points were identified along the Pareto front, of which decreased the natural frequency error by greater than 2.84% and further increased the orthogonality between mode shape vectors. Therefore, it has been demonstrated that both steps of the methodology are critical to significantly reduce the overall errors of the system and to generate a finite element (FE) model that best describes physical reality. Additionally, the methodology introduced in this work generated a feasible computational runtime allowing for it to be easily adapted to widespread applications.

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Avitabile, P. , and Pechinsky, F. , 1998, “ The Coordinate Orthogonality Check (CORTHOG),” Mech. Syst. Signal Process., 12(3), pp. 395–414. [CrossRef]
Allemang, R. J. , 2003, “ The Modal Assurance Criterion Twenty Years of Use and Abuse,” J. Sound Vib., 37(8), pp. 14–23.
Imregun, M. , and Visser, W. J. , 1991, “ A Review of Model Updating Techniques,” Shock Vib. Dig., 23(1), pp. 9–20. [CrossRef]
Mottershead, J. E. , and Friswell, M. I. , 1993, “ Model Updating in Structural Dynamics: A Survey,” J. Sound Vib., 167(2), pp. 347–375. [CrossRef]
Friswell, M. , and Mottershead, J. E. , 2013, Finite Element Model Updating in Structural Dynamics, Vol. 38, Springer, Berlin.
Ewins, D. J. , 2000, Modal Testing: Theory and Practice, Vol. 2, Research Studies Press, Letchworth, UK.
MathWorks, 2017, MatLab Programming Fundamentals, The MathWorks, Natick, MA.
Mottershead, J. E. , Link, M. , and Friswell, M. I. , 2011, “ The Sensitivity Method in Finite Element Model Updating: A Tutorial,” J. Mech. Syst. Signal Process., 25(7), pp. 2275–2296. [CrossRef]
Modak, S. V. , Kundra, T. K. , and Nakra, B. C. , 2000, “ Model Updating Using Constrained Optimization,” J. Mech. Res. Commun., 27(5), pp. 543–551. [CrossRef]
Sehgal, S. , and Kumar, H. , 2016, “ Structural Dynamic Model Updating Techniques: A State of the Art Review,” Arch. Comput. Methods Eng., 23(3), pp. 515–533. [CrossRef]
Modak, S. V. , 2014, “ Model Updating Using Uncorrelated Modes,” J. Sound Vib., 333(11), pp. 2297–2322. [CrossRef]
Messac, A. , and Mattson, C. A. , 2002, “ Generating Well-Distributed Sets of Pareto Points for Engineering Design Using Physical Programming,” Optim. Eng., 3(4), pp. 431–450. [CrossRef]
Das, I. , and Dennis, J. E. , 1997, “ A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems,” Struct. Optim., 14(1), pp. 63–69. [CrossRef]
Koski, J. , 1985, “ Defectiveness of Weighting Method in Multi-Criterion Optimization of Structures,” Numer. Methods Biomed. Eng., 1(6), pp. 333–337.
Kim, I. Y. , and De Weck, O. L. , 2005, “ Adaptive Weighted-Sum Method for Bi-Objective Optimization: Pareto Front Generation,” Struct. Multidiscip. Optim., 29(2), pp. 149–158. [CrossRef]
Kim, G. , and Park, Y. S. , 2014, “ An Improved Procedure for Updating Finite Element Model Based on an Interactive Multiobjective Programming,” Mech. Syst. Signal Process., 43(1–2), pp. 260–271. [CrossRef]
Nakayama, H. , and Furukawa, K. , 1985, “ Satisficing Trade-Off Method With an Application to Multiobjective Structural Design,” Large Scale Syst., 8, pp. 47–57.
Nakayama, H. , 1999, Advances in Multicriteria Analysis: Aspiration Level Approach to Interactive Multi-Objective Programming and Its Applications, Kluwer Academic, Boston, MA.
Nakayama, H. , 1992, “ Trade-Off Analysis Using Parametric Optimization Techniques,” Eur. J. Oper. Res., 60(1), pp. 87–98. [CrossRef]
Konak, A. , Coit, D. W. , and Smith, A. E. , 2006, “ Multi-Objective Optimization Using Genetic Algorithms: A Tutorial,” Reliab. Eng. Syst. Saf., 91(9), pp. 992–1007. [CrossRef]
Deb, K. , 2014, “ Multi-Objective Optimization,” Search Methodologies, Springer, Boston, MA.
Deb, K. , 2001, Multi-Objective Optimization Using Evolutionary Algorithms, Vol. 16, Wiley, Hoboken, NJ.
Goldberg, D. E. , 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Boston, MA.
Kim, I. Y. , and de Weck, O. L. , 2005, “ Variable Chromosome Length Genetic Algorithm for Progressive Refinement in Topology Optimization,” Struct. Multidiscip. Optim., 26(9), pp. 445–456. [CrossRef]
Kim, G. H. , and Park, Y. S. , 2004, “ An Improved Updating Parameter Selection Method and Finite Element Model Update Using Multiobjective Optimization Technique,” J. Mech. Syst. Signal Process., 18(1), pp. 59–78. [CrossRef]
Cheng, F. Y. , and Li, D. , 1998, “ Genetic Algorithm Development for Multiobjective Optimisation of Structures,” AIAA J., 36(6), pp. 1105–1112. [CrossRef]
Christodoulou, K. , Ntotsios, E. , Papadimitriou, C. , and Panetsos, P. , 2008, “ Structural Model Updating and Prediction Variability Using Pareto Optimal Models,” Comput. Methods Appl. Mech. Eng., 198, pp. 18–149. [CrossRef]
Jaishi, B. , and Ren, W. X. , 2007, “ Finite Element Model Updating Based on Eigenvalue and Strain Energy Residuals Using Multiobjective Optimization Technique,” Mech. Syst. Signal Process., 21(5), pp. 2295–2317. [CrossRef]
Jin, S. S. , Cho, S. , Jung, H. J. , Lee, J. J. , and Yun, C. B. , 2014, “ A New Multi-Objective Approach to Finite Element Model Updating,” J. Sound Vib., 333(11), pp. 2323–2338. [CrossRef]
Deb, K. , and Gupta, S. , 2011, “ Understanding Knee Point in Bi-Criteria Problems and Their Implications as Preferred Solution Principles,” Eng. Optim., 43(11), pp. 1175–1204. [CrossRef]
Deb, K. , Pratap, A. , Agarwal, S. , and Meyarivan, T. , 2002, “ A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Duff, I. S. , Grimes, R. G. , and Lewis, J. G. , 1992, Users' Guide for the Harwell-Boeing Sparse Matrix Collection, Rutherford Appleton Library, Didcot, UK, Report No. RAL-92-086.
O'Callahan, J. , Avitabile, P. , and Riemer, R. , 1989, “ System Equivalent Reduction Expansion Process (SEREP),” Seventh International Modal Analysis Conference, Las Vegas, NV, Jan. 30–Feb. 2, pp. 29–37.
Guyan, R. J. , 1965, “ Reduction of Stiffness and Mass Matrices,” AIAA J., 3(2), p. 380. [CrossRef]
Avitabile, P. , Pechinsky, F. , and O'Callahan, J. , 1992, “ Study of Modal Vector Correlation Using Various Techniques for Model Reduction,” International Modal Analysis Conference, San Diego, CA, Feb. 3–7, pp. 572–583.
Avitabile, P. , and Pechinsky, F. , 1994, “ Coordinate Orthogonality Check (CORTHOG),” 12th International Modal Analysis Conference, Honolulu, HI, Jan. 31–Feb. 3, p. 573.
Foster, T. , 1993, “ Evaluation of DOF Selection for Modal Vector Correlation and Expansion Studies,” M.Sc. thesis, University of Massachusetts Lowell, Lowell, MA.
Mains, M. , and Vold, H. , 1995, “ Investigation of the Effects of Transducer Cross-Sensitivity and Misalignment Error on Modal Vector Correlation,” 13th International Modal Analysis Conference, Nashville, TN, Feb. 13–16, pp. 1048–1056.
Avitabile, P. , 2017, Modal Testing: A Practitioner's Guide, Wiley, Hoboken, NJ.
Warwick, B. T. , Kim, I. Y. , and Mechefske, C. K. , 2018, “ Substructuring Verification of a Rear Fuselage Mounted Twin-Engine Aircraft,” J. Aerosp. Sci. Technol. (in press).
Warwick, B. T. , Mechefske, C. K. , and Kim, I. Y. , 2018, “ Effect of Stiffener Configuration on Bulkhead Modal Parameters,” ASME Paper No. DETC2018-85385.
MathWorks, 2016, MatLab Optimization Toolbox—User's Guide, The MathWorks, Natick, MA.


Grahic Jump Location
Fig. 1

Visual representation of the crowding distance for solution x with respect to objectives 1 and 2 (based off Fig. 2(b) in Ref. [20])

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Fig. 2

Experimental setup as used by Warwick et al. [40,41]

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Fig. 3

CORTHOG of the original data set

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Fig. 4

(a) Original POC [40] and (b) post-CORTHOG POC

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Fig. 5

Bend angles of the optimal solutions along the Pareto front

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Fig. 6

Pareto front of optimal solutions

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Fig. 7

Natural frequency correlation for solutions: (a) B1, (b) B2, (c) B3, and (d) B4

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Fig. 8

POC for solutions: (a) B1, (b) B2, (c) B3, and (d) B4



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