The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic ba...

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Veröffentlicht in:Journal of sound and vibration Jg. 425; S. 301 - 323
Hauptverfasser: Liao, Haitao, Wu, Wenwang, Fang, Daining
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Ltd 07.07.2018
Elsevier Science Ltd
Schlagworte:
Computer programming
Condensation
Harmonic balance method
Maratos effect
Mathematical analysis
Matrix methods
Nonlinear response
Nonlinear systems
Optimization
Periodic solution
Quadratic programming
Reduced SQP method
Worst case resonance
Maratos effect
Periodic solution
Reduced SQP method
Worst case resonance
Harmonic balance method
ISSN:0022-460X, 1095-8568
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Zusammenfassung:A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.
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ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2017.12.020