• East Asian mathematical journal
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• 제32권2호
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• pp.193-215
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• 2016

There are three subjects in the study. First, after investigating the development process of the method of infinite descent and the reduction to absurdity, we prove them to be equivalent each other. Second, we apply the method of infinite descent to some problems in textbook and compare it with the reduction to absurdity. Finally, we discuss on teaching proofs with the method of infinite descent.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 춘계 학술발표회 논문집
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• pp.101-108
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• 2002

This paper presents an input and system identification technique for a free-field system using forced vibration data. Identification is carried out on geotechnical experiment site at Yong-jong Island where Inchon International Airport being constructed. The identified quantities are the input load as well as the shear moduli of the free-field soil regions. The dynamic response analysis on the free-field system is carried out using the finite element method incorporating the infinite element formulation fur the unbounded layered soil medium. The criterion function for the parameter estimation is constructed using the frequency response amplitude ratios of the dynamic responses measured at several points of the free-field, so that the information on the input loading may be excluded. The constrained steepest descent method is employed to obtain the revised parameters. The simulated dynamic responses using the identified parameters and input load show excellent agreements with the measured responses.

• 전기학회논문지
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• 제57권6호
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• pp.915-923
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• 2008

This paper focuses on optimal tuning of nonlinear parameters of a dual-input power system stabilizer(dual-input PSS), which can improve the system damping performance immediately following a large disturbance. Until recently, various PSS models have developed to bring stability and reliability to power systems, and some of these models are used in industry applications. However, due to non-smooth nonlinearities from the interaction between linear parameters(gains and time constants of linear controllers) and nonlinear parameters(saturation output limits), the output limit parameters cannot be determined by the conventional tuning methods based on linear analysis. Only ad hoc tuning procedures('trial and error' approach) have been used. Therefore, the steepest descent method is applied to implement the optimal tuning of the nonlinear parameters of the dual-input PSS. The gradient required in this optimization technique can be computed from trajectory sensitivities in hybrid system modeling with the differential-algebraic-impulsive-switched(DAIS) structure. The optimal output limits of the dual-input PSS are evaluated by time-domain simulation in both a single machine infinite bus(SMIB) system and a multi-machine power system in comparison with those of a single-input PSS.