• Earthquakes and Structures
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• v.9 no.5
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• pp.937-956
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• 2015

Seismic isolation systems decouple structures from ground motions to protect them from seismic events. Seismic isolation devices have been implemented in many full-scale buildings and bridges because of their simplicity, economic effectiveness, inherent stability, and reliability. It is well known that the most uncertain aspect for obtaining the accurate responses of an isolated structure from seismic events is the seismic loading itself. It is needed to know the seismic response distributions of the isolated structure resulting from the randomness of earthquakes when probabilistic designing or probabilistic evaluating an isolated structure. Earthquake time histories are useful and often an essential element for designing or evaluating isolated structures. However, it is very challenging to gather the design and evaluation information for an isolated structure from many seismic analyses. In order to evaluate the seismic performance of an isolated structure, numerous nonlinear dynamic analyses need to be performed, but this is impractical. In this paper, the concept of the stochastic response database (SRD) is defined to obtain the seismic response distributions of an isolated structure instantaneously, thereby significantly reducing the computational efforts. An equivalent model of the isolated structure is also developed to improve the applicability and practicality of the SRD. The effectiveness of the proposed methodology is numerically verified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.296-309
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• 2022

Timer options are one of the contingent claims that, for given the variance budget, its payoff depends on a random maturity in terms of the realized variance unlike the standard European vanilla option with a fixed time maturity. Since it was first launched by Société Générale Corporate and Investment Banking in 2007, the valuation of the timer options under several stochastic environment for the volatility has been conducted by many researches. In this study, we propose the pricing of timer power options combined with standard timer options and the index of the power to the underlying asset for the investors to actualize lower risks and higher returns at the same time under the uncertain markets. By using the asymptotic analysis, we obtain the first-order approximation of timer power options. Moreover, we demonstrate that our solution has been derived accurately by comparing it with the solution from the Monte-Carlo method. Finally, we analyze the impact of the stochastic volatility with regards to various parameters on the timer power options numerically.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.171-171
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• 2020

Decision making strategies should consider both adaptiveness and robustness in order to deal with two main characteristics of climate change: non-stationarity and deep uncertainty. Especially, robust strategies are different from traditional optimal strategies in the sense that they are satisfactory over a wider range of uncertainty and may act as a key when confronting climate change. In this study, a new framework named Robust Stochastic Dynamic Programming (R-SDP) is proposed, which couples previously developed robust optimization (RO) into the objective function and constraint of SDP. Two main approaches of RO, feasibility robustness and solution robustness, are considered in the optimization algorithm and consequently, three models to be tested are developed: conventional-SDP (CSDP), R-SDP-Feasibility (RSDP-F), and R-SDP-Solution (RSDP-S). The developed models were used to derive optimal monthly release rules in a single reservoir, and multiple simulations of the derived monthly policy under inflow scenarios with varying mean and standard deviations are undergone. Simulation results were then evaluated with a wide range of evaluation metrics from reliability, resiliency, vulnerability to additional robustness measures. Evaluation results were finally visualized with advanced visualization tools that are used in multi-objective robust decision making (MORDM) framework. As a result, RSDP-F and RSDP-S models yielded more risk averse, or conservative, results than the CSDP model, and a trade-off relationship between traditional and robustness metrics was discovered.

• Steel and Composite Structures
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• v.44 no.5
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• pp.651-676
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• 2022

Most of the experimental, theoretical, and numerical studies on the stability of functionally graded composites are deterministic, while there are full of complex interactions of variables with an inherently probabilistic nature, this paper presents a non-intrusive framework to investigate the stochastic nonlinear buckling behaviors of porous functionally graded cylindrical shells exposed to inevitable source-uncertainties. Euler-Lagrange equations are theoretically derived based on the three variable refined shear deformation theory. Closed-form solutions for the shell buckling loads are achieved by solving the deterministic eigenvalue problems. The analytical results are verified with numerical results obtained from finite element analyses that are conducted in the commercial software ABAQUS. The non-intrusive framework is completed by integrating the Monte Carlo simulation with the verified closed-form solutions. The convergence studies are performed to determine the effective pseudorandom draws of the simulation. The accuracy and efficiency of the framework are verified with statistical results that are obtained from the first and second-order perturbation techniques. Eleven cases of individual and compound uncertainties are investigated. Sensitivity analyses are conducted to figure out the five cases that have profound perturbative effects on the shell buckling loads. Complete probability distributions of the first three critical buckling loads are completely presented for each profound uncertainty case. The effects of the shell thickness, volume fraction index, and stochasticity degree on the shell buckling load under compound uncertainties are studied. There is a high probability that the shell has non-unique buckling modes in stochastic environments, which should be known for reliable analysis and design of engineering structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.537-549
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• 2001

The effect of partially restrained(PR) connections and the uncertainties in them on the reliability of steel frames subjected to seismic loading is addressed. A stochastic finite element method(SFEM) is proposed combining the concepts of the response surface method(RSM), the finite element method(FEM), the first-order reliability method (FORM), and the iterative linear interpolation scheme. The behavior of PR connections is captured using moment-relative rotation curves, and is represented by the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The seismic loading is applied in the time domain for realistic representation. The reliability of steel frames in the presence of PR connections is calculated considering all major sources of nonlinearity. The algorithm is clarified with the help of an example.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.5
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• pp.463-469
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• 2016

In this study, a virtual specimen with a linear continuous gradient of void ratio (FGM: Functional Graded Material) is constructed using low-order probability functions of two real cement paste specimens. Two real specimens with difference void ratios are taken from X-ray CT to construct the virtual specimen. A virtual specimen with a gradient void distribution, whose average void ratio is between void ratios of two homogeneous real specimens, is constructed using a stochastic optimization approach. The void ratio distribution is assumed to be linear, and continuously varies in the vertical direction. In this study, a gradient term of void ratio is incorporated into the objective function as well as low-order probability functions from the previous research. To confirm the effect of gradient void distribution on the material response, air permeability is evaluated using finite element analysis. The analysis results are compared with experimental results, and confirm the effect of gradient void distribution on permeability.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.813-826
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• 2015

This research deals with an estimation method for kinetic reaction model. The kinetic reaction model is a model to explain spread or changing process based on interaction between species on the Biochemical area. This model can be applied to a model for disease spreading as well as a model for system Biology. In the search, we assumed that the spread of species is stochastic and we construct the reaction model based on stochastic movement. We utilized Gillespie algorithm in order to construct likelihood function. We introduced a Bayesian estimation method using Markov chain Monte Carlo methods that produces more stable results. We applied the Bayesian estimation method to the Lotka-Volterra model and gene transcription model and had more stable estimation results.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.33 no.2
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• pp.123-129
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• 2015

The Kalman filter has been widely used in the kinematic GPS positioning due to its flexibility and efficiency in computational points of view. At the same time, the relative positioning technique also provided the high precision positioning results by removing the systematic errors in the measurements significantly. However, the positioning quality may be degraded following to longer in baseline length. For this case, it is required that the remaining atmospheric effects, such as double-difference ionospheric delay and zenith wet delay, should be properly modeled by examining the characteristics of the stochastic processes. In general, atmospheric effects are estimated with the assumption of random walk, or the first-order Gauss-Markov stochastic process, which requires the precise modeling on the corresponding process noises. Therefore, we determined and provided the parameters for modelling the process noises for atmospheric effects. The auto-correlation functions are empirically determined at first, and then the parameters are extracted from the empirical auto-correlation function. In fact, the test results can be either applied directly, or used as guidance values for the modeling of process noises in the kinematic GPS positioning.

• Water for future
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• v.28 no.2
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• pp.169-180
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• 1995

The cost of a looped pipe network is affected by a set of loop flows. The mathematical model for optimizing the looped pipe network is expressed in the optimal set of loop flows to apply to a stochastic optimization method. Because the feasible region of the looped pipe network problem is nonconvex with multiple local optima, the Modified Stochastic Probing Method is suggested to efficiently search the feasible region. The method consists of two phase: i) a global search phase(the stochastic probing method) and ii) a local search phase(the nearest neighbor method). While the global search sequentially improves a local minimum, the local search escapes out of a local minimum trapped in the global search phase and also refines a final solution. In order to test the method, a standard test problem from the literature is considered for the optimal design of the paralled expansion of an existing network. The optimal solutions thus found have significantly smaller costs than the ones reported previously by other researchers.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.2
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• pp.1-13
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• 2010

This paper proposes an optimal design method for the nonlinear seismic isolated bridge. The probabilities of failure at the pier and the seismic isolator are considered as objective functions for optimal design, and a multi-objective optimization technique is employed to efficiently explore a set of multiple solutions optimizing mutually-conflicting objective functions at the same time. In addition, a stochastic linearization method is incorporated into the multi-objective optimization framework in order to effectively estimate the stochastic responses of the bridge without performing numerous nonlinear time history analyses during the optimization process. As a numerical example to demonstrate the efficiency of the proposed method, the Nam-Han river bridge is taken into account, and the proposed method and the existing life-cycle-cost based design method are both applied for the purpose of comparing their seismic performances. The comparative results demonstrate that the proposed method not only shows better seismic performance but also is more economical than the existing cost-based design method. The proposed method is also proven to guarantee improved performance under variations in seismic intensity, in bandwidth and in the predominant frequency of the seismic event.