• Title/Summary/Keyword: sensitivity analysis

### Sensitivity Analysis of Stochastic User Equilibrium in a Multi-Modal Network (다수단 확률적 사용자 균형의 민감도 분석)

• Kim, Byeong-Gwan;Im, Yong-Taek
• Journal of Korean Society of Transportation
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• v.28 no.5
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• pp.117-129
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• 2010
• This study presents a sensitivity analysis method for stochastic user equilibrium of multi-modal network flows. We consider a multi-modal network consisting of a road network for passenger cars physically separated from a transit network for public transport. We first establish a sensitivity analysis method with respect to arbitrary link parameters and perform a sensitivity analysis with respect to link capacity and transit line frequency as practical link parameters. Next, We establish a sensitivity analysis method and perform the sensitivity analysis with respect to modal split by passenger car and public transit. As with the elasticity of economics, these results can be important information for analyzing changes in travel behavior due to the changes in operation and policy of transportation facilities, as well as for analyzing the effects of these operational changes and policies. These results also can be utilized as a tool to constitute a multi-modal network design problem by using cooperative game theory.

### Consistent Displacement Load Method for Nonlinear Semi-Analytical Design Sensitivity Analysis (준해석적 비선형 설계민감도를 위한 보정변위하중법)

• Lee, Min-Uk;Yoo, Jung-Hun;Lee, Tae-Hee
• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1209-1216
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• 2005
• Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

### Uncertainty in Sensitivity Analysis of Architectural Design Variables for Heating and Cooling Loads Depending on Usage Scenarios (건물 사용 시나리오에 따른 냉난방 부하 민감도 분석의 불확실성)

• Yoo, Young-Seo;Yi, Dong-Hyuk;Park, Cheol-Soo
• Journal of the Architectural Institute of Korea
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• v.37 no.11
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• pp.247-253
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• 2021
• It has been widely acknowledged that rational decision making at architectural design stage is important for energy efficient building design. In other words, the relationship between building energy use and design variables must be carefully analyzed. For this purpose, the global sensitivity analysis (GSA) can be a useful tool because GSA quantifies the unit change of a model's output against the unit change of the individual model input for the entire input space. With the use of GSA, the influence of each design variable can be quantified in terms of sensitivity index. However, such sensitivity index can be dependent on crude assumptions for building usage scenarios, e.g. occupant density, equipment density, infiltration rate, etc. In general, these parameters are set as deterministic values based on simulationist's subjective judgment, and it can be inferred that this subjective assmptions could cause uncertainty in sensitivity analysis. With this in mind, the authors propose a sensitivity analysis process for building energy design variables considering the uncertainty of building use scenarios. For this purpose, Sobol sensitivity analysis was performed on five design variables (wall U-value, fenestration SHGC, lighting power density, window U-value, window-wall ratio) according to assumptions of five building usage scenarios (occupant density, equipment density, infiltration rate, cooling and heating set-point temperatures). As a result, it is found that uncertainty in the sensitivity of design variables is significant and the sensitivity ranking of the design variables can vary. This indicates that in order to reach rational decision making, careful attention must be paid to selection of uncertain building usage scenarios, and stochastic sensitivity analysis must be employed.

### Sensitivity analysis based on complex variables in FEM for linear structures

• Advances in Computational Design
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• v.4 no.1
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• pp.15-32
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• 2019
• One of the efficient and useful tools to achieve the optimal design of structures is employing the sensitivity analysis in the finite element model. In the numerical optimization process, often the semi-analytical method is used for estimation of derivatives of the objective function with respect to design variables. Numerical methods for calculation of sensitivities are susceptible to the step size in design parameters perturbation and this is one of the great disadvantages of these methods. This article uses complex variables method to calculate the sensitivity analysis and combine it with discrete sensitivity analysis. Finally, it provides a new method to obtain the sensitivity analysis for linear structures. The use of complex variables method for sensitivity analysis has several advantages compared to other numerical methods. Implementing the finite element to calculate first derivatives of sensitivity using this method has no complexity and only requires the change in finite element meshing in the imaginary axis. This means that the real value of coordinates does not change. Second, this method has the lower dependency on the step size. In this research, the process of sensitivity analysis calculation using a finite element model based on complex variables is explained for linear problems, and some examples that have known analytical solution are solved. Results obtained by using the presented method in comparison with exact solution and also finite difference method indicate the excellent efficiency of the proposed method, and it can predict the sustainable and accurate results with the several different step sizes, despite low dependence on step size.

### Estimation of the vibration fatigue of a linear elastic system based on a desiign sensitivity analysis (설계 만감도 해석을 활용한 선형 시스템 진동내구 평가)

• Kim, Chan-Jung;Kim, Ku-Sik;Kang, Ho-Young;Jin, Yeo-Hwa;Lee, Bong-Hyun
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2010.10a
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• pp.491-496
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• 2010
• The direct design modification of problematic component is disallowed in order to sacrifice other major factors such as a stability or a major performance. So, the best design policy is to risvise the immature structural medchanism under the minimal design change as soon as possible. For this paper presents a new design sensitivity analysis based on transmissibility rtio (TR) of response acceleration to find a proper candidate for the minimal design modification. The new sensitivity analysis is based on the fact that the sensitivity of TR over a small design change is inversly proportinal to the magnitude of TR. The theory of proposed design sensitivity analysis is simulated with the variance of TR over a dynamic change. Then, new methodology is appplied for a linear elastic specimen to detect the most sensitive node over a design change using measured accleration data during uni-axial vibration test, The physical verification of the sensitivity method is conducted on the CAE model of a linear elastic specimen by adding concentration mass and the vibration fatigue of the simple specimen is analyzed to estimate the relationship between fatigue behaviors and sensitivity consequences.

### Sensitivity Analysis of Expected Project Completion Time in a PERT Network with Discrete Distributions (이산형 활동시간 분포를 갖는 PERT 네트워크에서 평균사업완성시간과의 민감도 분석)

• Cho, Jae-Gyeun;Park, Chul-Jae
• Journal of the Korea Industrial Information Systems Research
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• v.12 no.1
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• pp.108-117
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• 2007
• For a PERT network the sensitivity analyses are valuable tools for effective management and control of a project. In a previous article, a method was developed for the sensitivity analysis of the expected project completion time (${\mu}_{T}$) with respect to the expected duration of an activity (${\mu}_{i}$) under the assumption that the durations of activities are independent and normally distributed. In the present article, a method is presented for the sensitivity analysis of ${\mu}_{T}$ with respect to ${\mu}_{i}$ when the durations of activities are independent and follow discrete distributions, which utilizes the previous sensitivity analysis method with modifications. The accuracy of the proposed method is assessed using various example PERT networks, and the computational results indicate that the accuracy is comparable to that of direct Monte Carlo simulation.

### A Sensitivity Analysis of the OZIPR Modeling Result for the Seoul Metropolitan Area (OZIPR 모델링 결과의 민감도 분석)

• Lee, Sun-Hwa;Jin, Lan;Kim, Yong Pyo
• Particle and aerosol research
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• v.7 no.3
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• pp.99-108
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• 2011
• To establish area specific control strategies for the reduction of the ozone concentration, the Ozone Isopleth Plotting Package for Research(OZIPR) model has been widely used. However, the model results tend to changed by various input parameters such as the background concentration, emission amount of NOx and volatile organic compounds (VOCs), and meteorological condition. Thus, sensitivity analysis should be required to ensure the reliability of the result. The OZIPR modeling results for five local government districts in the Seoul Metropolitan Area (SMA) in June 2000 were used for the sensitivity analysis. The sensitivity analysis result showed that the modeling result of the SMA being VOC-limited region be still valid for a wide range of input parameters' variation. The estimated ozone concentrations were positively related with the initial VOCs concentrations while were negatively related with the initial NOx concentrations. But, the degree of the variations at each local district was different suggesting area specific characteristics being also important. Among the five local governments, Suwon was chosen to identify other variance through the period from April to September in 2000. The monthly modeling results show different ozone values, but still showing the characteristics of VOCs-limited region. Limitations due to not considering long range transport and transfer from neighbor area, limitation of input data, error between observed data and estimated data are all discussed.

### Optimal Design of Water Distribution Networks using the Genetic Algorithms:(II) -Sensitivity Analysis- (Genetic Algorithm을 이용한 상수관망의 최적설계: (II) -민감도 분석을 중심으로-)

• Shin, Hyun-Gon;Park, Heekyun
• Journal of Korean Society of Water and Wastewater
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• v.12 no.2
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• pp.50-58
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• 1998
• Genetic Algorithm (GA) consists of selection, reproduction, crossover and mutation processes and many parameters including population size, generation number, the probability of crossover (Pc) and the probability of mutation (Pm). Determining values of the parameters is found critical in the whole optimization process and a sensitivity analysis with them seems mandatory. This paper tries to demonstrate such importance of sensitivity analysis of GA using an example water supply tunnel network of the New York City. For optimization of the network with GA, Pc and Pm vary from 0.5 to 0.9 by an increment of 0.1 and from 0.01 to 0.05 by an increment of 0.01, respectively, while fixing both the population size and the generation number to 100. This sensitivity analysis results in an optimum design of 22.3879 million dollars at the values of 0.8 and 0.01 for Pc and Pm, respectively. In addition, the probability of recombination (Pr) is introduced to check its applicability in the GA optimization of water distribution network. When Pr is 0.05 with the same values of Pc and Pm as above, the optimum design costs 20.9077 million dollars. This is lower than the cost of 22.3879 million dollars for the case of not using Pr by 6.6%. These results indicate that conducting a sensitivity analysis with parameter values and using Pr are useful in the optimization of WDN.

### A Study on the Support location Optimizations of the Beams using the Genetic Algorithm and the Sensitivity Analysis. (민감도가 고려된 유전 알고리듬을 이용한 보 구조물의 지지점 최적화에 관한 연구)

• 이재관;신효철
• Journal of KSNVE
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• v.10 no.5
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• pp.783-791
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• 2000
• This describes a study on the support location optimizations of the beams using the genetic algorithm and the sensitivity analysis. The genetic algorithm is a probabilistic method searching the optimum at several points simultaneously and requiring only the values of the object and constraint functions. It has therefore more chances to find the global solution and can be applied to the various problems. Nevertheless, it has such a shortcoming that it takes too many calculations, because it is ineffective in local search. While the traditional method using sensitivity analysis is of great advantage in searching the near optimum. thus the combination of the two techniques will make use of the individual advantages, that is, the superiority in global searching form the genetic algorithm and that in local searching form the sensitivity analysis. In this thesis, for the practical applications, the analysis is conducted by FEB ; and as the shapes of structures are taken as the design variation, it requires re-meshing for every analysis. So if it is not properly controlled, the result of the analysis is affected and the optimized solution amy not be the real one. the method is efficiently applied to the problems which the traditional methods are not working properly.

### Fatigue Damage Prediction Using Design Sensitivity Analysis (설계 민감도 해석을 활용한 피로 손상도 예측방법)

• Kim, Chan-Jung;Lee, Bong-Hyun;Jeon, Hyun-Cheol;Jo, Hyeon-Ho;Kang, Yeon-June
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.2
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• pp.123-129
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• 2012
• It was previously suggested the design sensitivity analysis based on transmissibility function to identify the most sensitive response location over a small design modification. On the other hand, energy isoclines were used to predict the fatigue damage with acceleration response only. Both of previous studies commonly tackle the engineering problem using the acceleration response alone such that it may be possible to investigate the relationship between sensitivity analysis and accumulated fatigue damage. In this paper, it is suggested the novel method of vibration fatigue prediction using design sensitivity analysis to enhance the accuracy of predicted accumulated fatigue. Uni-axial vibration testing is performed with a simple notched specimen and the prediction of fatigue damage is conducted using accelerations measured at different locations. It can be concluded that the accuracy of predicted fatigue damage is proportional to the sensitivity index of the responsible location.