• Title/Summary/Keyword: 콜모고로프 상수

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Realization of water distribution system digital twin model using parameter calibration model (상수도관망 디지털트윈 구현을 위한 해석 프로그램 매개변수 검보정 모형 개발)

  • Lee, Jaeyeon;Park, Jaehong;Lee, Seungyub
    • Proceedings of the Korea Water Resources Association Conference
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    • 2022.05a
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    • pp.182-182
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    • 2022
  • 4차산업 기술이 상수도 관망 분야에도 활발히 도입되며 스마트워터 구축에 기술적인 기반이 마련되고 있다. 이중 디지털트윈의 경우 컴퓨터에 현실 속 사물의 쌍둥이를 만들고, 현실에서 발생할 수 있는 상황을 컴퓨터로 시뮬레이션함으로써 결과를 미리 예측하는 기술로 정의된다. 즉, 디지털트윈의 핵심기술은 시각화와 시뮬레이션 모형의 연계로 실시간 상황 표출뿐만 아니라 시뮬레이션 모형 입력값의 미래 변화를 추정하여 해당 사물의 상태를 예측하는 것이라고 할 수 있다. 상수도 관망의 경우도 디지털트윈 모형 구축 시 정교한 시뮬레이션 모형과 연계를 통해 관측 데이터의 표출과 함께 미관측 지점의 데이터를 추정 및 표출하는 것이 중요하다. 본 연구에서는 디지털트윈 모형 구축에 가장 필수적이라고 할 수 있는 상수도 관망의 해석 프로그램 매개변수 검보정 모형을 소개한다. 대표적인 상수도 관망해석 프로그램인 EPANET2.2의경우 입력값으로 주로 수요량과 관로의 조도계수를 요구하며, 본 연구에서는 수요량은 알고 있는 것으로 가정하고 관로의 조도계수만 Markov-Chain Monte Carlo (MCMC)를 사용하여 검보정한다. 해당 모형은 (1) 실시간 조도계수 추정이 가능하면, (2) 동시에 누수 탐지가 가능하고, (3) 관로의 기능적 노후를 정의하여 향후 디지털트윈 모형 구현 시 관로 노후를 표출할 수 있는 기반을 구축한다. 우선 실시간 조도계수 추정은 데이터베이스와 연동하여 진행하며, MCMC 모형을 활용한 관로 별 조도계수의 분포에 따라 정상범위 내 변동이 발생하는지 여부를 판단한다. 이때 정상범위를 벗어난 변동이 발생하는 경우 잠재적 누수가 존재하는 것으로 가정하며, 콜모고로프-스미르노프(KS) 테스트를 통해 이를 판단한다. 기능적 노후는 관로의 통수능과 연관이 있으며, 추정한 조도계수에 따른 관로의 통수능을 산정하여 결과를 표출한다. 본 연구에서 제안한 모형은 향후 상수도 관망 디지털트윈 구현에 핵심 요소기술로 활용할 수 있을 것으로 기대한다.

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The study for NHPP Software Reliability Model based on Kappa(2) distribution (Kappa(2) NHPP에 의한 소프트웨어 신뢰성 모형에 관한 연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Computer Industry Society
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    • v.6 no.5
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    • pp.689-696
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    • 2005
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the Kappa(2) reliability model, which can capture the nomotonic decreasing nature of the failure occurrence rate per fault. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on sum of the squared errors and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using real data set, SYS2(Allen P.Nikora and Michael R.Lyu), for the sake of proposing two parameter of the Kappa distribution, was employed. This analysis of failure data compared with the Kappa model and the existing model using arithmetic and Laplace trend tests, bias tests is presented.

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The Study for NHPP Software Reliability Growth Model based on Exponentiated Exponential Distribution (지수화 지수 분포에 의존한 NHPP 소프트웨어 신뢰성장 모형에 관한 연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Society of Computer and Information
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    • v.11 no.5 s.43
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    • pp.9-18
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    • 2006
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the exponentiated exponential distribution reliability model, which maked out efficiency substituted for gamma and Weibull model(2 parameter shape illustrated by Gupta and Kundu(2001) Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE, AIC statistics and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using NTDS data set for the sake of proposing shape parameter of the exponentiated exponential distribution was employed. This analysis of failure data compared with the exponentiated exponential distribution model and the existing model (using arithmetic and Laplace trend tests, bias tests) is presented.

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The Study for NHPP Software Reliability Model based on Chi-Square Distribution (카이제곱 NHPP에 의한 소프트웨어 신뢰성 모형에 관한 연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Society of Computer and Information
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    • v.11 no.1 s.39
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    • pp.45-53
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    • 2006
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the $x^2$ reliability model, which can capture the increasing nature of the failure occurrence rate per fault. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE, AIC statistics and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using real data set, SYS2(Allen P.Nikora and Michael R.Lyu), for the sake of proposing shape parameter of the $x^2$ distribution using the degree of freedom, was employed. This analysis of failure data compared with the $x^2$ model and the existing model using arithmetic and Laplace trend tests, Kolmogorov test is presented.

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Estimation on the Power Spectral Densities of Daily Instantaneous Maximum Fluctuation Wind Velocity (변동풍속의 파워 스펙트럴 밀도에 관한 평가)

  • Oh, Jong Seop
    • Journal of Korean Society of Disaster and Security
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    • v.10 no.2
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    • pp.21-28
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    • 2017
  • Wind turbulence data is required for engineering calculations of gust speeds, mean and fluctuating loading. Spectral densities are required as input data for methods used in assessing dynamic response. This study is concerned with the estimation of daily instantaneous maximum wind velocity in the meteorological major cities (selected each 6 points) during the yearly 1987-2016.12.1. The purpose of this paper is to present the power spectral densities of the daily instantaneous maximum wind velocity. In the processes of analysis, used observations data obtained at Korea Meteorological Adminstration(KMA), it is assumed as a random processes. From the analysis results, in the paper estimated power spectral densities function(Blunt model) shows a very closed with von Karman and Solari's spectrum models.

Infinite Failure NHPP Software Mixture Reliability Growth Model Base on Record Value Statistics (기록값 통계량에 기초한 무한고장 NHPP 소프트웨어 혼합 신뢰성장 모형에 관한 연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul;Kim, Kyung-Soo
    • Convergence Security Journal
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    • v.7 no.3
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    • pp.51-60
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    • 2007
  • Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, exponential distribution and Rayleigh distribution model was reviewed, proposes the mixture reliability model, which made out efficiency substituted for situation for failure time Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using S27 data set for the sake of proposing shape parameter of the mixture distribution was employed. This analysis of failure data compared with the mixture distribution model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.

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The Study for ENHPP Software Reliability Growth Model Based on Kappa(2) Coverage Function (Kappa(2) 커버리지 함수를 이용한 ENHPP 소프트웨어 신뢰성장모형에 관한 연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.12
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    • pp.2311-2318
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    • 2007
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. Accurate predictions of software release times, and estimation of the reliability and availability of a software product require Release times of a critical element of the software testing process : test coverage. This model called Enhanced non-homogeneous Poission process(ENHPP). In this paper, exponential coverage and S-shaped model was reviewed, proposes the Kappa coverage model, which make out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE statistics and Kolmogorov distance, for the sake of efficient model, was employed. Numerical examples using real data set for the sake of proposing Kappa coverage model was employed. This analysis of failure data compared with the Kappaa coverage model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.

The Study for NHPP Software Reliability Growth Model based on Burr Distribution (Burr 분포를 이용한 NHPP소프트웨어 신뢰성장모형에 관한 연구)

  • Kim, Hee-Cheul;Park, Jong-Goo
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.3
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    • pp.514-522
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    • 2007
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this parer, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the Burr distribution reliability model, which making out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE, AIC statistics and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using real data set for the sake of proposing shape parameter of the Burr distribution was employed. This analysis of failure data compared with the Burr distribution model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.