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Spatial Interpolation of Gauge Measured Rainfall Using Compressed Sensing
류수록,송준진,김용구,정성화,도영해,이규원 한국기상학회 2021 Asia-Pacific Journal of Atmospheric Sciences Vol.57 No.2
In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n (n m) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks. In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n ( n ≫ m ) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks.
류수록(Soorok Ryu),이상혁(Sang-Hyuk Lee) 한국지능시스템학회 2008 한국지능시스템학회논문지 Vol.18 No.2
데이터 분석을 위하여 데이터의 불확실성에 대한 측도로서 퍼지 집합에 대한 엔트로피를 소개하였고, 또한 데이터간의 유사도를 나타내는 유사측도를 구성하였다. 퍼지 소속 함수간의 유사측도는 거리측도를 이용하여 구성하였고, 제안한 유사측도를 증명을 통하여 확인하였다. 제안한 유사측도의 유용성을 확인하기 위하여 신뢰성 있는 데이터추출 예제에 적용하였다. 적용결과를 퍼지 엔트로피와 통계적 지식을 통하여 얻어진 이전의 결과와 비교하였다. For data analysis, fuzzy entropy is introduced as the measure of fuzziness, similarity measure is also constructed to represent similarity between data. Similarity measure between fuzzy membership functions is constructed through distance measure, and the proposed similarity measure are proved. Application of proposed similarity measure to the example of reliable data selection is also carried out. Application results are compared with the previous results that is obtained through fuzzy entropy and statistical knowledge.
Application of Similarity Measure for Fuzzy C-Means Clustering to Power System Management
박동혁,이상혁,박현정,류수록 한국지능시스템학회 2008 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.8 No.1
A FCM with locational price and regional information between locations are proposed in this paper. Any point in a networked system has its own values indicating the physical characteristics of that networked system and regional information at the same time. The similarity measure used for FCM in this paper is defined through the system-wide characteristic values at each point. To avoid the grouping of geometrically distant locations with similar measures, the locational information are properly considered and incorporated in the proposed similarity measure. We have verified that the proposed measure has produced proper classification of a networked system, followed by an example of a networked electricity system.
Fuzzy Entropy Construction based on Similarity Measure
Park Hyun Jeong(박현정),Insuk Yang(양인석),Soorok Ryu(류수록),Sang H. Lee(이상혁) 한국지능시스템학회 2008 한국지능시스템학회논문지 Vol.18 No.2
In this paper we derived fuzzy entropy that is based on similarity measure. Similarity measure represents the degree of similarity between two informations, those informations characteristics are not important. First we construct similarity measure between two informations, and derived entropy functions with obtained similarity measure. Obtained entropy is verified with proof. With the help of one-to-one similarity is also obtained through distance measure, this similarity measure is also proved in our paper.