• Title/Summary/Keyword: Upper Bound Solution

Search Result 115, Processing Time 0.022 seconds

Stability Condition for Discrete Interval System with Unstructured Uncertainty and Time-Varying Delay Time (비구조화된 불확실성과 시변 지연 시간을 갖는 이산 구간 시스템의 안정조건)

  • Hyung-seok Han
    • Journal of Advanced Navigation Technology
    • /
    • v.25 no.6
    • /
    • pp.551-556
    • /
    • 2021
  • In this paper, we deal with the stability condition of linear interval discrete systems with time-varying delays and unstructured uncertainty. For the interval discrete system which has interval matrix as its system matrices, time-varying delay time within some interval value and unstructured uncertainty which can include non-linearity and be expressed by only its magnitude, the stability condition is proposed. Compared with the previous result derived by using a upper bound solution of the Lyapunov equation, the new results are derived by the form of simple inequality based on Lyapunov stability condition and have the advantage of being more effective in stability application. Furthermore, the proposed stable conditions are very comprehensive and powerful, including the previously published stable conditions of various linear discrete systems. The superiority of the new condition is proven in the derivation process, and the utility and superiority of the proposed condition are examined through numerical example.

Image Processing Technology for Analyzing the Heating State of Carbon Fiber Surface Heating Element (탄소섬유 면상발열체의 발열 상태 분석을 위한 영상처리 기술)

  • Cho, Joon-Ho;Hwang, Hyung-Soo
    • Journal of the Korea Academia-Industrial cooperation Society
    • /
    • v.19 no.2
    • /
    • pp.683-688
    • /
    • 2018
  • In this study, we analyzed the heat generation state of a flat heating element by using image processing technology in conjunction with carbon fiber. The flat heating element is manufactured by chopping the carbon fiber to a small size and bonding it again using a dispersing agent. The solution of carbon fiber, bound together using the dispersant, is then filtered onto the nonwoven fabric. The last step is to obtain flat carbon fibers in the form of nonwoven fabrics for the purpose of drying the filtered carbon fibers. In the flat heating element, electricity may be applied to the carbon fiber on the surface produced in this manner. In this study, the flat heating element was analyzed by four methods. The analysis of the heat generation characteristics and heating rate of the flat heating element confirmed that the fabricated sheet heating element corresponds to a normal army. The analysis of the insulation coating and flat heating element module, which can be used for actual product manufacturing, involves two dimensional image analysis using image processing technology. The thermal image analysis of the flat heating element is a programming technique that not only analyzes the heat generation state in both two and three dimensions, but also displays the upper and lower 15 to 20% ranges of temperature corresponding to the heat generation in the image. In the final analysis, it is possible to easily find the erroneous part in the manufacturing process by directly showing the state of the fabricated flat heating element on the screen. By combining this image analysis method of the flat heating element with the existing method, we were able to more accurately analyze the heat generation state.

Consideration of Bentonite Cake Existing on Vertical Cutoff Wall in Slug Test Analysis (벤토나이트 케익을 고려한 연직차수벽의 순간변위시험(slug test) 해석)

  • Lim, Jeehee;Nguyen, The-Bao;Lee, Dongseop;Ahn, Jaeyoon;Choi, Hangseok
    • Journal of the Korean Geotechnical Society
    • /
    • v.29 no.6
    • /
    • pp.5-17
    • /
    • 2013
  • Slug tests can be adopted to estimate hydraulic conductivity of the slurry trench wall backfill for its abilities to reflect the in-situ performance of the construction. A comprehensive three-dimensional numerical model is developed to simulate the slug test in a slurry trench wall considering the presence of bentonite cake on the interface boundaries between the wall and the surrounding soil formation. Influential factors such as wall width (i.e., proximity of wall boundary), well deviation, vertical position of well intake section, compressibility of wall backfill, etc. are taken into account in the model. A series of simulation results are examined to evaluate the bentonite cake effect in analyzing practical slug test results in the slurry trench wall. The results show that the modified line-fitting method can be used without any correction factor for the slug test in the slurry trench wall with the presence of bentonite cake. A case study is reanalyzed with the assumption of existing bentonite cake. The results are compared with the previously reported results by the approaches assuming no bentonite cake (constant-head boundary) or upper-bound solution (no-flux boundary). The case study demonstrates the bentonite cake effect and the validity of the modified line-fitting method in the estimation of the hydraulic conductivity of the slurry wall backfill.

Corporate Bond Rating Using Various Multiclass Support Vector Machines (다양한 다분류 SVM을 적용한 기업채권평가)

  • Ahn, Hyun-Chul;Kim, Kyoung-Jae
    • Asia pacific journal of information systems
    • /
    • v.19 no.2
    • /
    • pp.157-178
    • /
    • 2009
  • Corporate credit rating is a very important factor in the market for corporate debt. Information concerning corporate operations is often disseminated to market participants through the changes in credit ratings that are published by professional rating agencies, such as Standard and Poor's (S&P) and Moody's Investor Service. Since these agencies generally require a large fee for the service, and the periodically provided ratings sometimes do not reflect the default risk of the company at the time, it may be advantageous for bond-market participants to be able to classify credit ratings before the agencies actually publish them. As a result, it is very important for companies (especially, financial companies) to develop a proper model of credit rating. From a technical perspective, the credit rating constitutes a typical, multiclass, classification problem because rating agencies generally have ten or more categories of ratings. For example, S&P's ratings range from AAA for the highest-quality bonds to D for the lowest-quality bonds. The professional rating agencies emphasize the importance of analysts' subjective judgments in the determination of credit ratings. However, in practice, a mathematical model that uses the financial variables of companies plays an important role in determining credit ratings, since it is convenient to apply and cost efficient. These financial variables include the ratios that represent a company's leverage status, liquidity status, and profitability status. Several statistical and artificial intelligence (AI) techniques have been applied as tools for predicting credit ratings. Among them, artificial neural networks are most prevalent in the area of finance because of their broad applicability to many business problems and their preeminent ability to adapt. However, artificial neural networks also have many defects, including the difficulty in determining the values of the control parameters and the number of processing elements in the layer as well as the risk of over-fitting. Of late, because of their robustness and high accuracy, support vector machines (SVMs) have become popular as a solution for problems with generating accurate prediction. An SVM's solution may be globally optimal because SVMs seek to minimize structural risk. On the other hand, artificial neural network models may tend to find locally optimal solutions because they seek to minimize empirical risk. In addition, no parameters need to be tuned in SVMs, barring the upper bound for non-separable cases in linear SVMs. Since SVMs were originally devised for binary classification, however they are not intrinsically geared for multiclass classifications as in credit ratings. Thus, researchers have tried to extend the original SVM to multiclass classification. Hitherto, a variety of techniques to extend standard SVMs to multiclass SVMs (MSVMs) has been proposed in the literature Only a few types of MSVM are, however, tested using prior studies that apply MSVMs to credit ratings studies. In this study, we examined six different techniques of MSVMs: (1) One-Against-One, (2) One-Against-AIL (3) DAGSVM, (4) ECOC, (5) Method of Weston and Watkins, and (6) Method of Crammer and Singer. In addition, we examined the prediction accuracy of some modified version of conventional MSVM techniques. To find the most appropriate technique of MSVMs for corporate bond rating, we applied all the techniques of MSVMs to a real-world case of credit rating in Korea. The best application is in corporate bond rating, which is the most frequently studied area of credit rating for specific debt issues or other financial obligations. For our study the research data were collected from National Information and Credit Evaluation, Inc., a major bond-rating company in Korea. The data set is comprised of the bond-ratings for the year 2002 and various financial variables for 1,295 companies from the manufacturing industry in Korea. We compared the results of these techniques with one another, and with those of traditional methods for credit ratings, such as multiple discriminant analysis (MDA), multinomial logistic regression (MLOGIT), and artificial neural networks (ANNs). As a result, we found that DAGSVM with an ordered list was the best approach for the prediction of bond rating. In addition, we found that the modified version of ECOC approach can yield higher prediction accuracy for the cases showing clear patterns.

Ensemble Learning with Support Vector Machines for Bond Rating (회사채 신용등급 예측을 위한 SVM 앙상블학습)

  • Kim, Myoung-Jong
    • Journal of Intelligence and Information Systems
    • /
    • v.18 no.2
    • /
    • pp.29-45
    • /
    • 2012
  • Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.