• Title/Summary/Keyword: Polynomial mathematical model

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Design of Sliding Mode Fuzzy Controller for Vibration Reduction of Large Structures (대형구조물의 진동 감소를 위한 슬라이딩 모드 퍼지 제어기의 설계)

  • 윤정방;김상범
    • Journal of the Earthquake Engineering Society of Korea
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    • v.3 no.3
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    • pp.63-74
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    • 1999
  • A sliding mode fuzzy control (SMFC) algorithm is presented for vibration of large structures. Rule-base of the fuzzy inference engine is constructed based on the sliding mode control, which is one of the nonlinear control algorithms. Fuzziness of the controller makes the control system robust against the uncertainties in the system parameters and the input excitation. Non-linearity of the control rule makes the controller more effective than linear controllers. Design procedure based on the present fuzzy control is more convenient than those of the conventional algorithms based on complex mathematical analysis, such as linear quadratic regulator and sliding mode control(SMC). Robustness of presented controller is illustrated by examining the loop transfer function. For verification of the present algorithm, a numerical study is carried out on the benchmark problem initiated by the ASCE Committee on Structural Control. To achieve a high level of realism, various aspects are considered such as actuator-structure interaction, modeling error, sensor noise, actuator time delay, precision of the A/D and D/A converters, magnitude of control force, and order of control model. Performance of the SMFC is examined in comparison with those of other control algorithms such as $H_{mixed 2/{\infty}}$ optimal polynomial control, neural networks control, and SMC, which were reported by other researchers. The results indicate that the present SMFC is an efficient and attractive control method, since the vibration responses of the structure can be reduced very effectively and the design procedure is simple and convenient.

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Development of Cationic Dyeable Polyamide Substrates by Pretreatment with Synthetic Tanning Agent: Statistical Optimization and Analysis

  • Son, Young-A;Ravikumar, K.;Bae, Jin-Seok
    • Textile Coloration and Finishing
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    • v.21 no.5
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    • pp.41-50
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    • 2009
  • Design of experiments (DoE) concept was successfully applied to determine the optimum processing conditions that yield maximum % exhaustion for berberine interaction with synthetic tanning agent pretreated polyamide substrates. The potential of synthetic tanning agent to provide anionic sites on the polyamide for berberine interaction which is cationic in nature was tested to increase the % exhaustion of berberine in this article. Experiments were designed according to Central Composite Rotatable Design (CCRD). The three factors for synthetic tanning agent pretreatment and two factors for berberine interaction each at five different levels, including central and axial points were considered. Experiments were conducted in a laboratory scale infra-red treatment instrument according to CCRD. For each response, second order polynomial models were developed using multiple linear regression analysis incorporating linear, interactions and squared effects of all variables and then optimized. The significance of the mathematical model developed was ascertained using Excel regression (solver) analysis module. Analysis of variance (ANOVA) was performed to check the adequacy and accuracy of the fitted models. The response surfaces and contour maps showing the interaction of process variables were constructed. Applying Monte Carlo simulation, response surface and contour plots, optimum operating conditions were found and at this optimum point, % exhaustion of 81% and 74% respectively for synthetic tanning agent pretreatment and berberine interaction were observed and subsequently the results were experimentally investigated.

Optical Method to Determine Gait Parameters Using Position Sensitive Detector

  • Jung, Gu-In;Kim, Ji-Sun;Lee, Tae-Hee;Choi, Ju-Hyeon;Oh, Han-Byeol;Kim, A-Hee;Goh, Bong-Jun;Kim, Jun-Sik;Lee, Eun-Suk;Jun, Jae-Hoon
    • Journal of Electrical Engineering and Technology
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    • v.10 no.5
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    • pp.2155-2161
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    • 2015
  • This study suggests an optical method to measure cardinal of gait (step width, step length, and stride length) with position sensitive detector (PSD). The effect of reflector’s shape (flat and cylinder) on the PSD output voltage was examined for the application of the suggested system to real situations with a curved shape reflector (e.g. shoes). Various mathematical models were evaluated to find the optimal equation for the distance measurement. Considering the effect of shape on detected signal, the inverse polynomial model was developed. The suggested method is simple to operate, low in cost, small in size, and can evaluate gait parameters in real time. This method is expected to be useful in the field of rehabilitation and sport science

Evaluation of Dynamic p-y Curve Based on the Numerical Analysis (수치해석기반의 동적 p-y 곡선 산정)

  • Park, Jeong-Sik;Jeong, Sang-Seom
    • Journal of the Korean Geotechnical Society
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    • v.33 no.12
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    • pp.59-73
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    • 2017
  • Numerical analysis using 3D finite element program (PLAXIS 3D) evaluated the interaction of soil - pile structure under dynamic surface loading. The dynamic p-y curve of the 1-g shaking table experiment by numerical analysis was calculated, and the parametric studies were presented by considering the pile-soil condition, the pile tip condition, and the loading condition. The frequency of 1.4 Hz is almost equal to the natural frequency of the pile - soil system. The p and y values of resonance phenomenon are significantly different from the results of other frequencies. The results can be summarized by a third order polynomial function representing the trend line in the p-y curve. In the case of a single pile, the shape of the dominant curve was found to be an ellipse by mathematical proof. The elliptic equation can be used for the dynamic design or analysis of soil-pile system.

Robo-Advisor Algorithm with Intelligent View Model (지능형 전망모형을 결합한 로보어드바이저 알고리즘)

  • Kim, Sunwoong
    • Journal of Intelligence and Information Systems
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    • v.25 no.2
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    • pp.39-55
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    • 2019
  • Recently banks and large financial institutions have introduced lots of Robo-Advisor products. Robo-Advisor is a Robot to produce the optimal asset allocation portfolio for investors by using the financial engineering algorithms without any human intervention. Since the first introduction in Wall Street in 2008, the market size has grown to 60 billion dollars and is expected to expand to 2,000 billion dollars by 2020. Since Robo-Advisor algorithms suggest asset allocation output to investors, mathematical or statistical asset allocation strategies are applied. Mean variance optimization model developed by Markowitz is the typical asset allocation model. The model is a simple but quite intuitive portfolio strategy. For example, assets are allocated in order to minimize the risk on the portfolio while maximizing the expected return on the portfolio using optimization techniques. Despite its theoretical background, both academics and practitioners find that the standard mean variance optimization portfolio is very sensitive to the expected returns calculated by past price data. Corner solutions are often found to be allocated only to a few assets. The Black-Litterman Optimization model overcomes these problems by choosing a neutral Capital Asset Pricing Model equilibrium point. Implied equilibrium returns of each asset are derived from equilibrium market portfolio through reverse optimization. The Black-Litterman model uses a Bayesian approach to combine the subjective views on the price forecast of one or more assets with implied equilibrium returns, resulting a new estimates of risk and expected returns. These new estimates can produce optimal portfolio by the well-known Markowitz mean-variance optimization algorithm. If the investor does not have any views on his asset classes, the Black-Litterman optimization model produce the same portfolio as the market portfolio. What if the subjective views are incorrect? A survey on reports of stocks performance recommended by securities analysts show very poor results. Therefore the incorrect views combined with implied equilibrium returns may produce very poor portfolio output to the Black-Litterman model users. This paper suggests an objective investor views model based on Support Vector Machines(SVM), which have showed good performance results in stock price forecasting. SVM is a discriminative classifier defined by a separating hyper plane. The linear, radial basis and polynomial kernel functions are used to learn the hyper planes. Input variables for the SVM are returns, standard deviations, Stochastics %K and price parity degree for each asset class. SVM output returns expected stock price movements and their probabilities, which are used as input variables in the intelligent views model. The stock price movements are categorized by three phases; down, neutral and up. The expected stock returns make P matrix and their probability results are used in Q matrix. Implied equilibrium returns vector is combined with the intelligent views matrix, resulting the Black-Litterman optimal portfolio. For comparisons, Markowitz mean-variance optimization model and risk parity model are used. The value weighted market portfolio and equal weighted market portfolio are used as benchmark indexes. We collect the 8 KOSPI 200 sector indexes from January 2008 to December 2018 including 132 monthly index values. Training period is from 2008 to 2015 and testing period is from 2016 to 2018. Our suggested intelligent view model combined with implied equilibrium returns produced the optimal Black-Litterman portfolio. The out of sample period portfolio showed better performance compared with the well-known Markowitz mean-variance optimization portfolio, risk parity portfolio and market portfolio. The total return from 3 year-period Black-Litterman portfolio records 6.4%, which is the highest value. The maximum draw down is -20.8%, which is also the lowest value. Sharpe Ratio shows the highest value, 0.17. It measures the return to risk ratio. Overall, our suggested view model shows the possibility of replacing subjective analysts's views with objective view model for practitioners to apply the Robo-Advisor asset allocation algorithms in the real trading fields.

Protein Requirements of the Korean Rockfish Sebastes schlegeli (조피볼락 Sebastes schlegeli의 단백질 요구량)

  • LEE Jong Yun;KANG Yong Jin;LEE Sang-Min;KIM In-Bae
    • Journal of Aquaculture
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    • v.6 no.1
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    • pp.13-27
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    • 1993
  • In order to determine the protein requirements of the Korean rockfish Sebastes schlegeli six isocaloric diets containing crude protein level from 20\%\;to\;60\%$ were fed to two groups of fish, small and large size, with the initial average body weight of 8 g and 220 g respectively. White fish meal was used as a sole protein source. Daily weight gain, daily protein retention. daily energy retention, feed efficiency, protein retention efficiency and energy retention efficiency were significantly affected by the dietary protein content (p< 0.05). The growth parameters (that is, daily weight gain, daily protein retention and daily energy retention) increased up to $44\%$ protein level with no additional response above this point. The protein requirements were determined from daily weight gain using two different mathematical models. Second order polynomial regression analysis showed that maximum daily weight gain occurred at $56.7\%\;and\;50.6\%$ protein levels for the small size group and the large size group, respectively. However the protein requirements, determined by the broken line model, appeared to be about $40\%$ for both groups. Nutrient utilization also suggested that the protein requirements of both groups were close to $40\%$. When daily protein intake was considered, daily protein requirements per 100g of fish, estimated by the broken line model, were 0.99g and 0.35g for the small and large size groups respectively. Based on these results, a $40\%$ dietary crude protein level could be recommended for the optimum growth and efficient nutrient utilization of the Korean rockfish weighing between 8g and 300g.

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