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Approximations to the normal probability distribution Function using Operators of Continuous-valued Logic

ACTA CYBERNETICA 2018年第3期23卷 829-852页

作者： Dombi, Jozsef Jonas, Tamas Univ Szeged Dept Comp Algorithms & Artificial Intelligence Arpad Ter 2 H-6720 Szeged Hungary Eotvos Lorand Univ Inst Business Econ Szep Utca 2 H-1053 Budapest Hungary

In this study, novel approximation methods to the standard normal probability distribution function are introduced. The techniques presented are founded on applications of certain operators of continuous-valued logic. It is demonstrated here that application of the averaging Dombi conjunction operator to two symmetric Sigmoid fuzzy membership functions results in a function that is identical with Tocher's approximation to the standard normal probability distribution function. Next, an approximation connected with a unary fuzzy modifier operator is discussed. Namely, the so-called Kappa function is applied for constructing a novel probability distribution function. It is shown here that the asymptotic Kappa function is just the Sigmoid function and the proposed Quasi Logistic probability distribution function can be utilized to approximate the standard normal probability distribution function. It is also explained how the new probability distribution function is connected with the generator function of Dombi operators. The proposed approximation formula is very simple as it has only one constant parameter. It does not include any exponential term, but has a good approximation accuracy and fulfills certain requirements that only a few of the known approximation formulas do.

关键词： continuous logic Dombi operators sigmoid function normal probability distribution approximation

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Fuzzy adaptive particle swarm optimization for bidding strategy in uniform price spot market

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IEEE TRANSACTIONS ON POWER SYSTEMS 2007年第4期22卷 2152-2160页

作者： Bajpai, P. Singh, S. N. Indian Inst Technol Dept Elect Engn Kanpur 208016 Uttar Pradesh India

In a deregulated electricity market, generators have to optimally bid to maximize their profit under incomplete information of other competing generators. This paper addresses an optimal bidding strategy of a thermal generator in a uniform price spot market considering a precise model of nonlinear operating cost function and minimum up/down constraints of unit commitment. The bidding behaviors of other competing generators are described using normal probability distribution function. Bidding strategy of a generator for each trading period in a day-ahead market is solved by fuzzy adaptive particle swarm optimization (FAPSO), where inertia weight is dynamically adjusted using fuzzy evaluation. FAPSO can dynamically follow the frequently changing market demand and supply in each trading interval. The effectiveness of the proposed approach is tested with examples and the results are compared with the solutions obtained using genetic algorithm (GA) approach and other versions of PSO.

关键词： bidding strategies electricity market fuzzy inference Monte Carlo simulation normal probability distribution particle swarm optimization

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A methodology for normal distribution-based statistical characterization of long-term insolation by means of historical data

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SOLAR ENERGY 2015年 122卷 440-454页

作者： Sedic, Almir Pavkovic, Danijel Firak, Mihajlo INA Ind Zagreb 10000 Croatia Fac Mech Engn & Naval Architecture Zagreb 10002 Croatia

Solar system size and related profitable operation with shortest possible return-of-investment period are key enabling factors for a wider commercial use of solar energy systems and further developments of related technologies. Accordingly, the collection and statistical characterization of long-term solar energy (insolation) data may be regarded as an essential step in solar power system design, which should yield probable safety margins of the solar energy system based on the past (historical) data and their estimated statistical properties. To this end, this paper proposes a statistical approach to long-term solar energy availability characterization based on analysis of historical insolation data, augmented by a normalization procedure implementing straightforward data set transformations. The proposed approach has produced a normalized set of probability distributions for the solar energy data collected for the Zagreb (Republic of Croatia) greater metropolitan area over a 10-year period, which can be used for the assessment of energy availability of a prospective solar power system. The proposed methodology has been validated by means of statistical normality (goodness-of-fit) criteria, such as those included in Shapiro Wilk, Kolmogorov-Smirnov, Lilliefors and Chi-square tests. These tests have been first used to indicate the discrepancy of the original (crude) insolation data probability distribution with respect to normal distribution. A comparative analysis based on Weibull probability distribution has further confirmed that statistical characterization based on original data set may not be able to provide favorable results. After suitable data set transformations have been applied, the statistical validation tests have confirmed the transformed data set normal probability distribution hypothesis. The normalized model was additionally validated through comparison of probability levels of transformed data with the probability of occurrence of actual (crude se

关键词： Insolation Long-term solar system assessment normal probability distribution Data set transformation

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Development of predictive criteria for supercritical n alkane adsorption data on 5A zeolite using the Gaussian adsorption isotherm model

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MICROPOROUS AND MESOPOROUS MATERIALS 2012年 151卷 368-379页

作者： Loughlin, Kevin F. Abouelnasr, Dana Amer Univ Sharjah Dept Chem Engn Univ City Sharjah U Arab Emirates

Supercritical adsorption data available in the literature for C-1 to nC(12) n alkanes on 5A zeolite are correlated using the Gaussian adsorption model and subsequently used to predict any supercritical isotherm for these systems. This isotherm model has three parameters: q(max) the saturation loading: the 50% adsorbate loading pressure P-50: and the standard deviation sigma. The latter two parameters are deduced from a log plot of the isotherm pressure P vs. the inverse Gaussian cumulative frequency distribution plot phi(-1)(theta). The slope of this plot is sigma and the y-intercept is log P-50. The temperature dependency of P-50 is deduced from a plot of log P-50 vs. 1/T: this is actually the isosteric heat of adsorption plot at 50% loading with slope proportional to the negative heat of adsorption at 50% loading (4.5 g/100 g Z). The model is tested using 63 supercritical n alkane isotherms from the literature on 5A zeolite. The 63 isotherms from 18 different studies are fitted with the model using a q(max) of 9 g/100 g Z applicable to n alkane/5A isotherms in the supercritical temperature range. The mean standard deviation sigma is observed to be 0.960 with a standard deviation of 0.127. All 63 isotherms reduce to one characteristic curve when theta is plotted against (P/P-50)(1/sigma). The isosteres of P-50 indicate heats of adsorption (-Delta H-50) that are equal to or greater than literature values at zero loading (-Delta H-0);the difference between the two is negligible for low carbon numbers rising to over 10 kcal/mol at higher carbon numbers (nC(10)). This is expected as the heat of adsorption is calculated at 50% loading. The values of P-50 are predicted by correlating the slope and intercept of the isosteres with carbon number;the slope derives from the heat of adsorption (-Delta H-50). Using q(max) = 9 g/100 g Z. sigma = 1, and predicted P-50 values, any supercritical isotherm may be predicted. The Henry constant K-H may also be predicted using P-50, sig

关键词： Isotherm normal probability distribution Alkanes 5A zeolite Supercritical

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Emergent dynamics of spiking neurons with fluctuating threshold

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2017年 46卷 126-134页

作者： Bhattacharjee, Anindita Das, M. K. Amity Univ Amity Coll Commerce & Finance Sect 125 Noida 201302 UP India Univ Delhi South Campus Inst Informat & Commun Benito Juarez Rd New Delhi 110021 India

Role of fluctuating threshold on neuronal dynamics is investigated. The threshold function is assumed to follow a normal probability distribution. Standard deviation of inter-spike interval of the response is computed as an indicator of irregularity in spike emission. It has been observed that, the irregularity in spiking is more if the threshold variation is more. A significant change in modal characteristics of Inter Spike Intervals (ISI) is seen to occur as a function of fluctuation parameter. Investigation is further carried out for coupled system of neurons. Cooperative dynamics of coupled neurons are discussed in view of synchronization. Total and partial synchronization regimes are depicted with the help of contour plots of synchrony measure under various conditions. Results of this investigation may provide a basis for exploring the complexities of neural communication and brain functioning. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Fluctuating threshold normal probability distribution Coupled neurons Synchronization

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A NOTE ON THE TRANSFORMATION OF POSSIBILISTIC INFORMATION INTO PROBABILISTIC INFORMATION FOR INVESTMENT DECISIONS

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FUZZY SETS AND SYSTEMS 1993年第2期56卷 175-182页

作者： GUPTA, CP Shri Ram College of Commerce Delhi University Delhi 110007 India

Investment decisions of a firm take place in a highly competitive environment. Any attempt to capture the reality in such decisions often results in fuzzy information behaving like fuzzy restrictions. But, for decision making, probabilistic data may be more effective rather than possibilistic data. Therefore, possibilistic data need to be transformed into probabilistic data and this needs a suitable possibility/probability consistency principle (PPCP). This note provides a PPCP and shows that under certain conditions fuzzy information about cashflows can be approximated by normal probability distribution. Then, the tools of the probability theory can be applied for such decisions.

关键词： INVESTMENT DECISIONS SYMMETRICAL FUZZY NUMBERS probability MEASURE normal probability distribution POSSIBILITY MEASURE ENTROPY

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Characterization on the Rocking Vibration of Rigid Blocks under Horizontal Harmonic Excitations

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING 2012年第2期13卷 229-236页

作者： Jeong, Man-Yong Yang, In-Young Chosun Univ Dept Mech Design Engn Kwangju 501750 South Korea Numazu Coll Technol Dept Digital Engn Shizuoka 4108501 Japan

This investigation deals with characteristics of rocking vibration of rigid block subjected to the horizontal harmonic excitations. Nonlinear rocking system may include minute changes of system parameters, such as friction and restitution coefficients depending on contact conditions between the block and the base, and friction force that may vary as the block moves. This paper is the first part of the examination how minute changes of the above system parameters are related with minute changes of friction coefficients. A numerical analysis program has been developed to solve nonlinear motion equations for rocking motion of a rigid block subjected to horizontal base excitation. Natural changes of friction coefficient are simulated by random numbers with a normal probability distribution. Analytical results have shown that rocking responses are very sensitive to small changes of friction conditions between the block and the base. Minute changes of the friction coefficients make rocking response unstable and greatly change the response distribution itself Because of the dynamic nature of friction coefficients changes, experimental rocking responses are not recurring.

关键词： Rocking vibration Nonlinear Poincare section normal probability distribution Bifurcation diagram

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normal probability and Heuristics based Path Planning and Navigation System for Mapped Roads 12

Normal Probability and Heuristics based Path Planning and Na...

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12th International Conference on Communication Networks (ICCN) / 12th International Conference on Data Mining and Warehousing (ICDMW) / 12th International Conference on Image and Signal Processing (ICISP)

作者： Amith, A. L. Singh, Amrinder Harsha, H. N. Prasad, N. R. Shrinivasan, Lakshmi MS Ramaiah Inst Technol Bangalore 560054 Karnataka India

In a hybrid road network with multiple paths to same location having prior geographical knowledge, successful navigation for mobile robots is one of the main challenges. Path planning is one of the most important issues in the navigation process which enables the selection and identification of a suitable path for the robot to traverse in the workspace area. Path-planning for mapped roads can be considered as the process of navigating a mobile robot around a configured road map, which provides optimized path by considering roughness of roads. In this paper, we propose a novel navigation algorithm for outdoor environments, which permits robots to travel from one static node to another along a planned path. It utilizes normal probability weight distribution (NPWD) to assign weights between two nodes dynamically. Heuristics based shortest path (HSP) algorithm is employed to solve complex optimization problems concerned with real-world scenarios. The experiments performed on categorized road databases show significant improvement in timings and complexity of system. Our results justify the effectiveness for the implementation of driver-assist system. (C) 2016 The Authors. Published by Elsevier B.V.

关键词： Algorithm Heuristics normal probability distribution Optimization Path Planning Probabilistic Robotics

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Determining the spatio-temporal response of downstream coarse sediment sorting process in the Chel river (North Bengal, India) using cluster analysis

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MODELING EARTH SYSTEMS AND ENVIRONMENT 2021年第2期7卷 1353-1372页

作者： Ghosh, Debarshi Saha, Snehasish Univ North Bengal Dept Geog Dhupguri Girls Coll Dhupguri W Bengal India Univ North Bengal Dept Geog & Appl Geog Darjeeling W Bengal India

The fluvial transportation efficiency related to rainstorm events is important to understand the variability of sediment sorting process in the channel. The supply limitation of different size of sediment grades in downstream reveals the nature of geomorphological scale of response (spatio-temporal). Pebble count method has been attempted here for determination of d(50) (median) particle size associated with frequency distribution of sediment samples from 13 study reaches on the basis of standard sediment grade scale of Wentworth and modified Udden-Wentworth grain scale seasonally. Intra temporal variability (IATV) and inter temporal variability (IETV) results were categorized under hierarchical cluster analysis to view the sediment movement downstream from minimum distance algorithm. On the piedmont, the bed configuration is mostly boulder infested of heavier size class (> 256 mm) and that remains greater than 86% in pre-monsoon condition. It comes out on the basis of random mixing of sediment load (> 2 mm) while transporting as discharge. In Chel basin, the process of sediment load dispersal indicates less heterogeneity in the sediment sorting process towards downstream. The haphazard distribution of very coarse to medium boulders (4096-512 mm) up to reach 6 indicates the limit of channel competency. The paper seeks to know the seasonal variability in the sediment dispersal process i.e. finding the reach wise variability of the sediment mixing process downstream and the sediment supply limits of median particle size.

关键词： Sediment sorting Frequency distribution curve normal probability distribution Hierarchical cluster ANOVA

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Atmospheric Corrosivity Estimation at Electrical Control Unit Room by Multichannel Quartz Crystal Microbalance Corrosion Sensors

Atmospheric Corrosivity Estimation at Electrical Control Uni...

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3rd Japan-Korea Workshop for Young Foundry Engineers (YFE)

作者： Fujii, Kazumi Ohashi, Kenya Hashimoto, Tadahiko Hara, Nobuyoshi Hitachi Ltd Hitachi Res Lab Dept Mat Res Power Plants Hitachi Ibaraki 3191292 Japan Hitachi Ltd Informat & Control Syst Div Hitachi Ibaraki 3191293 Japan Tohoku Univ Grad Sch Engn Dept Mat Sci Sendai Miyagi 9808579 Japan

In order to evaluate the atmospheric corrosivity in an electrical control unit room in a steelmaking plant by using quartz crystal microbalance (QCM) sensors, the temperature, relative humidity and corrosion rates of metals on QCM were monitored for five months. The metals employed for sensing corrosive gases were silver, copper and cobalt. The concentrations of the corrosive gases were estimated from the data of corrosion rates for these metals considering relative humidity. The temperature, relative humidity, and the corrosion rates in a given day were distributed according to the normal probability law. The concentrations of H2S, SO2 and NO2 were estimated from the mean values of the relative humidity and the corrosion rates of silver, copper and cobalt, which derived from the normal probability plots. The concentrations thus obtained were roughly close to those analyzed by conventional analytical methods. The atmospheric corrosivity will be able to estimate based on the monitoring of the corrosion rate with multichannel QCM sensors. [doi:10.2320/matertrans.M2011238]

关键词： electrical control unit temperature relative humidity corrosion rate silver copper cobalt quartz crystal microbalance inverse estimation hydrogen sulfide sulfur dioxide nitrogen dioxide normal probability distribution

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