Search results for: stochastic uncertainty analysis

Authors: Tomoaki Hashimoto

Abstract:

Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: Optimal control, stochastic systems, quantum systems, stabilization.

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Authors: Seon Soon Choi

Abstract:

The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: Crack size, Fatigue crack propagation, Magnesium alloys, Probability distribution, Specimen thickness.

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Authors: Michael R. Johnson, Ian P. McCarthy

Abstract:

There is a growing body of evidence to support the proposition of product take back for remanufacturing particularly within the context of Extended Producer Responsibility (EPR). Remanufacturing however presents challenges unlike that of traditional manufacturing environments due to its high levels of uncertainty which may further distract organizations from considering its potential benefits. This paper presents a novel modeling approach for evaluating the uncertainty of part failures within the remanufacturing process and its impact on economic and environmental performance measures. This paper presents both the theoretical modeling approach and an example of its use in application.

Keywords: Remanufacturing, Demanufacturing, Extended Producer Responsibility, Sustainability, Uncertainty.

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Authors: S. Chadsuthi, W. Triampo, C. Modchang, P. Kanthang, D. Triampo, N. Nuttavut

Abstract:

We present analysis of spatial patterns of generic disease spread simulated by a stochastic long-range correlation SIR model, where individuals can be infected at long distance in a power law distribution. We integrated various tools, namely perimeter, circularity, fractal dimension, and aggregation index to characterize and investigate spatial pattern formations. Our primary goal was to understand for a given model of interest which tool has an advantage over the other and to what extent. We found that perimeter and circularity give information only for a case of strong correlation– while the fractal dimension and aggregation index exhibit the growth rule of pattern formation, depending on the degree of the correlation exponent (β). The aggregation index method used as an alternative method to describe the degree of pathogenic ratio (α). This study may provide a useful approach to characterize and analyze the pattern formation of epidemic spreading

Keywords: spatial pattern epidemics, aggregation index, fractaldimension, stochastic, long-rang epidemics

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Authors: Paramet Nualmuenwai, Chutima Prommak

Abstract:

This paper presents the IP traffic analysis. The traffic was collected from the network of Suranaree University of Technology using the software based on the Simple Network Management Protocol (SNMP). In particular, we analyze the distribution of the aggregated traffic during the hours of peak load and light load. The traffic profiles including the parameters described the traffic distributions were derived. From the statistical analysis applying three different methods, including the Kolmogorov Smirnov test, Anderson Darling test, and Chi-Squared test, we found that the IP traffic distribution is a non-normal distribution and the distributions during the peak load and the light load are different. The experimental study and analysis show high uncertainty of the IP traffic.

Keywords: IP traffic analysis, IP traffic distribution, Traffic uncertainty

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Authors: Leila Jafari, Viliam Makis

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-based maintenance, economic manufacturing quantity, safety stock, stochastic demand.

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Authors: Xin Zhao, Yin-fan Zhu, Wei-ping Wang, Qun Li

Abstract:

The Influence Diagrams (IDs) is a kind of Probabilistic Belief Networks for graphic modeling. The usage of IDs can improve the communication among field experts, modelers, and decision makers, by showing the issue frame discussed from a high-level point of view. This paper enhances the Time-Sliced Influence Diagrams (TSIDs, or called Dynamic IDs) based formalism from a Discrete Event Systems Modeling and Simulation (DES M&S) perspective, for Exploring Analysis (EA) modeling. The enhancements enable a modeler to specify times occurred of endogenous events dynamically with stochastic sampling as model running and to describe the inter- influences among them with variable nodes in a dynamic situation that the existing TSIDs fails to capture. The new class of model is named Dynamic-Stochastic Influence Diagrams (DSIDs). The paper includes a description of the modeling formalism and the hiberarchy simulators implementing its simulation algorithm, and shows a case study to illustrate its enhancements.

Keywords: Time-sliced influence diagrams, discrete event systems, dynamic-stochastic influence diagrams, modeling formalism, simulation algorithm.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: C. Ardil

Abstract:

Aircraft have different capabilities and specifications according to the required strategic goals and objectives in operations. With various types on the market with different aircraft characteristics, it becomes difficult to select a suitable aircraft for certain operations and requirements. The entropy weighting method (EWM) is a useful, highly consistent, and reliable method for obtaining the weights of the criteria and is worth integrating with the decision uncertainty distance (DUD) method, which is more applicable and requires less computation than other methods. An illustrative example is presented to demonstrate the validity and usability of the proposed methodology. Comparing the ranking results matches the distance-based approach, which is the technique for order preference by similarity to ideal solution (TOPSIS) method, which shows the robustness of the entropy DUD hybrid method. Validity analysis shows that the proposed hybrid multiple criteria decision-making analysis (MCDMA) methodology is quantitatively stable and reliable.

Keywords: aircraft selection, decision uncertainty distance (DUD), multiple criteria decision making analysis, MCDMA, TOPSIS

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Authors: Nasser Shamskia, Seyyed Habib Rahmati, Hassan Haleh , Seyyedeh Hoda Rahmati

Abstract:

The main criteria of designing in the most hydraulic constructions essentially are based on runoff or discharge of water. Two of those important criteria are runoff and return period. Mostly, these measures are calculated or estimated by stochastic data. Another feature in hydrological data is their impreciseness. Therefore, in order to deal with uncertainty and impreciseness, based on Buckley-s estimation method, a new fuzzy method of evaluating hydrological measures are developed. The method introduces triangular shape fuzzy numbers for different measures in which both of the uncertainty and impreciseness concepts are considered. Besides, since another important consideration in most of the hydrological studies is comparison of a measure during different months or years, a new fuzzy method which is consistent with special form of proposed fuzzy numbers, is also developed. Finally, to illustrate the methods more explicitly, the two algorithms are tested on one simple example and a real case study.

Keywords: Fuzzy Discharge, Fuzzy estimation, Fuzzy ranking method, Hydrological data

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Authors: Edikan E. Akpanibah, Okwigbedi Oghen’Oro

Abstract:

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

Keywords: DC pension fund, Hamilton-Jacobi-Bellman, optimal investment strategies, power transformation method, stochastic, voluntary contribution.

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Authors: Om Parkash, C.P.Gandhi

Abstract:

Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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Authors: Seon Soon Choi

Abstract:

It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to find the effect of load ratio on probability distribution of the fatigue crack propagation life at a specified grown crack size and to confirm the good probability distribution in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: Load ratio, fatigue crack propagation life, Magnesium alloys, probability distribution.

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Authors: Syeda Maria Ali Shah, Asif Mansoor, Talat Sharafat Rehmani, Safia Mirza

Abstract:

The stock market of any country acts as a predictor of the economy. The spread of the COVID-19 pandemic has severely impacted the global financial markets. Besides, it has also critically affected the economy of Pakistan. In this study, we consider the role of the Karachi Stock Exchange (KSE) with regard to the Pakistan Stock Exchange and quantify the impact on macroeconomic variables in presence of COVID-19. The suitable macroeconomic variables are used to quantify the impact of COVID-19 by developing the stochastic model. The sufficiency of the computed model is attained by means of available techniques in the literature. The estimated equations are used to forecast the impact of pandemic on macroeconomic variables. The constructed model can help the policymakers take counteractive measures for restricting the influence of viruses on the Karachi Stock Market.

Keywords: COVID-19, Karachi Stock Market, macroeconomic variables, stochastic model, forecasting.

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Authors: Fang Shu, Li Lihua, Zhang Ping

Abstract:

A general stochastic spatial MIMO channel model is proposed for evaluating various MIMO techniques in this paper. It can generate MIMO channels complying with various MIMO configurations such as smart antenna, spatial diversity and spatial multiplexing. The modeling method produces the stochastic fading involving delay spread, Doppler spread, DOA (direction of arrival), AS (angle spread), PAS (power azimuth Spectrum) of the scatterers, antenna spacing and the wavelength. It can be applied in various MIMO technique researches flexibly with low computing complexity.

Keywords: MIMO channel, Spatial Correlation, DOA, AS, PAS.

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Authors: Elena M. Capitanul, Carlos A. Nunes Cosenza, Walid El Moudani, Felix Mora Camino

Abstract:

The construction of a new airport or the extension of an existing one requires massive investments and many times public private partnerships were considered in order to make feasible such projects. One characteristic of these projects is uncertainty with respect to financial and environmental impacts on the medium to long term. Another one is the multistage nature of these types of projects. While many airport development projects have been a success, some others have turned into a nightmare for their promoters. This communication puts forward a new approach for airport investment risk assessment. The approach takes explicitly into account the degree of uncertainty in activity levels prediction and proposes milestones for the different stages of the project for minimizing risk. Uncertainty is represented through fuzzy dual theory and risk management is performed using dynamic programming. An illustration of the proposed approach is provided.

Keywords: Airports, fuzzy logic, risk, uncertainty.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

Abstract:

This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

Keywords: Stochastic models, ARIMA, extreme streamflow, Karkheh River.

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Authors: Zakari Yaou, Lirong Cui

Abstract:

In a product development process, understanding the functional behavior of the system, the role of components in achieving functions and failure modes if components/subsystem fails its required function will help develop appropriate design validation and verification program for reliability assessment. The integration of these three issues will help design and reliability engineers in identifying weak spots in design and planning future actions and testing program. This case study demonstrate the advantage of unascertained theory described in the subjective cognition uncertainty, and then applies blind number (BN) theory in describing the uncertainty of the mechanical system failure process and the same time used the same theory in bringing out another mechanical reliability system model. The practical calculations shows the BN Model embodied the characters of simply, small account of calculation but betterforecasting capability, which had the value of macroscopic discussion to some extent.

Keywords: Mechanical structure Design, time-dependent stochastic process, unascertained information, blind number theory.

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Authors: Gábor Szűcs, Gyula Sallai

Abstract:

The goal of this paper is to find Wardrop equilibrium in transport networks at case of uncertainty situations, where the uncertainty comes from lack of information. We use simulation tool to find the equilibrium, which gives only approximate solution, but this is sufficient for large networks as well. In order to take the uncertainty into account we have developed an interval-based procedure for finding the paths with minimal cost using the Dempster-Shafer theory. Furthermore we have investigated the users- behaviors using game theory approach, because their path choices influence the costs of the other users- paths.

Keywords: Dempster-Shafer theory, S-O and U-Otransportation network, uncertainty of information, Wardropequilibrium.

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

Abstract:

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic.

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: Noise, signal-to-noise ratio, stochastic signals, variance estimation.

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Authors: Zhen Wu, David Lupien St-Pierre, Georges Abdul-Nour

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In decision making under strict uncertainty, decision makers have to choose a decision without any information about the states of nature. The classic criteria of Laplace, Wald, Savage, Hurwicz and Starr are introduced and compared in a case study of sewer network planning. Furthermore, results from different criteria are discussed and analyzed. Moreover, this paper discusses the idea that decision making under strict uncertainty (DMUSU) can be viewed as a two-player game and thus be solved by a solution concept in game theory: Nash equilibrium.

Keywords: Decision criteria, decision making, sewer network planning, strict uncertainty.

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: M. Safaei, M. Seifert, K. D. Thoben

Abstract:

Supply network management adopts a systematic and integrative approach to managing the operations and relationships of various parties in a supply network. The objective of the manufactures in their supply network is to reduce inventory costs and increase customer satisfaction levels. One way of doing that is to synchronize delivery performance. A supply network can be described by nodes representing the companies and the links (relationships) between these nodes. Uncertainty in delivery time depends on type of network relationship between suppliers. The problem is to understand how the individual uncertainties influence the total uncertainty of the network and identify those parts of the network, which has the highest potential for improving the total delivery time uncertainty.

Keywords: Delivery time uncertainty, Distribution function, Statistical method, Supply Network.

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Authors: Mikhail Vladimirovich Deryabin, Morten Willatzen

Abstract:

In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.

Keywords: cylindrical quantum dots, electronic eigen energies, red and white Gaussian noise, ensemble averaging effects.

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes

Abstract:

This article deals with the conceptual modeling under uncertainty. First, the division of information systems with their definition will be described, focusing on those where the construction of a conceptual model is suitable for the design of future information system database. Furthermore, the disadvantages of the traditional approach in creating a conceptual model and database design will be analyzed. A comprehensive methodology for the creation of a conceptual model based on analysis of client requirements and the selection of a suitable domain model is proposed here. This article presents the expert system used for the construction of a conceptual model and is a suitable tool for database designers to create a conceptual model.

Keywords: Conceptual model, conceptual modeling, database, methodology, uncertainty, information system, entity, attribute, relationship, conceptual domain model, fuzzy.

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Authors: Xianqing Liu, Shouming Zhong, Fuli Zhong, Zijian Liu

Abstract:

In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, some simulation figures are carried out to support the analytical findings.

Keywords: stochastically bounded, global stability, Holling II functional response, white noise, Markovian switching.

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Authors: J. Levendovszky, I. Koncz, P. Boros

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The paper is concerned with developing stochastic delay mechanisms for efficient multicast protocols and for smooth mobile handover processes which are capable of preserving a given Quality of Service (QoS). In both applications the participating entities (receiver nodes or subscribers) sample a stochastic timer and generate load after a random delay. In this way, the load on the networking resources is evenly distributed which helps to maintain QoS communication. The optimal timer distributions have been sought in different p.d.f. families (e.g. exponential, power law and radial basis function) and the optimal parameter have been found in a recursive manner. Detailed simulations have demonstrated the improvement in performance both in the case of multicast and mobile handover applications.

Keywords: Multicast communication, stochactic delay mechanisms.

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