Rahman Farnoosh and Ebrahimi Morteza
The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind.
Abstract
Purpose
The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind.
Design/methodology/approach
A numerical algorithm consisted of the combined use of the successive substitution method and Monte Carlo simulation is established for the solution of Fredholm integral equations of the second kind.
Findings
Owing to the application of the present method, the variance of the solution is reduced. Therefore, this method achieves several orders of magnitude improvement in accuracy over the conventional Monte Carlo method.
Practical implications
Numerical tests are performed in order to show the efficiency and accuracy of the present paper. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes CPU time at Pentium IV‐2.4 GHz PC.
Originality/value
This paper provides a new efficient method to solve Fredholm integral equations of the second kind and discusses basic advantages of the present method.
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Keywords
Rahman Farnoosh and Arezoo Hajrajabi
The purpose of this paper is to consider the stochastic differential equation of the RL electrical circuit as the dynamic model of a state space system when the current in the…
Abstract
Purpose
The purpose of this paper is to consider the stochastic differential equation of the RL electrical circuit as the dynamic model of a state space system when the current in the circuit is hidden and corrupted by the measurement noise. Estimation of the corrupted current and the values of missing or unknown parameters (resistance, the observed current variance in the measurement model, the mean and variance of the current prior distribution) which are the main concern in electrical engineering is considered.
Design/methodology/approach
Optimal filtering is proposed for estimation of the hidden current from the noisy observations. Also, the problem of analyzing this model based on estimation of the unknown parameters is addressed from the likelihood‐based and Bayesian perspective.
Findings
Computational techniques for parameter estimation are carried out by the Maximum likelihood (ML) approach using Expectation‐Maximization type optimization and Bayesian Monte Carlo perspective using Metropolis‐Hastings scheme. The explicit formulas for the ML estimator are obtained and it is shown that the smoothers, the filters and the predictions for the current have the best confidence intervals, respectively. Some numerical simulation examples which are performed by R programming software are considered to show the efficiency and applicability of the proposed approaches. Results show an excellent estimation of the parameters based on these approaches.
Practical implications
Due to the fact that in an empirical situation of electrical engineering, observing the current in the circuit regardless of the measurement noise and knowing the exact value of the parameters are unrealistic assumptions, this paper can be used in various types of real time projects.
Originality/value
To the best of the authors' information, the problem of analyzing the state space model of RL electrical circuit has not been studied before. Furthermore, the estimation of the hidden current as the state of the system and estimation of the unknown parameters of the model via both ML and Bayesian approaches have been investigated for the first time in the present study.
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Rahman Farnoosh, Parisa Nabati, Ramazan Rezaeyan and Morteza Ebrahimi
The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit…
Abstract
Purpose
The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance.
Design/methodology/approach
By adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE).
Findings
Owing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler‐Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise.
Practical implications
Numerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV‐2.4 GHz PC.
Originality/value
It is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.
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Abstract
Purpose
This study aims to explore the spatio-temporal dynamic characteristics and influencing factors of the coordination degree of the three systems of digital economy, energy and human habitat in Western China and to provide academic research support for promoting coordinated and sustainable development in similar regions of the world.
Design/methodology/approach
Based on system theory and sustainable development theory, this study primarily uses the coupled coordination degree model to assess the degree of coordination between the three systems.
Findings
The findings of this study indicate that: The three systems’ overall coordination is low. The distribution of the degree of coordination has spatial differences and its coefficient of variation is small. The probability of the coordination type changing for the better is greater than that of the opposite, and neighboring provinces interact with one another. The old-age dependence ratio, the resident population’s urbanization rate and public budget expenditure have the strongest gray association with the degree of coordination.
Practical implications
This study’s findings will be valuable for policymakers in developing policies to promote the coordinated and sustainable growth of the region’s digital economy, energy and human habitat. Additionally, the findings will aid in facilitating regional exchanges and cooperation to enhance the level of sustainable development.
Social implications
This study’s findings will contribute to increased social interest in coordinating sustainable growth in the digital economy, energy and human habitat.
Originality/value
This study examines the digital economy, energy and human habitat within the same framework and investigates spatial spillover effects using spatial Markov chains.
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Agung Sutrisno and Vikas Kumar
The purpose of this paper is to introduce the integrated model of the Preference Selection Index (PSI) and the prospect theory as new means to appraise the impact of supply chain…
Abstract
Purpose
The purpose of this paper is to introduce the integrated model of the Preference Selection Index (PSI) and the prospect theory as new means to appraise the impact of supply chain sustainability risks based on five pillars of sustainability. Research has shown that sustainability risk assessment has a strong positive impact on improving the performance of enterprises.
Design/methodology/approach
This study adopts a new decision support model for assessing supply chain sustainability risk based on additional failure mode and effect analysis parameters and its integration with PSI methodology and prospect theory. A case example of the supply chain small and medium enterprise (SME) producing fashion have been used in this study.
Findings
The result of this study reveals some critical supply chain sustainability risks affecting the sustainability of enterprises under study.
Research limitations/implications
The use of a limited sample is often associated as a limitation in the research studies and this study is based on findings from SMEs in the fashion retail supply chain. This preliminary study provides academics and practitioners an exemplar of supply chain sustainability risk assessment using integration of the PSI method and prospect theory.
Practical implications
The result of this study is beneficial for practitioners, particularly owner–managers of SMEs who can use this study as guidance on how to consider risk behavior to identify and select the critical sustainability risks and plan mitigating strategies accordingly.
Originality/value
Scientific studies on using the PSI and its integration with prospect theory as means to assess the criticality of supply chain sustainability risks is very rare. To the best of the authors’ knowledge, this is the first paper that presents the integrated model of the PSI and prospect theory to rank supply chain sustainability risks based on five pillars of sustainability.