Search results for: stochastic control

Authors: Yifu Ding, Vijay Avinash, Malcolm McCulloch

Abstract:

As the proliferation of decentralized energy systems, the UK power system allows small-scale entities such as microgrids (MGs) to tender multiple energy services including energy arbitrage and frequency responses (FRs). However, its operation requires the balance between the uncertain renewable generations and loads in real-time and has to fulfill their provision requirements of contract services continuously during the time window agreed, otherwise it will be penalized for the under-delivered provision. To hedge against risks due to uncertainties and maximize the economic benefits, we propose a stochastic model predictive control (SMPC) framework to optimize its operation for the multi-service provision. Distinguished from previous works, we include a detailed economic-degradation model of the lithium-ion battery to quantify the costs of different service provisions, as well as accurately describe the changing dynamics of the battery. Considering a branch of load and generation scenarios and the battery aging, we formulate a risk-averse cost function using conditional value at risk (CVaR). It aims to achieve the maximum expected net revenue and avoids severe losses. The framework will be performed on a case study of a PV-battery grid-tied microgrid in the UK with real-life data. To highlight its performance, the framework will be compared with the case without the degradation model and the deterministic formulation.

Keywords: model predictive control (MPC), battery degradation, frequency response, microgrids

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Authors: M. J. Shofa, A. Hidayatno, O. M. Armand

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MRP as a production control system is appropriate for the deterministic environment. Unfortunately, most production systems such as customer demands are stochastic. Demand-Driven MRP (DDMRP) is a new approach for inventory control system, and it deals with demand uncertainty. The objective of this paper is to compare the MRP and DDMRP work for a long lead time and uncertain demand in terms of on-hand inventory levels. The evaluation is conducted through a discrete event simulation using purchased part data from an automotive company. The result is MRP gives 50,759 pcs / day while DDMRP gives 34,835 pcs / day (reduce 32%), it means DDMRP is more effective inventory control than MRP in terms of on-hand inventory levels.

Keywords: Demand-Driven MRP, long lead time, MRP, uncertain demand

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: H. M. Soroush

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The problem of scheduling products and services for on-time deliveries is of paramount importance in today’s competitive environments. It arises in many manufacturing and service organizations where it is desirable to complete jobs (products or services) with different weights (penalties) on or before their due dates. In such environments, schedules should frequently decide whether to schedule a job based on its processing time, due-date, and the penalty for tardy delivery to improve the system performance. For example, it is common to measure the weighted number of late jobs or the percentage of on-time shipments to evaluate the performance of a semiconductor production facility or an automobile assembly line. In this paper, we address the problem of scheduling a set of jobs on a server where processing times or due-dates of jobs are random variables and fixed weights (penalties) are imposed on the jobs’ late deliveries. The goal is to find the schedule that minimizes the expected weighted number of tardy jobs. The problem is NP-hard to solve; however, we explore three scenarios of the problem wherein: (i) both processing times and due-dates are stochastic; (ii) processing times are stochastic and due-dates are deterministic; and (iii) processing times are deterministic and due-dates are stochastic. We prove that special cases of these scenarios are solvable optimally in polynomial time, and introduce efficient heuristic methods for the general cases. Our computational results show that the heuristics perform well in yielding either optimal or near optimal sequences. The results also demonstrate that the stochasticity of processing times or due-dates can affect scheduling decisions. Moreover, the proposed problem is general in the sense that its special cases reduce to some new and some classical stochastic single machine models.

Keywords: number of late jobs, scheduling, single server, stochastic

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to the low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effect of these random errors, they must be accurately modeled. Where the key is the successful implementation that depends on how well the noise statistics of the inertial sensors is selected. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors

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Authors: Mansour H. Alkmim, Adriano T. Fabro, Marcus V. G. De Morais

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In this paper, a global direct search optimization algorithm to reduce vibration of a tuned liquid column damper (TLCD), a class of passive structural control device, is presented. The objective is to find optimized parameters for the TLCD under stochastic load from different wind power spectral density. A verification is made considering the analytical solution of an undamped primary system under white noise excitation. Finally, a numerical example considering a simplified wind turbine model is given to illustrate the efficacy of the TLCD. Results from the random vibration analysis are shown for four types of random excitation wind model where the response PSDs obtained showed good vibration attenuation.

Keywords: generalized pattern search, parameter optimization, random vibration analysis, vibration suppression

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Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

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Authors: Katja Ignatieva, Patrick Wong

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We investigated the dynamics of high frequency energy prices, including crude oil and electricity prices. The returns of underlying quantities are modelled using various parametric models such as stochastic framework with jumps and stochastic volatility (SVCJ) as well as non-parametric alternatives, which are purely data driven and do not require specification of the drift or the diffusion coefficient function. Using different statistical criteria, we investigate the performance of considered parametric and nonparametric models in their ability to forecast price series and volatilities. Our models incorporate possible seasonalities in the underlying dynamics and utilise advanced estimation techniques for the dynamics of energy prices.

Keywords: stochastic volatility, affine jump-diffusion models, high frequency data, model specification, markov chain monte carlo

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Authors: Kun Huang

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This paper investigates whether the combination of local and stochastic volatility models can be calibrated exactly to any arbitrage-free implied volatility surface of European option. The risk neutral Brownian Bridge density is applied for calibration of the leverage function of our Hybrid model. Furthermore, the tails of marginal risk neutral density are generated by Generalized Extreme Value distribution in order to capture the properties of asset returns. The local volatility is generated from the arbitrage-free implied volatility surface using stochastic volatility inspired parameterization.

Keywords: arbitrage free implied volatility, calibration, extreme value distribution, hybrid model, local volatility, risk-neutral density, stochastic volatility

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: area-based traffic, car-following model, micro-simulation, stochastic modeling

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Authors: Abeer Amayri, Akif A. Bulgak

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Due to today’s globalization as well as outsourcing practices of the companies, the Supply Chain (SC) performances have become more dependent on the efficient movement of material among places that are geographically dispersed, where there is more chance for disruptions. One such disruption is the quality and delivery uncertainties of outsourcing. These uncertainties could lead the products to be unsafe and, as is the case in a number of recent examples, companies may have to end up in recalling their products. As a result of these problems, there is a need to develop a methodology for selecting suppliers globally in view of risks associated with low quality and late delivery. Accordingly, we developed a two-stage stochastic model that captures the risks associated with uncertainty in quality and delivery as well as a solution procedure for the model. The stochastic model developed simultaneously optimizes supplier selection and purchase quantities under price discounts over a time horizon. In particular, our target is the study of global organizations with multiple sites and multiple overseas suppliers, where the pricing is offered in suppliers’ local currencies. Our proposed methodology is applied to a case study for a US automotive company having two assembly plants and four potential global suppliers to illustrate how the proposed model works in practice.

Keywords: global supply chains, quality, stochastic programming, supplier selection

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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: J. J. Vargas, N. Prieto, L. A. Toro

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Control charts are commonly used to monitor processes involving either variable or attribute of quality characteristics and determining the control limits as a critical task for quality engineers to improve the processes. Nonetheless, in some applications it is necessary to include an estimation of efficiency. In this paper, the ability to define the efficiency of an industrial process was added to a control chart by means of incorporating a data envelopment analysis (DEA) approach. In depth, a Bayesian estimation was performed to calculate the posterior probability distribution of parameters as means and variance and covariance matrix. This technique allows to analyse the data set without the need of using the hypothetical large sample implied in the problem and to be treated as an approximation to the finite sample distribution. A rejection simulation method was carried out to generate random variables from the parameter functions. Each resulting vector was used by stochastic DEA model during several cycles for establishing the distribution of each efficiency measures for each DMU (decision making units). A control limit was calculated with model obtained and if a condition of a low level efficiency of DMU is presented, system efficiency is out of control. In the efficiency calculated a global optimum was reached, which ensures model reliability.

Keywords: data envelopment analysis, DEA, Multivariate control chart, rejection simulation method

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time.

Keywords: mathematical expectation, filtration, anomalous noise, memory

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Authors: Seon Soon Choi

Abstract:

The essential purpose is to present the good fatigue crack propagation model describing a stochastic fatigue crack growth behavior in a rolled magnesium alloy, AZ31, under various load ratio conditions. Fatigue crack propagation experiments were carried out in laboratory air under four conditions of load ratio, R, using AZ31 to investigate the crack growth behavior. The stochastic fatigue crack growth behavior was analyzed using an interpolation of random variable, Z, introduced to an empirical fatigue crack propagation model. The empirical fatigue models used in this study are Paris-Erdogan model, Walker model, Forman model, and modified Forman model. It was found that the random variable is useful in describing the stochastic fatigue crack growth behaviors under various load ratio conditions. The good probabilistic model describing a stochastic fatigue crack growth behavior under various load ratio conditions was also proposed.

Keywords: magnesium alloys, fatigue crack propagation model, load ratio, interpolation of random variable

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Colin O’Hare, Zili Zho, Thomas Sneddon

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The Australian superannuation system has received high praise for its participation rates and level of funding in retirement yet it is only 25 years old. In recent years, with increasing longevity and persistent lower rates of investment return, how adequate will the funds accumulated through a superannuation system be? In this paper we take Australia as a case study and build a stochastic model of accumulation and decummulation of funds and determine the expected number of years a fund may last an individual in retirement.

Keywords: component, mortality, stochastic models, superannuation

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Daniel Fundi Murithi

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Missing data is a real bane in many surveys. To overcome the problems caused by missing data, partial deletion, and single imputation methods, among others, have been proposed. However, problems such as discarding usable data and inaccuracy in reproducing known population parameters and standard errors are associated with them. For regression and stochastic imputation, it is assumed that there is a variable with complete cases to be used as a predictor in estimating missing values in the other variable, and the relationship between the two variables is linear, which might not be realistic in practice. In this project, we estimate population total in presence of missing values in two-phase sampling. Instead of regression or stochastic models, non-parametric model based regression model is used in imputing missing values. Empirical study showed that nonparametric model-based regression imputation is better in reproducing variance of population total estimate obtained when there were no missing values compared to mean, median, regression, and stochastic imputation methods. Although regression and stochastic imputation were better than nonparametric model-based imputation in reproducing population total estimates obtained when there were no missing values in one of the sample sizes considered, nonparametric model-based imputation may be used when the relationship between outcome and predictor variables is not linear.

Keywords: finite population total, missing data, model-based imputation, two-phase sampling

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Authors: Mahmoud M. Othman, Almoataz Y. Abdelaziz, Yasser G. Hegazy

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This paper presents a load control strategy based on modification of the Big Bang Big Crunch optimization method. The proposed strategy aims to determine the optimal load to be controlled and the corresponding time of control in order to minimize the energy purchased from substation. The presented strategy helps the distribution network operator to rely on the renewable energy sources in supplying the system demand. The renewable energy sources used in the presented study are modeled using the diagonal band Copula method and sequential Monte Carlo method in order to accurately consider the multivariate stochastic dependence between wind power, photovoltaic power and the system demand. The proposed algorithms are implemented in MATLAB environment and tested on the IEEE 37-node feeder. Several case studies are done and the subsequent discussions show the effectiveness of the proposed algorithm.

Keywords: big bang big crunch, distributed generation, load control, optimization, planning

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Authors: Mizan Ahmed, Srikanth Venkatesan

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Geological and tectonic framework indicates that Bangladesh is one of the most seismically active regions in the world. The Bengal Basin is at the junction of three major interacting plates: the Indian, Eurasian, and Burma Plates. Besides there are many active faults within the region, e.g. the large Dauki fault in the north. The country has experienced a number of destructive earthquakes due to the movement of these active faults. Current seismic provisions of Bangladesh are mostly based on earthquake data prior to the 1990. Given the record of earthquakes post 1990, there is a need to revisit the design provisions of the code. This paper compares the base shear demand of three major cities in Bangladesh: Dhaka (the capital city), Sylhet, and Chittagong for earthquake scenarios of magnitudes 7.0MW, 7.5MW, 8.0MW and 8.5MW using a stochastic model. In particular, the stochastic model allows the flexibility to input region specific parameters such as shear wave velocity profile (that were developed from Global Crustal Model CRUST2.0) and include the effects of attenuation as individual components. Effects of soil amplification were analysed using the Extended Component Attenuation Model (ECAM). Results show that the estimated base shear demand is higher in comparison with code provisions leading to the suggestion of additional seismic design consideration in the study regions.

Keywords: attenuation, earthquake, ground motion, Stochastic, seismic hazard

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Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

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In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

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Authors: Chi Zhang, Hua-Peng Chen

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With the increasingly demanding resources in the word, renewable and clean energy has been considered as an alternative way to replace traditional ones. Thus, one of practical examples for using wind energy is wind turbine, which has gained more attentions in recent research. Like most offshore structures, the blades, which is the most critical components of the wind turbine, will be subjected to millions of loading cycles during service life. To operate safely in marine environments, the blades are typically made from fibre reinforced composite materials to resist fatigue delamination and harsh environment. The fatigue crack development of blades is uncertain because of indeterminate mechanical properties for composite and uncertainties under offshore environment like wave loads, wind loads, and humid environments. There are three main delamination failure modes for composite blades, and the most common failure type in practices is subjected to mixed mode loading, typically a range of opening (mode 1) and shear (mode 2). However, the fatigue crack development for mixed mode cannot be predicted as deterministic values because of various uncertainties in realistic practical situation. Therefore, selecting an effective stochastic model to evaluate the mixed mode behaviour of wind turbine blades is a critical issue. In previous studies, gamma process has been considered as an appropriate stochastic approach, which simulates the stochastic deterioration process to proceed in one direction such as realistic situation for fatigue damage failure of wind turbine blades. On the basis of existing studies, various Paris Law equations are discussed to simulate the propagation of the fatigue crack growth. This paper develops a Paris model with the stochastic deterioration modelling according to gamma process for predicting fatigue crack performance in design service life. A numerical example of wind turbine composite materials is investigated to predict the mixed mode crack depth by Paris law and the probability of fatigue failure by gamma process. The probability of failure curves under different situations are obtained from the stochastic deterioration model for comparisons. Compared with the results from experiments, the gamma process can take the uncertain values into consideration for crack propagation of mixed mode, and the stochastic deterioration process shows a better agree well with realistic crack process for composite blades. Finally, according to the predicted results from gamma stochastic model, assessment strategies for composite blades are developed to reduce total lifecycle costs and increase resistance for fatigue crack growth.

Keywords: Reinforced fibre composite, Wind turbine blades, Fatigue delamination, Mixed failure mode, Stochastic process.

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Authors: Xiang Zhang, David Rey, S. Travis Waller

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Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: parameter calibration, sequential quadratic programming, stochastic user equilibrium, traffic assignment, transportation planning

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Authors: Yen-Po Wang, Ming-Chih Huang, Ming-Lian Chang

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A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.

Keywords: damage locating vectors, deterministic-stochastic subspace system, shaking table tests, system identification

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Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research field. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method with the unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with the unknown probability distribution.

Keywords: optimal control, stochastic systems, discrete time systems, probabilistic constraints

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Authors: Mohanad Al-Behadili, Djamila Ouelhadj

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In this paper, a specific type of vehicle routing problem under stochastic demand (SVRP) is considered. This problem is of great importance because it models for many of the real world vehicle routing applications. This paper used a robust optimisation model to solve the problem along with the novel Simulation-Particle Swarm Optimisation (Sim-PSO) approach. The proposed Sim-PSO approach is based on the hybridization of the Monte Carlo simulation technique with the PSO algorithm. A comparative study between the proposed model and the Sim-PSO approach against other solution methods in the literature has been given in this paper. This comparison including the Analysis of Variance (ANOVA) to show the ability of the model and solution method in solving the complicated SVRP. The experimental results show that the proposed model and Sim-PSO approach has a significant impact on the obtained solution by providing better quality solutions comparing with well-known algorithms in the literature.

Keywords: stochastic vehicle routing problem, robust optimisation model, Monte Carlo simulation, particle swarm optimisation

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Authors: Vinayak Bassi, Rajpreet Singh

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Over the years, with the emergence of sophisticated computers and algorithms, finance has been quantified using computational prowess. Asset valuation has been one of the key components of quantitative finance. In fact, it has become one of the embryonic steps in determining risk related to a portfolio, the main goal of quantitative finance. This study comprises a drawing comparison between valuation output generated by two stochastic dynamic models, namely Black-Scholes and Dupire’s bi-dimensionality model. Both of these models are formulated for computing the valuation function for a portfolio of European options using Monte Carlo simulation methods. Although Monte Carlo algorithms have a slower convergence rate than calculus-based simulation techniques (like FDM), they work quite effectively over high-dimensional dynamic models. A fidelity gap is analyzed between the static (historical) and stochastic inputs for a sample portfolio of underlying assets. In order to enhance the performance efficiency of the model, the study emphasized the use of variable reduction methods and customizing random number generators to implement parallelization. An attempt has been made to further implement the Dupire’s model on a GPU to achieve higher computational performance. Furthermore, ideas have been discussed around the performance enhancement and bottleneck identification related to the implementation of options-pricing models on GPUs.

Keywords: monte carlo, stochastic models, computational finance, parallel programming, scientific computing

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Authors: Nikolaos Mamalis

Abstract:

The work of the eminent architect and composer has undoubtedly been influenced both by his architecture and collaboration with Le Corbusier and by the conquests of the musical avant-garde of the 20th century (Schoenberg, Messian, Bartock, electroacoustic music). It is known that the golden mean and the Fibonacci sequence played a momentous role in the Architectural Avant-garde (Modulor) and expanded on musical pursuits. Especially in the 50s (serialism), it was a structural tool for composition. Xenakis' architectural and musical work (Sacrifice, Metastasis, Rebonds, etc.) received the influence of the Golden Section, as has been repeatedly demonstrated. However, the idea of this retrospective sequence and the reflection raised by the search for new proportions, both in the architectural and the musical work of Xenakis, was not limited to constituting a step, a workable formula that acted unifyingly with regard to the other parameters of the musical work, or as an aesthetic model that makes sense - philosophically and poetically - an anthropocentric dimension as in other composers (see Luigi Nono) ̇ triggered a qualitative leap, an opening of the composer to the assimilation of mathematical concepts and scientific types in music and the consolidation of new sound horizons of stochastic music.

Keywords: golden ratio, music, space, stochastic music

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