Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3057

Search results for: parameter estimation

3057 Parameter Estimation of Induction Motors by PSO Algorithm

Authors: A. Mohammadi, S. Asghari, M. Aien, M. Rashidinejad

Abstract:

After emergent of alternative current networks and their popularity, asynchronous motors became more widespread than other kinds of industrial motors. In order to control and run these motors efficiently, an accurate estimation of motor parameters is needed. There are different methods to obtain these parameters such as rotor locked test, no load test, DC test, analytical methods, and so on. The most common drawback of these methods is their inaccuracy in estimation of some motor parameters. In order to remove this concern, a novel method for parameter estimation of induction motors using particle swarm optimization (PSO) algorithm is proposed. In the proposed method, transient state of motor is used for parameter estimation. Comparison of the simulation results purtuined to the PSO algorithm with other available methods justifies the effectiveness of the proposed method.

Keywords: induction motor, motor parameter estimation, PSO algorithm, analytical method

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3056 Parameter Estimation via Metamodeling

Authors: Sergio Haram Sarmiento, Arcady Ponosov

Abstract:

Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

Procedia PDF Downloads 388
3055 Online Battery Equivalent Circuit Model Estimation on Continuous-Time Domain Using Linear Integral Filter Method

Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: electric circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square

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3054 Off-Line Parameter Estimation for the Induction Motor Drive System

Authors: Han-Woong Ahn, In-Gun Kim, Hyun-Seok Hong, Dong-Woo Kang, Ju Lee

Abstract:

It is important to accurately identify machine parameters for direct vector control. To obtain the parameter values, traditional methods can be used such as no-load and rotor locked tests. However, there are many differences between values obtained from the traditional tests and actual values. In addition, there are drawbacks that additional equipment and cost are required for the experiment. Therefore, it is hard to temporary operation to estimate induction motor parameters. Therefore, this paper deals with the estimation algorithm of induction motor parameters without a motor operation and the measurement from additional equipment such as sensors and dynamometer. The validity and usefulness of the estimation algorithm considering inverter nonlinearity is verified by comparing the conventional method with the proposed method.

Keywords: induction motor, parameter, off-line estimation, inverter nonlinearity

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3053 Mathematics Model Approaching: Parameter Estimation of Transmission Dynamics of HIV and AIDS in Indonesia

Authors: Endrik Mifta Shaiful, Firman Riyudha

Abstract:

Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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3052 Considering the Reliability of Measurements Issue in Distributed Adaptive Estimation Algorithms

Authors: Wael M. Bazzi, Amir Rastegarnia, Azam Khalili

Abstract:

In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation method based on incremental distributed least mean-square (IDLMS) algorithm. The proposed method contains two phases: I) Estimation of each sensors observation noise variance, and II) Estimation of the desired parameter using the estimated observation variances. To deal with the reliability of measurements, in the second phase of the proposed algorithm, the step-size parameter is adjusted for each sensor according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the IDLMS algorithm in the same condition.

Keywords: adaptive filter, distributed estimation, sensor network, IDLMS algorithm

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3051 Comparative Analysis of Two Approaches to Joint Signal Detection, ToA and AoA Estimation in Multi-Element Antenna Arrays

Authors: Olesya Bolkhovskaya, Alexey Davydov, Alexander Maltsev

Abstract:

In this paper two approaches to joint signal detection, time of arrival (ToA) and angle of arrival (AoA) estimation in multi-element antenna array are investigated. Two scenarios were considered: first one, when the waveform of the useful signal is known a priori and, second one, when the waveform of the desired signal is unknown. For first scenario, the antenna array signal processing based on multi-element matched filtering (MF) with the following non-coherent detection scheme and maximum likelihood (ML) parameter estimation blocks is exploited. For second scenario, the signal processing based on the antenna array elements covariance matrix estimation with the following eigenvector analysis and ML parameter estimation blocks is applied. The performance characteristics of both signal processing schemes are thoroughly investigated and compared for different useful signals and noise parameters.

Keywords: antenna array, signal detection, ToA, AoA estimation

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3050 Parameter Estimation in Dynamical Systems Based on Latent Variables

Authors: Arcady Ponosov

Abstract:

A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

Procedia PDF Downloads 241
3049 Parameter Estimation of Gumbel Distribution with Maximum-Likelihood Based on Broyden Fletcher Goldfarb Shanno Quasi-Newton

Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

Abstract:

Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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3048 Continuous Differential Evolution Based Parameter Estimation Framework for Signal Models

Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

Abstract:

In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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3047 On Parameter Estimation of Simultaneous Linear Functional Relationship Model for Circular Variables

Authors: N. A. Mokhtar, A. G. Hussin, Y. Z. Zubairi

Abstract:

This paper proposes a new simultaneous simple linear functional relationship model by assuming equal error variances. We derive the maximum likelihood estimate of the parameters in the simultaneous model and the covariance. We show by simulation study the small bias values of the parameters suggest the suitability of the estimation method. As an illustration, the proposed simultaneous model is applied to real data of the wind direction and wave direction measured by two different instruments.

Keywords: simultaneous linear functional relationship model, Fisher information matrix, parameter estimation, circular variables

Procedia PDF Downloads 248
3046 Parameter Estimation for the Mixture of Generalized Gamma Model

Authors: Wikanda Phaphan

Abstract:

Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

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3045 Reliability and Probability Weighted Moment Estimation for Three Parameter Mukherjee-Islam Failure Model

Authors: Ariful Islam, Showkat Ahmad Lone

Abstract:

The Mukherjee-Islam Model is commonly used as a simple life time distribution to assess system reliability. The model exhibits a better fit for failure information and provides more appropriate information about hazard rate and other reliability measures as shown by various authors. It is possible to introduce a location parameter at a time (i.e., a time before which failure cannot occur) which makes it a more useful failure distribution than the existing ones. Even after shifting the location of the distribution, it represents a decreasing, constant and increasing failure rate. It has been shown to represent the appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents the reliability computations and probability weighted moment estimation of three parameter model. A comparative analysis is carried out between three parameters finite range model and some existing bathtub shaped curve fitting models. Since probability weighted moment method is used, the results obtained can also be applied on small sample cases. Maximum likelihood estimation method is also applied in this study.

Keywords: comparative analysis, maximum likelihood estimation, Mukherjee-Islam failure model, probability weighted moment estimation, reliability

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3044 Lithium-Ion Battery State of Charge Estimation Using One State Hysteresis Model with Nonlinear Estimation Strategies

Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

Abstract:

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: state of charge estimation, battery modeling, one-state hysteresis, filtering and estimation

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3043 New Estimation in Autoregressive Models with Exponential White Noise by Using Reversible Jump MCMC Algorithm

Authors: Suparman Suparman

Abstract:

A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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3042 Estimation of Stress-Strength Parameter for Burr Type XII Distribution Based on Progressive Type-II Censoring

Authors: A. M. Abd-Elfattah, M. H. Abu-Moussa

Abstract:

In this paper, the estimation of stress-strength parameter R = P(Y < X) is considered when X; Y the strength and stress respectively are two independent random variables of Burr Type XII distribution. The samples taken for X and Y are progressively censoring of type II. The maximum likelihood estimator (MLE) of R is obtained when the common parameter is unknown. But when the common parameter is known the MLE, uniformly minimum variance unbiased estimator (UMVUE) and the Bayes estimator of R = P(Y < X) are obtained. The exact con dence interval of R based on MLE is obtained. The performance of the proposed estimators is compared using the computer simulation.

Keywords: Burr Type XII distribution, progressive type-II censoring, stress-strength model, unbiased estimator, maximum-likelihood estimator, uniformly minimum variance unbiased estimator, confidence intervals, Bayes estimator

Procedia PDF Downloads 344
3041 Introduction of Robust Multivariate Process Capability Indices

Authors: Behrooz Khalilloo, Hamid Shahriari, Emad Roghanian

Abstract:

Process capability indices (PCIs) are important concepts of statistical quality control and measure the capability of processes and how much processes are meeting certain specifications. An important issue in statistical quality control is parameter estimation. Under the assumption of multivariate normality, the distribution parameters, mean vector and variance-covariance matrix must be estimated, when they are unknown. Classic estimation methods like method of moment estimation (MME) or maximum likelihood estimation (MLE) makes good estimation of the population parameters when data are not contaminated. But when outliers exist in the data, MME and MLE make weak estimators of the population parameters. So we need some estimators which have good estimation in the presence of outliers. In this work robust M-estimators for estimating these parameters are used and based on robust parameter estimators, robust process capability indices are introduced. The performances of these robust estimators in the presence of outliers and their effects on process capability indices are evaluated by real and simulated multivariate data. The results indicate that the proposed robust capability indices perform much better than the existing process capability indices.

Keywords: multivariate process capability indices, robust M-estimator, outlier, multivariate quality control, statistical quality control

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3040 Nonlinear Aerodynamic Parameter Estimation of a Supersonic Air to Air Missile by Using Artificial Neural Networks

Authors: Tugba Bayoglu

Abstract:

Aerodynamic parameter estimation is very crucial in missile design phase, since accurate high fidelity aerodynamic model is required for designing high performance and robust control system, developing high fidelity flight simulations and verification of computational and wind tunnel test results. However, in literature, there is not enough missile aerodynamic parameter identification study for three main reasons: (1) most air to air missiles cannot fly with constant speed, (2) missile flight test number and flight duration are much less than that of fixed wing aircraft, (3) variation of the missile aerodynamic parameters with respect to Mach number is higher than that of fixed wing aircraft. In addition to these challenges, identification of aerodynamic parameters for high wind angles by using classical estimation techniques brings another difficulty in the estimation process. The reason for this, most of the estimation techniques require employing polynomials or splines to model the behavior of the aerodynamics. However, for the missiles with a large variation of aerodynamic parameters with respect to flight variables, the order of the proposed model increases, which brings computational burden and complexity. Therefore, in this study, it is aimed to solve nonlinear aerodynamic parameter identification problem for a supersonic air to air missile by using Artificial Neural Networks. The method proposed will be tested by using simulated data which will be generated with a six degree of freedom missile model, involving a nonlinear aerodynamic database. The data will be corrupted by adding noise to the measurement model. Then, by using the flight variables and measurements, the parameters will be estimated. Finally, the prediction accuracy will be investigated.

Keywords: air to air missile, artificial neural networks, open loop simulation, parameter identification

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3039 Time Delay Estimation Using Signal Envelopes for Synchronisation of Recordings

Authors: Sergei Aleinik, Mikhail Stolbov

Abstract:

In this work, a method of time delay estimation for dual-channel acoustic signals (speech, music, etc.) recorded under reverberant conditions is investigated. Standard methods based on cross-correlation of the signals show poor results in cases involving strong reverberation, large distances between microphones and asynchronous recordings. Under similar conditions, a method based on cross-correlation of temporal envelopes of the signals delivers a delay estimation of acceptable quality. This method and its properties are described and investigated in detail, including its limits of applicability. The method’s optimal parameter estimation and a comparison with other known methods of time delay estimation are also provided.

Keywords: cross-correlation, delay estimation, signal envelope, signal processing

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3038 Identification of Wiener Model Using Iterative Schemes

Authors: Vikram Saini, Lillie Dewan

Abstract:

This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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3037 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov chain Monte Carlo method, maximum likelihood method, normal distribution

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3036 Confidence Intervals for Quantiles in the Two-Parameter Exponential Distributions with Type II Censored Data

Authors: Ayman Baklizi

Abstract:

Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths.

Keywords: asymptotic intervals, Bayes intervals, bootstrap, generalized pivot variables, two-parameter exponential distribution, quantiles

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3035 Parameter Estimation of False Dynamic EIV Model with Additive Uncertainty

Authors: Dalvinder Kaur Mangal

Abstract:

For the past decade, noise corrupted output measurements have been a fundamental research problem to be investigated. On the other hand, the estimation of the parameters for linear dynamic systems when also the input is affected by noise is recognized as more difficult problem which only recently has received increasing attention. Representations where errors or measurement noises/disturbances are present on both the inputs and outputs are usually called errors-in-variables (EIV) models. These disturbances may also have additive effects which are also considered in this paper. Parameter estimation of false EIV problem using equation error, output error and iterative prefiltering identification schemes with and without additive uncertainty, when only the output observation is corrupted by noise has been dealt in this paper. The comparative study of these three schemes has also been carried out.

Keywords: errors-in-variable (EIV), false EIV, equation error, output error, iterative prefiltering, Gaussian noise

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3034 Estimation of Fuel Cost Function Characteristics Using Cuckoo Search

Authors: M. R. Al-Rashidi, K. M. El-Naggar, M. F. Al-Hajri

Abstract:

The fuel cost function describes the electric power generation-cost relationship in thermal plants, hence, it sheds light on economical aspects of power industry. Different models have been proposed to describe this relationship with the quadratic function model being the most popular one. Parameters of second order fuel cost function are estimated in this paper using cuckoo search algorithm. It is a new population based meta-heuristic optimization technique that has been used in this study primarily as an accurate estimation tool. Its main features are flexibility, simplicity, and effectiveness when compared to other estimation techniques. The parameter estimation problem is formulated as an optimization one with the goal being minimizing the error associated with the estimated parameters. A case study is considered in this paper to illustrate cuckoo search promising potential as a valuable estimation and optimization technique.

Keywords: cuckoo search, parameters estimation, fuel cost function, economic dispatch

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3033 A Novel Stator Resistance Estimation Method and Control Design of Speed-Sensorless Induction Motor Drives

Authors: N. Ben Si Ali, N. Benalia, N. Zarzouri

Abstract:

Speed sensorless systems are intensively studied during recent years; this is mainly due to their economical benefit and fragility of mechanical sensors and also the difficulty of installing this type of sensor in many applications. These systems suffer from instability problems and sensitivity to parameter mismatch at low speed operation. In this paper an analysis of adaptive observer stability with stator resistance estimation is given.

Keywords: motor drive, sensorless control, adaptive observer, stator resistance estimation

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3032 Parameter Estimation with Uncertainty and Sensitivity Analysis for the SARS Outbreak in Hong Kong

Authors: Afia Naheed, Manmohan Singh, David Lucy

Abstract:

This work is based on a mathematical as well as statistical study of an SEIJTR deterministic model for the interpretation of transmission of severe acute respiratory syndrome (SARS). Based on the SARS epidemic in 2003, the parameters are estimated using Runge-Kutta (Dormand-Prince pairs) and least squares methods. Possible graphical and numerical techniques are used to validate the estimates. Then effect of the model parameters on the dynamics of the disease is examined using sensitivity and uncertainty analysis. Sensitivity and uncertainty analytical techniques are used in order to analyze the affect of the uncertainty in the obtained parameter estimates and to determine which parameters have the largest impact on controlling the disease dynamics.

Keywords: infectious disease, severe acute respiratory syndrome (SARS), parameter estimation, sensitivity analysis, uncertainty analysis, Runge-Kutta methods, Levenberg-Marquardt method

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3031 A Flexible Pareto Distribution Using α-Power Transformation

Authors: Shumaila Ehtisham

Abstract:

In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

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3030 Monte Carlo Methods and Statistical Inference of Multitype Branching Processes

Authors: Ana Staneva, Vessela Stoimenova

Abstract:

A parametric estimation of the MBP with Power Series offspring distribution family is considered in this paper. The MLE for the parameters is obtained in the case when the observable data are incomplete and consist only with the generation sizes of the family tree of MBP. The parameter estimation is calculated by using the Monte Carlo EM algorithm. The estimation for the posterior distribution and for the offspring distribution parameters are calculated by using the Bayesian approach and the Gibbs sampler. The article proposes various examples with bivariate branching processes together with computational results, simulation and an implementation using R.

Keywords: Bayesian, branching processes, EM algorithm, Gibbs sampler, Monte Carlo methods, statistical estimation

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3029 Application of the Discrete Rationalized Haar Transform to Distributed Parameter System

Authors: Joon-Hoon Park

Abstract:

In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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3028 Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models

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

Abstract:

This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model

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