Efficient parameter estimation of software reliability growth models using harmony search

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

One can find many reliability, availability, and maintainability (RAM) models proposed in the literature. However, such models become more complex day after day, as there is an attempt to capture equipment performance in a more realistic way, such as, explicitly addressing the effect of component ageing and degradation, surveillance activities, and corrective and preventive maintenance policies. Then, there is a need to fit the best model to real data by estimating the model parameters using an appropriate tool. This problem is not easy to solve in some cases since the number of parameters is large and the available data is scarce. This paper considers two main failure models commonly adopted to represent the probability of failure on demand (PFD) of safety equipment: (1) by demand‐caused and (2) standby‐related failures. It proposes a maximum likelihood estimation (MLE) approach for parameter estimation of a reliability model of demand‐caused and standby‐related failures of safety components exposed to degradation by demand stress and ageing that undergo imperfect maintenance. The case study considers real failure, test, and maintenance data for a typical motor‐operated valve in a nuclear power plant. The results of the parameters estimation and the adoption of the best model are discussed.

It is well known that the type of data distribution in the independent variable(s) may affect many statistical procedures. This paper investigates and illustrates the effect of different types of covariates on the parameter estimation of a binary logistic regression model. A simulation study with different sample sizes and different types of covariates (uniform, normal, skewed) was carried out. Results showed that parameter estimation of binary logistic regression model is severely overestimated when sample size is less than 150 for covariate which have normal and uniform distribution while the parameter is underestimated when the distribution of covariate is skewed. Parameter estimation improves for all types of covariates when sample size is large, that is at least 500.

Load forecasting is a crucial aspect of electric power system planning and operation. This paper presents a heuristic approach for optimal parameter estimation of long term load forecast models. The problem is viewed as an optimization one in which the goal is to minimize the total estimation error by properly adjusting the model coefficients. A particle swarm optimization algorithm is developed to minimize the error associated with the estimated model parameters. Real data of Egyptian network is used to perform this study. Results are reported and compared to those obtained using the well known least error squares estimation technique. Comparison results are in favor of the proposed approach which signifies its potential as a promising estimation tool.

This paper presents a combined approach for parameter estimation in models of primary production. The focus is on gross primary production and nutrient assimilation by seaweeds.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

Parameter and uncertainty estimation in stochastic differential equation models with multi-rate data and nonstationary disturbances

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Parameter estimation for grey system models: A nonlinear least squares perspective

Block Matching (BM) is considered to be the most efficient technique for Motion Estimation (ME) in Video Compression. Many algorithms have been developed for BM which includes classical as well as metaheuristic methods. Harmony Search (HS), Differential Evolution (DE), Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO) are the metaheuristic methods used for this purpose. This paper explores a way to formulate a BM algorithm by using Cuckoo Search — a metaheuristic optimization algorithm which is mainly inspired by the breeding behavior of some cuckoo species which shows an obligate brood parasitism. Levy flight behavior of some fruit flies and birds is also incorporated in Cuckoo Search.

A Bayesian procedure is presented for parameter estimation in nonlinear flood event models. We derive a pooling diagnostic using Bayes factors to identify when it is reasonable to pool model parameters across storm events. A case study involving a quasi‐distributed, nonlinear flood event model and five watersheds in the southwest of Western Australia is presented to illustrate the capabilities and utility of the procedure. The results indicate that Markov chain Monte Carlo methods based on the Metropolis‐Hastings algorithm are useful tools for parameter estimation. We find that pooling is not justified for the model and data at hand. This suggests that current practices in nonlinear flood event modeling may be in need of urgent review.

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE's domain of definitionD, using only temperature information in a small subdomainE⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample's remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.

Accurately simulating photovoltaic (PV) modules requires precise parameter extraction, a complex task due to the nonlinear nature of these systems. This study introduces the Mother Tree Optimization with Climate Change (MTO-CL) algorithm to address this challenge by enhancing parameter estimation for a solar PV three-diode model. MTO-CL improves optimization performance by incorporating climate change-inspired adaptations, which affect two key phases: elimination (refreshing 20% of suboptimal solutions) and distortion (slight adjustments to 80% of remaining solutions). This balance between exploration and exploitation allows the algorithm to dynamically and effectively identify optimal parameters. Compared to seven alternative methods, MTO-CL shows superior performance in parameter estimation for various solar modules, including ST40 and SM55, across different irradiances and temperatures. It achieves exceptionally low Root Mean Square Error (RMSE) values from 0.0025A to 0.0165A and Mean Squared Error (MSE) values between 6.2 × 10^-6 and 2.7 × 10^-4, while also significantly minimizing power errors, ranging from 22.86 mW to 239.40 mW. These results demonstrate MTO-CL's effectiveness in improving the accuracy and reliability of PV system modeling, offering a robust tool for enhanced solar energy applications.

The Bayes principle is applied to the joint model selection and parameter estimation of GTD model to explore the prior information. An algorithm using RJ-MCMC is designed. It not only has better model selection and parameter estimation performance than the non-Bayes algorithms, but also solves the mixed parameter estimation problem in GTD model effectively. The advantage of this algorithm is especially evident at low SNR, for short data and with closely-spaced components. Simulations verify the effectiveness of this algorithm.