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Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and controlled, especially when dealing with nonlinearity and imperfect plant models. In this study, we propose a nonlinear dynamic multiple-input multiple-output (MIMO) plant model. This model is then transformed through linearization, a technique frequently utilized in the analysis and modeling of fractional processes, and decoupling for decentralized fixed-structure H-infinity robust control design. Simulation tests based on MATLAB and SIMULINK are subsequently executed. Numerous assessments are conducted to evaluate tracking performance, external disturbance rejection, and plant parameter fluctuations to gauge the effectiveness of the proposed model. The objective of this work is to provide a framework that anticipates potential outcomes, paving the way for implementing a reliable controller synthesis for MIMO-connected tanks in real-world scenarios. [ABSTRACT FROM AUTHOR]

This article proposes a methodology for diagnostics in a logistic regression with random intercept motivated by a biological study. The methodology includes local and global influence techniques allowing us to contrast the results of both types of influence. The proposed methodology is applied to a case study with real data to show its potential. This study corresponds to the reproduction of arachnids reporting how the local and global influence of atypical observations can modify the significance of parameters, and then the biological conclusions. The model fitting is evaluated through predictive indicators. The methodology is summarized in an algorithm and a demo example is implemented in R code to facilitate its application. To evaluate the performance of the methodology, Monte Carlo simulations are conducted. [ABSTRACT FROM AUTHOR]

Univariate Birnbaum-Saunders models have been widely applied to fatigue studies. Calculation of fatigue life is of great importance in determining the reliability of materials. We propose and derive new multivariate generalized Birnbaum-Saunders regression models. We use the maximum likelihood method and the EM algorithm to estimate their parameters. We carry out a simulation study to evaluate the performance of the corresponding maximum likelihood estimators. We illustrate the new models with real-world multivariate fatigue data. [ABSTRACT FROM AUTHOR]

We propose goodness-of-fit tests for Birnbaum-Saunders distributions with type-II right censored data. Classical goodness-of-fit tests based on the empirical distribution, such as Anderson-Darling, Cramér-von Misses, and Kolmogorov-Smirnov, are adapted to censored data, and evaluated by means of a simulation study. The obtained results are applied to real-world censored reliability data. [ABSTRACT FROM AUTHOR]

The Birnbaum-Saunders distribution has largely been applied to material fatigue and reliability studies to relate the time until failure to some type of cumulative damage. This damage is produced by the growth of a dominant crack in material specimens, the propagation of which is due to cyclic patterns of stress. However, the Birnbaum-Saunders model was constructed under restrictive conditions that may not be valid for certain applications. In particular, this model was developed assuming that the crack extension in each cycle has a constant s-mean over time. In this article, we assume the crack extensions in each cycle have a non-constant 8-mean. This leads us to introduce a non-central version of the Birnbaum-Saunders distribution. Specifically, a comprehensive description of the properties and characteristics of this new model is presented. The suitability of this non-central distribution is shown by using real, and simulated data. [ABSTRACT FROM AUTHOR]

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method. [ABSTRACT FROM AUTHOR]

This study investigates three regression models based on the Birnbaum–Saunders distribution. The first model is obtained directly through the Birnbaum–Saunders distribution; the second model is obtained via a logarithmic transformation in the response variable; and the third model employs a mean parametrization of this distribution. The primary objective of this study is to compare the performance of the three Birnbaum–Saunders regression models. The secondary objective is to provide a tool to choose the best model for regression when analysing data following a Birnbaum–Saunders distribution. By using Monte Carlo simulations and the R software, we evaluate the behaviour of the corresponding estimators, and of the Cox–Snell and randomized quantile residuals. An illustration with real data is provided to compare the investigated regression models. [ABSTRACT FROM AUTHOR]

Regression modelling where explanatory variables are measured with error is a common problem in applied sciences. However, if inappropriate analysis methods are applied, then unreliable conclusions can be made. This work deals with estimation and diagnostic analytics in regression modelling based on the Birnbaum–Saunders distribution using additive measurement errors. The maximum pseudo-likelihood and regression calibration methods are used for parameter estimation. We also carry out a residual analysis and apply global and local diagnostic techniques in order to detect anomalous and potentially influential observations. Simulations are conducted to validate the proposed approach and to evaluate performance. A real-world data set, related to earthquakes, is used to illustrate the new approach. [ABSTRACT FROM AUTHOR]

Microbial electrolysis cell (MEC) is a fundamental type of bio-electrochemical system. MEC is a novel and emerging renewable energy technology that is based on biomass. The behavior of the MEC system is highly nonlinear due to the complexity of its dynamics. For the desired optimal production of hydrogen, feedback control of MEC processes is necessary. Due to the novelty of MEC, limited research is available on its control. Studies on linear model-based robust control of MEC processes are missing. In this article, we develop a nonlinear dynamic model for MEC, linearize this model, and calculate a linear time-invariant transfer function. Based on this linearization, a fixed-structure, optimal and robust controller is proposed to achieve a fast-settling time exhibiting no overshoot and having zero steady-state error. The robustness of the developed controller is evaluated for parameter uncertainty, measurement noise, and disturbance rejection. Batch biomass processes are fed only at the start of each process cycle. The output does not follow the desired response when the substrate or biomass is consumed. Then, the error accumulates, and it causes the control effort to increase unboundedly. The existing literature on control of fed-batch MEC processes does not consider this integral windup phenomenon. In this article, we also develop an anti-windup control strategy to eliminate the integral windup error and to avoid any possible instability or destruction. The overall conclusion of our study is that the developed robust controller achieves a faster and more robust response than the existing controllers. We provide an anti-integral windup solution to eliminate windup errors in feedback control of fed-batch MEC processes. [Display omitted] • We design an optimal robust controller for a dynamic model of microbial electrolysis cells. • We linearize the non-linear model and calculate a time-invariant transfer function. • We evaluate uncertainty, noise, and disturbance of the controller. • We develop a strategy to eliminate windup error and avoid instability. • Our controller achieves a more fast and robust response than the existing controllers. [ABSTRACT FROM AUTHOR]

Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for disjoint principal component analysis based on an intelligent search. The method consists of a principal component analysis with constraints, allowing us to determine components that are linear combinations of disjoint subsets of the original variables. The effectiveness of the proposed method contributes to solve one of the crucial problems of multivariate analysis, that is, the interpretation of the vectorial subspaces in the reduction of the dimensionality. The method selects the variables that contribute the most to each of the principal components in a clear and direct way. Numerical results are provided to confirm the quality of the solutions attained by the proposed method. This method avoids a local optimum and obtains a high success rate when reaching the best solution, which occurs in all the cases of our simulation study. An illustration with environmental real data shows the good performance of the method and its potential applications. [ABSTRACT FROM AUTHOR]

Birnbaum-Saunders models have been widely used to describe data following positive-skew distributions. In this article, we introduce a bivariate Birnbaum-Saunders distribution which has the mean as one of its parameters, allowing us to mimic the standard parameterization of the normal distribution, but in an asymmetric framework. We derive some properties of the mean-based bivariate Birnbaum-Saunders distribution useful for statistical and reliability analyses. Maximum likelihood and modified moment estimations of the model parameters and associated inference are considered. A simulation study is conducted to evaluate the performance of the corresponding estimators and coverage probabilities of confidence intervals are also discussed. Finally, a real-world data analysis is carried out for illustrating the potential of the proposed model. [ABSTRACT FROM AUTHOR]

Longitudinal count responses are often analyzed with a Poisson mixed model. However, under overdispersion, these responses are better described by a negative binomial mixed model. Estimators of the corresponding parameters are usually obtained by the maximum likelihood method. To investigate the stability of these maximum likelihood estimators, we propose a methodology of sensitivity analysis using local influence. As count responses are discrete, we are unable to perturb them with the standard scheme used in local influence. Then, we consider an appropriate perturbation for the means of these responses. The proposed methodology is useful in different applications, but particularly when medical data are analyzed, because the removal of influential cases can change the statistical results and then the medical decision. We study the performance of the methodology by using Monte Carlo simulation and applied it to real medical data related to epilepsy and headache. All of these numerical studies show the good performance and potential of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Optimization seeks to find inputs for an objective function that result in a maximum or minimum. Optimization methods are divided into exact and approximate (algorithms). Several optimization algorithms imitate natural phenomena, laws of physics, and behavior of living organisms. Optimization based on algorithms is the challenge that underlies machine learning, from logistic regression to training neural networks for artificial intelligence. In this paper, a new algorithm called two-stage optimization (TSO) is proposed. The TSO algorithm updates population members in two steps at each iteration. For this purpose, a group of good population members is selected and then two members of this group are randomly used to update the position of each of them. This update is based on the first selected good member at the first stage, and on the second selected good member at the second stage. We describe the stages of the TSO algorithm and model them mathematically. Performance of the TSO algorithm is evaluated for twenty-three standard objective functions. In order to compare the optimization results of the TSO algorithm, eight other competing algorithms are considered, including genetic, gravitational search, grey wolf, marine predators, particle swarm, teaching-learning-based, tunicate swarm, and whale approaches. The numerical results show that the new algorithm is superior and more competitive in solving optimization problems when compared with other algorithms. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to the article "Successful aminolevulinic acid photodynamic therapy for recalcitrant severe hidradenitis suppurativa," by Antonio Guglielmetti, Juliana Bedoya, Maribel Acuna, Victor Leiva and Sergio Gonzalez, which was published in the previous issue of the journal.