Abstract In this paper, a robust approach to improve the performance of a condition monitoring process in industrial plants by using Pythagorean membership grades is presented. The FCM algorithm is modified by using Pythagorean fuzzy sets, to obtain a new variant of it called Pythagorean Fuzzy C-Means (PyFCM). In addition, a kernel version of PyFCM (KPyFCM) is obtained in order to achieve greater separability among classes, and reduce classification errors. The approach proposed is validated using experimental datasets and the Tennessee Eastman (TE) process benchmark. The results are compared with the results obtained with other algorithms that use standard and non-standard membership grades. The highest performance obtained by the approach proposed indicate its feasibility.

RESUMO Uma formulação recentemente desenvolvida para o problema de difusão anômala, a qual emprega um termo diferencial de quarta ordem, apresentou em determinadas situações observadas na literatura valores fisicamente irreais em sua solução. Neste trabalho é realizado um estudo do efeito coeficiente de difusão secundária visando contribuir para o entendimento do comportamento das soluções nessas situações. É implementada uma função para representar a variação da parcela sujeita a difusão primária e secundária, de acordo com a quantidade da propriedade em difusão. É apresentada a formulação para a solução desse novo modelo pelo Método de Diferenças Finitas. Os resultados obtidos são compatíveis com aqueles apresentados em trabalhos anteriores na literatura.

ABSTRACT A recent formulation for anomalous diffusion problems, which envolves a fourth-order differential term, has presented negative values in its solution for certain cases. This paper presents a study of the effect of secondary diffusion coefficient in order to contribute with the understanding of the solutions behavior in these situations. A function was implemented to represent the variation in the parcel subject to primary and secondary diffusion, according to the amount of the property in diffusion. The formulation for the solution of this new model by the Finite Difference Method is presented. The results obtained are compatible with those presented in previous works in the literature.

RESUMO Este artigo apresenta a metodologia para a solução de um problema de advecção e difusão bimodal unidimensional utilizando o Método de Diferenças Finitas. Além do termo de transporte advectivo e da difusão primária (que corresponde ao fluxo de Fick), a equação da difusão bimodal inclui um termo relativo à um fluxo secundário que é modelado por um termo diferencial de quarta ordem. O problema foi analisado para diferentes condições iniciais e de contorno, sendo os resultados compatíveis com os apresentados em trabalhos anteriores da literatura.

ABSTRACT This paper presents a methodology for the solution of a bimodal advection and diffusion problem using the Finite Differences Method. In addition to the advective transport term and primary diffusion (which corresponds to the Fick’s flux), the bimodal diffusion equation includes a term relative to a secondary flow that is modeled by a fourth order differential term. The problem was analyzed for different initial and boundary conditions and the results are compatible with those presented in previous studies in the literature.

The current industry requires of the fault diagnostic systems with a detection stage that can ensure a small number of false alarms and a quick detection of faults, regardless of their nature and magnitude. However, a common problem of the approaches based on the Multivariate Statistical Process Monitoring (MSPM) which are currently used for this purpose is the difficulty of them to detect small magnitude faults without incurring a high number of false alarms, and faults not detected. To overcome this drawback, in this paper is proposed a novel approach that combines the advantages of kernel methods, and a novel EWMA with enhanced dynamic to filter the T² Hotelling statistic used as the fault detection mechanism in a complex chemical process.

La industria actual requiere de sistemas de diagnóstico de fallos, que en su etapa de detección garanticen pocas falsas alarmas y logren detectar por demás, los fallos con la mayor rapidez posible independientemente de su naturaleza y magnitud. Sin embargo, un problema de los enfoques de monitoreo de procesos mediante estadística multivariada (MSPM) que son utilizados con este propósito es la incapacidad de detectar fallos de pequeña magnitud sin incurrir en un elevado número de falsas alarmas, u omitir gran cantidad de fallos que deben ser detectados. Como solución a este problema, en el presente trabajo se propone un esquema de trabajo que combina las ventajas de los métodos kernel y un novedoso enfoque EWMA con dinámica reforzada para filtrar el estadístico T² de Hotelling utilizado como mecanismo de detección en un proceso químico de gran escala.

In the present work the inverse problem of simultaneous heat and mass transfer modeled by Luikov equations is studied using a hybrid combination of the Levenberg-Marquardt (LM), Simulated Annealing (SA) and Artificial Neural Network (ANN) methods. The direct and inverse problems are described, formulated and solved. After the use of an experiment design technique, the hybrid combination ANN-LM-SA yielded good estimates for the heat and mass transfer problem of interest. The proper choice of the set of parameters to be estimated allowed the design of an experiment with higher sensitivity coefficients. One ANN was used to generate the initial guess for the LM, another one to approximate the gradient needed by LM, and, finally, the global minimum was searched using the SA. The experimental data considered in the inverse problem was generated using the solution for the direct problem with the addition of noise.

The radiative transfer phenomenon is modeled by an integro-differential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the participating medium, i.e., a medium that may absorb, scatter and emit radiation. In this sense, this work presents a study regarding the estimation of radiative properties in a one-dimensional participating medium by using two optimization heuristic methods, namely Simulated Annealing and Differential Evolution. First, a review of these two optimization techniques is presented. The direct radiative transfer problem solution, which is required for both optimization techniques, is obtained by using the Collocation Method. Finally, case-studies are presented aiming at illustrating the efficiency of these methodologies in the treatment of inverse radiative transfer problems.

A new concept of space radiator of variable emittance for satellite thermal control is presented. The radiator is composed of two stages which exchange heat through radiation between finned surfaces covered with variable emittance coatings, whose emissivity is increased with temperature. Under cold conditions the radiative heat coupling between the stages is minimal, preventing the equipment subcooling, while in hot conditions the heat exchange is increased. A steady-state mathematical model was developed and numerically coupled to an optimization algorithm, and a design optimization procedure was performed. Two optimization criteria were employed: minimization of the radiator mass and the power consumption of heater under cold conditions. The Generalized Extremal Optimization algorithm was used as the optimization tool. The design was then modeled in detail using the SINDA/Fluint package considering orbital conditions of the EQUARS satellite. The performance of the radiator concept proposed here was also compared to a conventional design, for the same operational conditions. It is envisioned that the utilization of such radiators in micro-satellites will lead to considerable electric power savings for safe heaters and may contribute to a longer satellite life. In the design trade-off, the cost for this saving is additional radiator mass and volume.

The steady state inverse radiative transfer problem in one-dimensional participating media is studied as an example of application of the new methodology presented in a accompanying paper by the authors [2]. Spectral methods are used for the appropriate analysis of the direct transport problem. For the inverse problem, we present a matrix that involves only values of the flux intensities at the boundary of the medium. Its columns are built with a set of linearly independent solutions for the system, which is formed when angular half-range prescribed boundary values and the complementary measured half-range boundary values are coupled. The final inverse albedo problem is treated as a full range two point boundary value problem. Test cases results are presented. Mathematical subject classification: 80A23, 15A29.

In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.