ABSTRACT Chemical engineering optimization represents a significant challenge due to the complexity of the mathematical models that are frequently required in this area. These models are normally associated with nonlinear equations that represent mass, energy, and momentum balances, which are submitted to physical, constitutive, environmental, and design limitations. The design of chemical systems is generally carried out by considering the model, the vector of design variables, and system parameters as deterministic values, i.e., small variations in these quantities do not affect the objective function. In this contribution, a new methodology based on a double loop iteration process to evaluate the influence of uncertainties on chemical engineering design is proposed. The inner optimization loop is used to find the solution associated with the highest probability value by using the so-called Inverse Reliability Analysis and the outer loop is the regular optimization loop used to determine the vector of design variables. For this aim, the Multi-Objective Optimization Water Cycle Algorithm is improved, adopting a mechanism of neighborhood exploration. For illustration purposes, the proposed methodology is applied to mathematical functions and to chemical engineering design. The obtained results demonstrate that the proposed strategy represents an interesting alternative to reliability design in chemical engineering.

Abstract This paper aims at analyzing the sensitivity of the structural response of flexible rotors subjected to uncertain interval parameters. The interval approach encompasses both an uncertainty and sensitivity analyses. The uncertainty analysis consists in computing the interval uncertain structural responses by using the global optimization method. The sensitivity analysis computes the normalized relative sensitivity indices that quantify the degree of importance of each uncertain interval parameter on the uncertain structural responses of the flexible rotor. The uncertain structural responses and the sensitivity of the flexible rotor subjected to interval parameters are analyzed in terms of the Frequency Response Function (FRF), orbits, Campbell diagram, and run-up operating condition. Numerical simulation results illustrate the interval approach conveyed.

Abstract In the present paper, a simplified homogenized beam theory is used in the context of a numerical investigation regarding the dynamic behavior of a rotating composite hollow shaft. For this aim, a horizontal flexible composite shaft and a rigid disc form the considered simple supported rotating system. The mathematical model of the rotor is derived from the Lagrange’s equation and the Rayleigh-Ritz method, which is obtained from the strain and kinetic energies of the disc and shaft, and the mass unbalance. In this case, a convergence procedure is carried out in terms of the vibration modes to obtain a representative model for the rotor system. Therefore, the proposed analysis is performed in both frequency and time domains, in which the frequency response functions, the unbalance responses, the Campbell diagram, and the orbits are numerically determined. Additionally, the instability threshold of the rotor system is obtained. This study illustrates the convenience of the composite hollow shafts for rotor dynamics applications.

Abstract In engineering systems design, theoretical deterministic solutions can be hardly applied directly to real-world scenarios. Basically, this is due to manufacturing limitations and environmental conditions under which the real system will operate. Therefore, a small variation in the design variables vector can result in a meaningful change on the theoretical optimal design as represented by the minimization of the corresponding vector of objective functions. In this context, it is important to develop methodologies that are able to produce solutions (even suboptimal) that are less sensitive to perturbations in the design variable vector and, consequently, leading to a robust optimal design. In this contribution, first the proposed approach is tested on various mathematical functions. Then, the methodology is applied to the design of two representative engineering systems through multi-objective optimization using the Firefly Colony Algorithm in association with the Effective Mean Concept is presented.The results obtained demonstrate that the design strategy conveyed represents an interesting alternative approach to obtain robust design for a number of engineering applications.

Abstract The components of flexible rotors are subjected to uncertainties. The main sources of uncertainties include the variation of mechanical properties. This contribution aims at analyzing the dynamics of flexible rotors under uncertain parameters modeled as fuzzy and fuzzy random variables. The uncertainty analysis encompasses the modeling of uncertain parameters and the numerical simulation of the corresponding flexible rotor model by using an approach based on fuzzy dynamic analysis. The numerical simulation is accomplished by mapping the fuzzy parameters of the deterministic flexible rotor model. Thereby, the flexible rotor is modeled by using both the Fuzzy Finite Element Method and the Fuzzy Stochastic Finite Element Method. Numerical simulations illustrate the methodology conveyed in terms of orbits and frequency response functions subject to uncertain parameters.

AbstractThis paper is dedicated to the analyses of the effect of uncertain parameters on the dynamic behavior of a flexible rotor containing two rigid discs and supported by two fluid film bearings. A stochastic method has been extensively used to model uncertain parameters, i.e., the so-called Monte Carlo simulation. However, in the present contribution, the inherent uncertainties of the bearings' parameters (i.e. the oil viscosity as a function of the oil temperature, and the radial clearance) are modeled by using a fuzzy dynamic analysis. This alternative methodology seems to be more appropriated when the stochastic process that models the uncertainties is unknown. The analysis procedure is confined to the time domain, being generated by the envelopes of the rotor orbits and the unbalance responses obtained from a run-down operating condition. The hydrodynamic supporting forces are determined by considering a nonlinear model, which is based on the solution of the dimensionless Reynolds' equation for cylindrical and short journal bearings. This numerical study illustrates the versatility and convenience of the mentioned fuzzy approach for uncertainty analysis. The results from the stochastic analysis are also presented for comparison purposes.

Nowadays, optimization techniques based on the analogy with swarming principles and collective activities of social species in nature have been used in the development of methodologies for solving a variety of real-world optimization problems. In this context, the social behavior of fish colonies has been recently explored to develop a novel algorithm, the so-called Fish Swarm Optimization Algorithm (FSOA), based on the behavior of fish swarm in search for food. In this paper, the FSOA is applied to four engineering systems, involving typical structural design and distillation column design. The results obtained are then compared with those obtained from other classical evolutionary approaches.

This paper presents a numerical study devoted to the evaluation of the possibility of monitoring and controlling the dynamic behavior of a rotating machine with a cracked shaft by using an Electro-Magnetic Actuator (EMA). The EMA is located at the mid-span of the rotor to provide active control. The opening and closure (breathing) of the crack is determined by the stress field over its cross section resulting from the dynamic bending moment. The system is nonlinear due to the fact that the crack parameters must be determined for each time step and the EMA introduces forces that are inversely proportional to the square of the gap value between the stator and the rotor. The model developed takes into account the behavior of the crack and the in uence of the EMA. Simulations were carried out to access the possibility of controlling the breathing mechanism. The results obtained demonstrate the possibility of using the EMA in order to keep the crack closed along the rotation of the rotor, thus forming a self-healing scheme for the cracked rotor.

The essence of structural health monitoring (SHM) is to develop systems based on nondestructive inspection (NDI) technologies for continuous monitoring, inspection and detection of structural damages. A new architecture of a remote SHM system based on Electromechanical Impedance (EMI) measures is described in the present contribution. The proposed environment is employed to automatically monitor the structural integrity of aircrafts and is composed by sensor networks, a signal conditioning system, a data acquisition hardware and a data processing system. The obtained results allow the accomplishment of structural condition-based maintenance strategies, in opposite to those based only on the usage time of the equipment. This approach increases the operational capacity of the structure without compromising the security of the flights. As the environment continually checks for the first signs of damage, possibly reducing or eliminating scheduled aircraft inspections, it could significantly decrease maintenance and repair expenses. Furthermore, the usage of this system allows the creation of a historical database of the aircrafts structural integrity, making possible the incremental development of a Damage Prognosis System (DPS). This work presents the proposed architecture and a set of experiments that were conducted in a representative aircraft structure (aircraft window) to demonstrate the effectiveness of the proposed system.

Flexible rotors are characterized by inherent uncertainties affecting the parameters that influence the dynamic responses of the system. In this context, the handling of variability in rotor dynamics is a natural and necessary extension of the modeling capability of the existing techniques of deterministic analysis. Among the various methods used to model uncertainties, the stochastic finite element method has received major attention, as it is well adapted for applications involving complex engineering systems of industrial interest. In the present contribution, the stochastic finite element method applied to a flexible rotor system, with random parameters modeled as random fields is presented. The uncertainties are modeled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method by using Karhunen-Loève expansions. The modeling procedure is confined to the frequency and time domain analyses, in which the envelopes of frequency response functions, the Campbell's diagram and the orbits of the stochastic flexible rotor system are generated. Also, Monte Carlo simulation method combined with the Latin Hypercube sampling is used as stochastic solver. After the presentation of the underlying theoretical formulations, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features of the stochastic modeling procedure of flexible rotor systems.

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.

Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. Therefore, by using appropriate electrical circuits, it is possible to dissipate strain energy and, as a consequence, vibration is suppressed through the added passive damping. From the electrical point of view, the piezoelectric element behaves like a capacitor in series with a controlled voltage source and the shunt circuit, commonly formed by an RL network, is tuned to dissipate the electrical energy, more efficiently in a given frequency band. It is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors (obtained from operational amplifiers). From the mechanical point of view, the vibration energy can be attenuated in a single mode, or in multiple modes, according to the design of the damping device and the frequency band of interest. This work is devoted to the study of passive damping systems for single modes or multiple modes, based on piezoelectric patches and resonant shunt circuits. The present contribution discusses the modeling of piezoelectric patches coupled to shunt circuits, where the basics of resonant shunt circuits (series and parallel topologies) are presented. Following, the devices used in passive control (piezoelectric patch and synthetic inductors) are analyzed from the electrical and experimental viewpoints. The modeling of multi-degree-of-freedom mechanical systems, including the effects of the passive damping devices is revisited, and, then a design methodology for the multi-modal case is defined. Also, it is briefly reviewed the optimization method used for design purposes, namely the LifeCycle Model. Finally, experimental results are reported, illustrating the success of using the methodology presented in passive damping applications applied to mechanical and mechatronic systems.

This paper examines two passive techniques for vibration reduction in mechanical systems: the first one is based on dynamic vibration absorbers (DVAs) and the second uses resonant circuit shunted (RCS) piezoceramics. Genetic algorithms are used to determine the optimal design parameters with respect to performance indexes, which are associated with the dynamical behavior of the system over selected frequency bands. The calculation of the frequency response functions (FRFs) of the composite structure (primary system + DVAs) is performed through a substructure coupling technique. A modal technique is used to determine the frequency response function of the structure containing shunted piezoceramics which are bonded to the primary structure. The use of both techniques simultaneously on the same structure is investigated. The methodology developed is illustrated by numerical applications in which the primary structure is represented by simple Euler-Bernoulli beams. However, the design aspects of vibration control devices presented in this paper can be extended to more complex structures.