The modeling of mechanical systems involves different parameters that are susceptible to uncertainties. Commonly, the variations result from the mathematical difficulty of representing the peculiarities of the dynamic systems and the lack of knowledge about the physical properties of the materials used in a given application. In this context, the analysis of uncertainties that affect the performance of the system is an important design issue. Uncertainty analysis of dynamic systems has been studied by applying techniques based on stochastic and fuzzy logic approaches. The fuzzy logic technique seems to be more appropriate when the stochastic process that characterizes the uncertainties is unknown. Therefore, in the present contribution, the inherent uncertainties affecting the performance of a horizontal rotating machine are modeled by using both stochastic and fuzzy logic-based analysis. These methodologies have been compared through numerical simulations in terms of the dynamic behavior of the system as represented by rotor orbits, unbalance responses, and frequency response functions. The proposed uncertainty analysis provides additional information that can be useful for design and maintenance purposes.
BaoNWangC (2015) A Monte Carlo simulation based inverse propagation method for stochastic model updating. Mechanical Systems and Signal Processing60–61: 928–944.
2.
Binder K (1979) Monte Carlo Methods in Statistical Physics. Berlin, FRG: Springer-Verlag.
3.
CadiniFGiolettaA (2016) A Bayesian Monte Carlo-based algorithm for the estimation of small failure probabilities of systems affected by uncertainties. Reliability Engineering and System Safety153: 15–27.
4.
CavaliniAAJrLara-MolinaFASalesTPet al. (2015a) Uncertainty analysis of a flexible rotor supported by fluid film bearings. Latin American Journal of Solids and Structures12(8): 1487–1504.
5.
Cavalini AA Jr, Dourado A, Lara-Molina FA and Steffen V Jr (2015b) Fuzzy uncertainty analysis of a tilting-pad journal bearing, In: ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2015, Boston, Massachusetts, USA, 2–5 August 2015, pp. 1–10. DOI:10.1115/DETC2015-47586.
6.
Cavalini AA Jr, Sanches L, Bachschmid N and Steffen V Jr (2016) Crack identification for rotating machines based on a nonlinear approach. Mechanical Systems and Signal Processing 79: 72–85.
7.
ChenYSchuhCA (2015) A coupled kinetic Monte Carlo–finite element mesoscale model for thermoelastic martensitic phase transformations in shape memory alloys. Acta Materialia83: 431–447.
8.
De AbreuGLCMMaestaMFLopesV Jret al. (2015) Active angular control of a sectioned airfoil using shape memory alloys and fuzzy controller. Journal of the Brazilian Society of Mechanical Sciences and Engineering37: 1555–1567.
9.
DidierJFaverjonBSinouJJ (2011) Analysing the dynamic response of a rotor system under uncertain parameters Polynomial Chaos expansion. Journal of Vibration and Control18: 712–732.
10.
DuboisDPradeH (1997) The three semantics of fuzzy sets. Fuzzy Sets and Systems90: 141–150.
11.
Ghanem RG and Spanos PD (1991) Stochastic Finite Elements – A Spectral Approach. New York, NY: Spring Verlag.
12.
HudsonATilleyDR (2014) Assessment of uncertainty in energy evaluations using Monte Carlo Simulations. Ecological Modelling271: 52–61.
13.
JensenHAMayorgaFPapadimitriouC (2015) Reliability sensitivity analysis of stochastic finite element models. Computer Methods in Applied Mechanics and Engineering296: 327–351.
14.
KaminskiM (2015) Structural stability and reliability of the underground steel tanks with the Stochastic Finite Element Method. Archives of Civil and Mechanical Engineering15(2): 593–602.
15.
KoroishiEHCavaliniAAJrDe LimaAMGet al. (2012) Stochastics modeling of flexible rotors. Journal of the Brazilian Society of Mechanical Sciences and Engineering34: 597–603.
16.
KoskoB (1990) Fuzzyness vs. probability. International Journal of General Systems17: 211–240.
17.
KunduADiazDelaOFAAdhikariSet al. (2014) A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems. Computer Methods in Applied Mechanics and Engineering270: 201–219.
18.
Lalanne M and Ferraris G (1998) Rotordynamics Prediction in Engineering. New York, NY, John Wiley & Sons, INC.
19.
Lara-Molina FA, Koroishi EH and Steffen V Jr (2015) Uncertainty analysis of flexible rotors considering fuzzy and fuzzy random parameters. Latin American Journal of Solid and Structures 12(10): 1807–1823.
20.
Loève M (1977) Probability Theory I. New York, NY: Springer Verlag.
21.
MöllerBBeerM (2004) Fuzzy Randomness, Uncertainty in Civil Engineering and Computational Mechanics, New York, NY: Springer-Verlag.
Newman MEJ and Barkema GT (2001) Monte Carlo Methods in Statistical Physics. Oxford, UK: Oxford University Press.
24.
NgoQHNguyenNPNguyenCNet al. (2015) Fuzzy sliding mode control of container cranes. International Journal of Control, Automation and Systems13(2): 419–425.
25.
OzbenTHuseyinogluMArslanN (2014) Fuzzy logic model for the prediction failure analysis of composite plates under various cure temperatures. Journal of the Brazilian Society of Mechanical Sciences and Engineering36: 443–448.
26.
Rao SS and Qiu Y (2011) A Fuzzy approach for the analysis of rotor-bearing systems with uncertainties, In: ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, USA, 28–31 August 2011, pp. 1033–1044. DOI: 10.1115/DETC2011-48528.
27.
RémondDFaverjonBSinouJJ (2011) Analysing the dynamic response of a rotor system under uncertain parameters Polynomial Chaos expansion. Journal of Vibration and Control18: 712–732.
28.
SeguíBFaverjonBJacquet-RichardetG (2013) Effects of random stiffness variations in multistage rotors using the Polynomial Chaos expansion. Journal of Sound and Vibration332: 4178–4192.
29.
SepahvandK (2016) Spectral stochastic finite element vibration analysis of fiber-reinforced composites with random fiber orientation. Composite Structures145: 119–128.
30.
SepahvandKNabihKMarburgS (2015) Collocation-based stochastic modeling of uncertain geometric mistuning in bladed rotor. Procedia IUTAM13: 53–62.
31.
SinouJJDidierJFaverjonB (2015) Stochastic non-linear response of a flexible rotor with local non-linearities. International Journal of Non-Linear Mechanics74: 92–99.
32.
SinouJJJacquelinE (2015) Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response. Mechanical Systems and Signal Processing50–51: 718–731.
33.
StefanouGSavvasDPapadrakakisM (2015) Stochastic finite element analysis of composite structures based on material microstructure. Composite Structures132: 384–392.
34.
StornRPriceK (1995) Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute12: 1–16.
35.
Valades-PelayoPJRomero-ParedesHArancibia-BulnesCAet al. (2016) Geometric optimization of a solar cubic-cavity multi-tubular thermochemical reactor using a Monte Carlo-finite element radiative transfer model. Applied Thermal Engineering98: 575–581.
36.
Vanderplaats GN (2007) Multidiscipline Design Optimization. Colorado Springs, CO: Vanderplaats Research & Development, Inc.
37.
Viana FAC, Venter G, Balabanov V, et al. (2007) On how to implement an affordable optimal Latin hypercube. In: ABCM 19th congress of mechanical engineering (COBEM 2007), Brasília, DF, Brazil, 5–9 November 2007, pp. 1–12.
38.
ZadehL (1965) Fuzzy sets. Information and Control8: 338–353.
39.
ZadehL (1968) Fuzzy sets as basis for a theory of possibility. Fuzzy Sets and Systems1: 3–28.
40.
ZhangJEllingwoodB (1994) Orthogonal series expansions of random fields in reliability analysis. Journal of Engineering and Mechanics120: 2660–2667.
