A Neural Network Identification Technique for a Foil-Air Bearing Under Variable Speed Conditions and Its Application to Unbalance Response Analysis

Hassan, Mohd Firdaus; Bonello, Philip

doi:10.1115/1.4033455

Cited by 14 publications

(10 citation statements)

References 20 publications

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“…synchronous unbalance response. For gas bearings (including FABs), the air-film pressure (and hence the bearing force) is not a normal function of the instantaneous journal displacements = [ ] T and velocities ′ since is actually related to ( ) through a time-based differential equation arising from the presence of ⁄ (or ̃⁄ ) in the compressible RE [26] (which is why is a component of in eq. ( 1)).…”

Section: Introductionmentioning

confidence: 99%

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

Bonello

2019

Mechanical Systems and Signal Processing

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106

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Campbell diagrams describe the variation with speed of the modes of low amplitude (linear) free vibration of a rotordynamic system about its static equilibrium condition, and are an important tool that aids the interpretation of the nonlinear response. However, Campbell diagrams for foil-air bearing (FAB) rotor systems are currently derived using the linear force coefficients (FC) method and individual modes have not been verified by transient nonlinear dynamic analysis (TNDA) at low amplitudes. In fact, significant discrepancies between FC and TNDA predictions for the stability of the leading (i.e. least damped) mode have been reported. This paper establishes for the first time a method for deriving Campbell diagrams of a generic FAB-rotor model that avoids the FC method. It is based on an eigenvalue analysis of the Jacobian matrix of the dynamical system. Through suitable scaling and the application of appropriate criteria, the multitude of eigenvectors of the Jacobian can be filtered to extract the relevant modes. Each mode is verified using TNDA with mode-specific initial conditions derived from the Campbell diagram analysis. The methodology is successfully tested on three cases in the literature, which respectively illustrate its applicability to complex bearing types (3-pad), complex foil models, and flexible rotors.

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Section: Introductionmentioning

confidence: 99%

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

Bonello

2019

Mechanical Systems and Signal Processing

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106

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“…As in [3,17], the RHBM [18,20] is employed as underpinning theory. The training data for the RNNs are generated using a "circular chirp excitation" method [21,22], which is shown by Al-Ghazal et al [22] to be more effective than the method used in [17].…”

Section: Figmentioning

confidence: 99%

“…The training data is generated by replacing the unbalance excitation in Fig. 2 by "circular chirp excitation" applied to the rotor at two locations, as shown in Fig 10. The circular chirp excitation [21,22] at each location = 1, 2 consists of a pair of forces ( ), ( ) in the x and y directions, with time histories in the form of orthogonally-phased harmonic functions of equal and constant amplitude and steadily-increasing frequency (chirp signals):…”

Section: Generation Of Input/output Training Data and Rnn Detailsmentioning

confidence: 99%

Improved non-invasive inverse problem method for the balancing of nonlinear squeeze-film damped rotordynamic systems

Cedillo

Al-Ghazal

Bonello

et al. 2019

Mechanical Systems and Signal Processing

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A non-invasive inverse problem method for rotor balancing relies on casing vibration readings and prior knowledge of the structure. Such a method is important for rotors that are inaccessible under operating conditions. This paper introduces a method for solving the quasi-implicit inverse problem that arises when identifying the required balancing correction for a rotor with only one weak linear connection to the casing, apart from the nonlinear connections. This is typical of aero-engine designs that use a retainer spring with only one of the nonlinear squeeze-film damper (SFD) bearings that support the rotor within the casing. The SFD journal displacements are estimated from casing vibration readings using identified inverse SFD models based on Recurrent Neural Networks (RNNs). The information from these is then used to enhance the condition of the explicit inverse problem set up in previous research for simpler configurations. The methodology is validated using simulated casing vibration readings. The reliability of the RNN inverse SFD models is first demonstrated. The second part of the validation shows that the novel enhanced explicit inverse problem method is essential for effective balancing of this previously unconsidered system. Repeatability and robustness to noise/model uncertainty are satisfactorily demonstrated and limitations discussed.The identification of the rotor unbalance from vibration measurements at the casing and/or the rotor is referred to as an "inverse" problem [3], in contrast to the "forward" problem, which refers to the prediction of the system vibration in response to a known unbalance distribution. Traditional balancing methods (which include the standard "trim" balancing procedures) [4][5][6][7][8] involve the use of several trial runs and the application of trial masses at fixed balancing planes. Such types of methods are typically based on two representative methods, the influence coefficients balancing method [5] and the modal balancing method [4]. Darlow [6] developed the Unified Balancing Approach (UBA) that combined the advantages of both previous methods. The UBA method involved the calculation of modal trial mass sets, based on the influence coefficient approach of using trial mass data. Foiles et al [7] provided a comprehensive review of the several direct methods for rotor balancing, which were based on the fundamentals of the influence coefficients method and modal method.Chen et al [9] proposed an optimisation technique based on nonlinear programming to determine the balancing corrections to be applied to prescribed planes. This method required a valid mathematical model of the rotor-dynamic system to use within the optimisation scheme. Unlike the methods of [4][5][6][7][8], the method of Chen et al [9] did not require several trial runs and trial masses since the optimisation was based on measurements from the initial (unbalanced) configuration. However, the method was still invasive since it required measurement of the vibration of the rotor. Moreover, the system ...

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“…But it is almost impossible when the system has many nonlinear parameters and severe dynamic. In this case, scientists use some methods like fuzzy logic or neural networks to identify the model of the system [7,8]. For instance, in [9], the neural network is used to estimate the inverse dynamic of the da Vinci surgical robot to enables estimation of the external environment forces.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

Sarbaz

Zamani

Manthouri

et al. 2022

Int. J. Fuzzy Syst.

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In this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi–Sugeno (T-S) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks.

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A Neural Network Identification Technique for a Foil-Air Bearing Under Variable Speed Conditions and Its Application to Unbalance Response Analysis

Cited by 14 publications

References 20 publications

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

Improved non-invasive inverse problem method for the balancing of nonlinear squeeze-film damped rotordynamic systems

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

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