Optimum Design of Mechanical Systems Involving Interval Parameters

2002 ◽  
Vol 124 (3) ◽  
pp. 465-472 ◽  
Author(s):  
S. S. Rao ◽  
Lingtao Cao
Keyword(s):  
Optimum Design ◽  
Mechanical Systems ◽  
Distribution Functions ◽  
Interval Methods ◽  
System Response ◽  
Uncertain Parameters ◽  
Engineering Systems ◽  
Interval Parameters ◽  
Computational Aspects ◽  
Range Of Values

The imprecision or uncertainty present in many engineering systems can be modeled using probabilistic, fuzzy or interval methods. This work presents the optimum design of uncertain mechanical systems using interval analysis for the prediction of system response. Each of the uncertain parameters is defined by a range of values. Since the interval ranges of response parameters is found to increase with an increase in the number and/or ranges of input interval parameters with the use of interval arithmetic operations, a truncation procedure is used to obtain approximate but reasonably accurate response of the system. This procedure is found to be simple, economical and fairly accurate. The optimum design of a brake is considered to illustrate the computational aspects of the methods. The procedures outlined in this work are quite general and can be used for the design of any uncertain mechanical system when either the probability distribution functions or the preference information of uncertain parameters are unknown.

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

A Time Variational Method for the Approximate Solution of Nonlinear Systems Undergoing Multiple-Frequency Excitations

2020 ◽  
Vol 15 (3) ◽  
Author(s):  
K. Prabith ◽  
I. R. Praveen Krishna
Keyword(s):  
Variational Method ◽  
Numerical Integration ◽  
Jacobian Matrix ◽  
Mechanical Systems ◽  
Approximation Error ◽  
System Response ◽  
Response Analysis ◽  
Multiple Frequency ◽  
Nonlinear Mechanical ◽  
Nonlinear Force

Abstract The main objective of this paper is to use the time variational method (TVM) for the nonlinear response analysis of mechanical systems subjected to multiple-frequency excitations. The system response, which is composed of fractional multiples of frequencies, is expressed in terms of a fundamental frequency that is the greatest common divisor of the approximated frequency components. Unlike the multiharmonic balance method (MHBM), the formulation of the proposed method is very simple in analyzing the systems with more than two excitation frequencies. In addition, the proposed method avoids the alternate transformation between frequency and time domains during the calculation of the nonlinear force and the Jacobian matrix. In this work, the performance of the proposed method is compared with that of numerical integration and the MHBM using three nonlinear mechanical models undergoing multiple-frequency excitations. It is observed that the proposed method produces approximate results during the quasi-periodic response analysis since the formulation includes an approximation of the incommensurate frequencies to commensurate ones. However, the approximation error is very small and the method reduces a significant amount of computational efforts compared to the other methods. In addition, the TVM is a recommended option when the number of state variables involved in the nonlinear function is high as it calculates the nonlinear force vector and the Jacobian matrix directly from the displacement vector. Moreover, the proposed method is far much faster than numerical integration in capturing the steady-state, quasi-periodic responses of the nonlinear mechanical systems.

Reliability-Based Analysis of Frequency of Closed-Loop Vibration Control Systems with Interval Parameters

2014 ◽  
Vol 644-650 ◽  
pp. 53-57
Author(s):  
Jin Gang Liu ◽  
Shi Peng Wang ◽  
Zhong Jun Zhang ◽  
Da Wei Jin ◽  
Feng Xiao Huang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Vibration Control ◽  
Control Systems ◽  
Present Method ◽  
Closed Loop ◽  
Uncertain Parameters ◽  
Convex Model ◽  
Interval Parameters ◽  
Closed Loop Systems ◽  
Random Eigenvalues

Using the convex model theory, the reliability-based analysis of frequency of the vibration control problem of structures with Interval parameters is discussed. Based on the theory of perturbation method, reliability analysis, and PNET method, the method of reliability-based analysis of eigenvalues of closed-loop vibration control systems with uncertain parameters is studied. And the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the reliability of frequency. The numerical results show that the present method is effective.

On Time Delay in Noncolocated Control of Flexible Mechanical Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 409-415 ◽  
Author(s):  
B. Yang ◽  
C. D. Mote
Keyword(s):  
Control System ◽  
Time Delay ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Vibration Measurement ◽  
System Response ◽  
Specific Time ◽  
Sensors And Actuators ◽  
Stabilizing Controllers ◽  
Flexible Mechanical System

A new method is presented for noncolocated control of flexible mechanical systems. The destabilizing effect of noncolocation of sensors and actuators is eliminated through introduction of specific time delay block(s) in the control system. The time delay constants in those blocks depend on the system eigenstructure. For a given flexible mechanical system, if there exists a time delay relation, the system response at one point can be exactly predicted from the vibration measurement at other point(s) of the system. In this case all stabilizing controllers from colocated control can be directly used. The time delay theory is verified by experiments on noncolocated control of a translating string.

scholarly journals A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Emmanuel D. Blanchard ◽  
Adrian Sandu ◽  
Corina Sandu
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Polynomial Chaos ◽  
Sampling Rate ◽  
Mechanical Systems ◽  
Posteriori Probability ◽  
Uncertain Parameters ◽  
A Posteriori ◽  
A Posteriori Probability ◽  
Polynomial Chaos Expansions

Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of such uncertainties on the system response. Many uncertain parameters cannot be measured accurately, especially in real time applications. Information about them is obtained via parameter estimation techniques. Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. This paper proposes a new computational approach for parameter estimation based on the extended Kalman filter (EKF) and the polynomial chaos theory for parameter estimation. The error covariances needed by EKF are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The proposed method is applied to a nonlinear four degree of freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. The main advantages of this method are an accurate representation of uncertainties via polynomial chaos, a computationally efficient update formula based on EKF, and the ability to provide a posteriori probability densities of the estimated parameters. The method is able to deal with non-Gaussian parametric uncertainties. The paper identifies and theoretically explains a possible weakness of the EKF with approximate covariances: numerical errors due to the truncation in the polynomial chaos expansions can accumulate quickly when measurements are taken at a fast sampling rate. To prevent filter divergence, we propose to lower the sampling rate and to take a smoother approach where time-distributed observations are all processed at once. We propose a parameter estimation approach that uses polynomial chaos to propagate uncertainties and estimate error covariances in the EKF framework. Parameter estimates are obtained in the form of polynomial chaos expansion, which carries information about the a posteriori probability density function. The method is illustrated on a roll plane vehicle model.

An Analysis of Pulse Control for Simple Mechanical Systems

1985 ◽  
Vol 107 (2) ◽  
pp. 123-131 ◽  
Author(s):  
Z. Prucz ◽  
T. T. Soong ◽  
A. Reinhorn
Keyword(s):  
Control Algorithm ◽  
Control Method ◽  
Excitation Frequency ◽  
Mechanical Systems ◽  
System Response ◽  
Control Parameters ◽  
Pulse Control ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
On Line

An efficient pulse control method for insuring safety of simple mechanical systems is developed and its sensitivity to the excitation frequency content and to various control parameters is studied. The control algorithm, consisting of applying pulse forces in a feedback fashion, is designed to insure that maximum system response is limited to safe values at all times. It is shown that the proposed algorithm is simple to implement and is efficient in controlling peak response in terms of on-line computation and pulse energy required. The technique is illustrated and analyzed for a single-degree-of-freedom linear system.

A Study of Factor Effects in Data From Factorial Experiments

2005 ◽  
Author(s):  
Xiang Li ◽  
Daniel D. Frey
Keyword(s):  
Robust Design ◽  
Meta Analysis ◽  
System Response ◽  
Data Sets ◽  
Engineering Systems ◽  
Factorial Experiments ◽  
Additional Increase ◽  
Efficient Planning ◽  
Effect Sparsity ◽  
Factor Interactions

This paper documents a meta-analysis of 113 data sets from published factorial experiments. The study quantifies regularities observed among factor effects and multi-factor interactions. Such regularities are known to be critical to efficient planning and analysis of experiments and to robust design of engineering systems. Three previously observed properties are analyzed — effect sparsity, hierarchy, and heredity. A new regularity is introduced and shown to be statistically significant. It is shown that a preponderance of active two-factor interaction effects are synergistic, meaning that when main effects are used to increase the system response, the interaction provides an additional increase. The potential implications for robust design are discussed.

The Dynamic Analysis of Multibody Systems with Uncertain Parameters Using Interval Method

2012 ◽  
Vol 152-154 ◽  
pp. 1555-1561 ◽  
Author(s):  
Jing Lai Wu ◽  
Yun Qing Zhang
Keyword(s):  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Uncertain Parameters ◽  
Algebraic Equations ◽  
Scanning Method ◽  
Inclusion Function ◽  
Bounded Interval ◽  
Interval Variables ◽  
Multibody Dynamic ◽  
Computational Aspects

The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling multibody dynamic systems in the presence of parametric uncertainties are proposed, where the uncertain parameters are modeled by uncertain-but-bounded interval variables which only need the bounds of uncertain parameters, not necessarily knowing the probabilistic distribution. The Chebyshev inclusion function which employs the truncated Chevbyshev series expansion to approximate the original function is proposed. Based on Chebyshev inclusion function, the algorithm for solving the nonlinear equations with interval parameters is proposed. Combining the HHT-I3 method, this algorithm is used to calculate the multibody systems dynamic response which is governed by differential algebraic equations (DAEs). A numerical example that is a slider-crank with uncertain parameters is presented, which shows that the novel methodology can control the overestimation effectively and is computationally faster than the scanning method.

Applicability of Common RANS Models for the Calculation of Transient Forced to Natural Convection

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Austen D. Fradeneck ◽  
Mark L. Kimber
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Latin Hypercube Sampling ◽  
Distribution Functions ◽  
Flow Reversal ◽  
Cumulative Distribution ◽  
Quality Data ◽  
System Response ◽  
Heated Plate

Abstract The applicability of several Reynolds averaged Navier–Stokes (RANS) turbulence models in calculating the transient evolution of a buoyancy-induced flow reversal along a vertical heated plate is analyzed through the use of validation quality experimental data from the Rotatable Buoyancy Tunnel (RoBuT) facility. This benchmark attempts to capture the transient evolution from downward forced convection to upward natural convection by removing power to the blower and allowing the buoyancy force emanating from the heated plate to gradually dominate as the primary driving force. Boundary conditions and system response quantities for the numerical model are supplied from the experiment every 0.2 s during the 18.2 s transient. ASME standards are used to quantify the numerical uncertainties while the input uncertainties are handled using a Latin hypercube sampling (LHS) method based on the steady-state conditions (t=0 s). Qualitative comparisons between numerical and experimental results at several downstream locations are supported using a validation metric based on the statistical disparity between the respective empirical and cumulative distribution functions (CDFs). The results from this study show that the standard linear eddy-viscosity models have difficulty in reproducing the complex features of the flow reversal in comparison with the more intricate turbulence models such as Reynolds stress models (RSM) and low-Reynolds number variants. This study also briefly highlights the difficulties of capturing validation quality data for three-dimensional multiphysics flow, while also providing insight for the design of future experimental efforts.

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