Mechanical Engineering - Research Publications
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ItemNo Preview AvailableUncertainty quantification and reduction using sensitivity analysis and Hessian derivatives(American Society of Mechanical Engineers, 2021-01-01)Abstract We study the use of Hessian interaction terms to quickly identify design variables that reduce variability of system performance. To start we quantify the uncertainty and compute the variance decomposition to determine noise variables that contribute most, all at an initial design. Minimizing the uncertainty is next sought, though probabilistic optimization becomes computationally difficult, whether by including distribution parameters as an objective function or through robust design of experiments. Instead, we consider determining the more easily computed Hessian interaction matrix terms of the variance-contributing noise variables and the variables of any proposed design change. We also relate the Hessian term coefficients to subtractions in Sobol indices and reduction in response variance. Design variable changes that can reduce variability are thereby identified quickly as those with large Hessian terms against noise variables. Furthermore, the Jacobian terms of these design changes can indicate which design variables can shift the mean response, to maintain a desired nominal performance target. Using a combination of easily computed Hessian and Jacobian terms, design changes can be proposed to reduce variability while maintaining a targeted nominal. Lastly, we then recompute the uncertainty and variance decomposition at the more robust design configuration to verify the reduction in variability. This workflow therefore makes use of UQ/SA methods and computes design changes that reduce uncertainty with a minimal 4 runs per design change. An example is shown on a Stirling engine design where the top four variance-contributing tolerances are matched with two design changes identified through Hessian terms, and a new design found with 20% less variance.
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ItemNo Preview AvailableIntegrated LCA-MFA Framework for Gold Production from Primary and Secondary Sources(Elsevier BV, 2021-01-01)
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ItemNo Preview AvailableOn Singular Perturbation for a Class of Discrete-Time Nonlinear Systems in the Presence of Limit Cycles of Fast Dynamics(IEEE, 2022)This paper extends the existing singular perturbation results to a class of nonlinear discrete-time systems whose fast dynamics have limit cycles. By introducing the discrete-time reduced averaged system, the main result (Theorem 1) shows that for a given fixed time interval, the solutions of the original system can be made arbitrarily close to the solutions of the reduced averaged system and the boundary layer system. From this result, the stability properties of the original system are obtained from the stability properties of the reduced averaged system and the boundary layer system. Simulation results support the theoretical findings.
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ItemVarying Joint Patterns and Compensatory Strategies Can Lead to the Same Functional Gait Outcomes: A Case Study(IEEE, 2022)This paper analyses joint-space walking mechanisms and redundancies in delivering functional gait outcomes. Multiple biomechanical measures are analysed for two healthy male adults who participated in a multi-factorial study and walked during three sessions. Both participants employed varying intra- and inter-personal compensatory strategies (e.g., vaulting, hip hiking) across walking conditions and exhibited notable gait pattern alterations while keeping task-space (functional) gait parameters invariant. They also preferred various levels of asymmetric step length but kept their symmetric step time consistent and cadence-invariant during free walking. The results demonstrate the importance of an individualised approach and the need for a paradigm shift from functional (task-space) to joint-space gait analysis in attending to (a)typical gaits and delivering human-centred human-robot interaction.
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ItemAveraging for nonlinear systems on Riemannian manifolds(IEEE, 2013)This paper provides a derivation of the averaging methods for nonlinear time-varying dynamical systems defined on Riemannian manifolds. We extend the results on ℝ n to Riemannian manifolds by employing the language of differential geometry.
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ItemIdle speed control using linear time varying model predictive control and discrete time approximations(IEEE, 2010-01-01)This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.
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ItemNew Stability Criteria for Switched Time-Varying Systems: Output-Persistently Exciting Conditions(IEEE, 2011-01-01)This paper proposes three tools to facilitate the verification of the output-persistently exciting (OPE) condition and simultaneously, provides new asymptotic stability criteria for uniformly globally stable switched systems. By introducing some related reference systems, the OPE condition of the original system can be reduced or simplified. Both the ideas of classic LaSalle invariance principle and nested Matrosov theorem are used to generate such reference systems. The effectiveness and flexibility of the proposed methods are demonstrated by two applications. From these applications, it can be seen that the flexibility of the proposed method produces a novel set of tools for checking uniform asymptotic stability of switched time-varying systems.
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ItemExtremum seeking control for nonlinear systems on compact Riemannian manifolds(IEEE Press, 2014)This paper formulates the extremum seeking control problem for nonlinear dynamical systems which evolve on Riemannian manifolds and presents stability results for a class of numerical algorithms defined in this context. The results are obtained based upon an extension of extremum seeking algorithms in Euclidean spaces and a generalization of Lyapunov stability theory for dynamical systems defined on Rimannian manifolds. We employ local properties of Lyapunov functions to extend the singular perturbation analysis on Riemannian manifolds. Consequently, the results of the singular perturbation on manifolds are used to obtain the convergence of extremum seeking algorithms for dynamical systems on Riemannian manifolds.
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ItemExtremum Seeking From 1922 To 2010(IEEE, 2010-01-01)Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.