Machine Learning-Informed Predictive Design and Analysis of Electrohydrodynamic Printing Systems

Electrohydrodynamic (EHD) processes are promising techniques for manufacturing nanoscopic products with different shapes (such as thin films, nanofibers, 2D/3D nanostructures, and nanoparticles) and materials at a low cost using simple equipment. A key challenge in their adoption by nonexperts is the requirement of enormous time and resources in identifying the optimum design/process parameters for the underlying material and EHD system. Machine learning (ML) has made exciting advancements in predictive modeling of different processes, provided it is trained on high-quality datasets at appropriate volumes. This article extends the suitability of such ML-enabled approaches to a new technological domain of EHD spraying and drop-on-demand printing. Different ML models like ridge regression, random forest regression, support vector regression, gradient boosting regression, and multilayer perceptron are trained and their performance using evaluation metrics like RMSE and R2_score is examined. Tree-based algorithms like gradient boosting regression are found to be the most suitable technique for modeling EHD processes. The trained ML models show substantially higher accuracy (average error < 5%) in replicating these nonlinear processes as compared to previously reported scaling laws (average error ≈ 42%) and are well suited for predictive modeling/analysis of the underlying EHD system and process.     

Chaos in fractional ordered Liu system

Present paper deals with fractional version of a dynamical system introduced by C. Liu, L. Liu and T. Liu [C. Liu, L. Liu, T. Liu, A novel three-dimensional autonomous chaos system, Chaos Solitons Fractals 39 (4) (2009) 1950–1958]. Numerical investigations on the dynamics of this system have been carried out. Properties of the system have been analyzed by means of Lyapunov exponents. Furthermore the minimum effective dimensions have been identified for chaos to exist in commensurate and incommensurate orders. It is noteworthy that the results obtained are consistent with the analytical conditions given in the literature.     

Stability of a class of discrete-time nonlinear recursive observers

This work provides a framework for nominal and robust stability analysis for a class of discrete-time nonlinear recursive observers (DNRO). Given that the system has linear output mapping, local observability and Jacobian matrices satisfying certain conditions, the nominal and robust stability of the DNRO is defined by the property of estimation error dynamics and is analyzed using Lyapunov theory. Moreover, a simultaneous state and parameter estimation scheme is shown to be Input-to-State Stable (ISS), and adaptively reduce plant-model mismatch on-line. Three design strategies of the DNRO that satisfy the stability results are given as examples, including the widely used extended Kalman filter, extended Luenberger observer, and the fixed gain observer.     

Unknown input modeling and robust fault diagnosis using black box observers

A key issue that needs to be addressed while performing fault diagnosis using black box models is that of robustness against abrupt changes in unknown inputs. A fundamental difficulty with the robust FDI design approaches available in the literature is that they require some a priori knowledge of the model for unmeasured disturbances or modeling uncertainty. In this work, we propose a novel approach for modeling abrupt changes in unmeasured disturbances when innovation form of state space model (i.e. black box observer) is used for fault diagnosis. A disturbance coupling matrix is developed using singular value decomposition of the extended observability matrix and further used to formulate a robust fault diagnosis scheme based on generalized likelihood ratio test. The proposed modeling approach does not require any a priori knowledge of how these faults affect the system dynamics. To isolate sensor and actuator biases from step jumps in unmeasured disturbances, a statistically rigorous method is developed for distinguishing between faults modeled using different number of parameters. Simulation studies on a heavy oil fractionator example show that the proposed FDI methodology based on identified models can be used to effectively distinguish between sensor biases, actuator biases and other soft faults caused by changes in unmeasured disturbance variables. The fault tolerant control scheme, which makes use of the proposed robust FDI methodology, gives significantly better control performance than conventional controllers when soft faults occur. The experimental evaluation of the proposed FDI methodology on a laboratory scale stirred tank temperature control set-up corroborates these conclusions.     

Robust stability of nonlinear model predictive control based on extended Kalman filter

This work deals with state estimation and process control for nonlinear systems, especially when nonlinear model predictive control (NMPC) is integrated with extended Kalman filter (EKF) as the state estimator. In particular, we focus on the robust stability of NMPC and EKF in the presence of plant-model mismatch. The convergence property of the estimation error from the EKF in the presence of non-vanishing perturbations is established based on our previous work [1]. In addition, a so-called one way interaction is shown that the EKF error is not influenced by control action from the NMPC. Hence, the EKF analysis is still valid in the output-feedback NMPC framework, even though there is no separation principle for general nonlinear systems. With this result, we study the robust stability of the output-feedback NMPC under the impact of the estimation error. It turns out the output-feedback NMPC with EKF is Input-to-State practical Stable (ISpS). Finally, two offset-free strategies of output-feedback NMPC are presented and illustrated through a simulation example.     

Data reduction algorithm based on principle of distributional equivalence for fault diagnosis

Historical data based fault diagnosis methods exploit two key strengths of multivariate statistical approaches, viz.: (i) data compression ability, and (ii) discriminatory ability. It has been shown that correspondence analysis (CA) is superior to principal components analysis (PCA) on both these counts (Detroja, Gudi, Patwardhan, & Roy, 2006a), and hence is more suited for the task of fault detection and isolation (FDI). In this paper, we propose a CA based methodology for fault diagnosis that can facilitate significant data reduction as well as better discrimination. The proposed methodology is based on the principle of distributional equivalence (PDE). The PDE is a property unique to the CA algorithm and can be very useful in analyzing large datasets. The principle, when applied to historical data sets for FDI, can significantly reduce the data matrix size without significantly affecting the discriminatory ability of the CA algorithm. This can significantly reduce computational load during statistical model building. The data reduction ability of the proposed methodology is demonstrated using a simulation case study involving benchmark quadruple tank laboratory process. The proposed methodology when applied to experimental data obtained from the quadruple tank process also demonstrated data reduction capabilities of the principle of distributional equivalence. The above aspect has also been validated for large-scale data sets using the benchmark Tennessee Eastman process simulation case study.     

Hybridization of stochastic reduced basis methods with polynomial chaos expansions

We propose a hybrid formulation combining stochastic reduced basis methods with polynomial chaos expansions for solving linear random algebraic equations arising from discretization of stochastic partial differential equations. Our objective is to generalize stochastic reduced basis projection schemes to non-Gaussian uncertainty models and simplify the implementation of higher-order approximations. We employ basis vectors spanning the preconditioned stochastic Krylov subspace to represent the solution process. In the present formulation, the polynomial chaos decomposition technique is used to represent the stochastic basis vectors in terms of multidimensional Hermite polynomials. The Galerkin projection scheme is then employed to compute the undetermined coefficients in the reduced basis approximation. We present numerical studies on a linear structural problem where the Youngs modulus is represented using Gaussian as well as lognormal models to illustrate the performance of the hybrid stochastic reduced basis projection scheme. Comparison studies with the spectral stochastic finite element method suggest that the proposed hybrid formulation gives results of comparable accuracy at a lower computational cost.     

On the Uçar prototype model with incommensurate delays

Differential-difference equations with multiple delays have applications in a variety of applied fields. We propose a prototype delay model introduced by Uçar involving two delays. Sufficient conditions for the stability of the model are given and used to study chaos. It is observed first time in the literature that the Uçar system shows not only two-scroll but also one-scroll chaotic attractors.     

Morphology,Mineralogy and Mixing of Individual Atmospheric Particles Over Kanpur (IGP): Relevance of Homogeneous Equivalent Sphere Approximation in Radiative Models

Estimation of the direct radiative forcing (DRF) by atmospheric particles is uncertain to a large extent owing to uncertainties in their morphology (shape and size), mixing states, and chemical composition. A region-specific database of the aforementioned physico-chemical properties (at individual particle level) is necessary to improve numerically-estimated optical and radiative properties. Till date, there is no detailed observation of the above mentioned properties over Kanpur in the Indo-Gangetic Plain (IGP). To fill this gap, an experiment was carried out at Kanpur (IITK; 26.52°N, 80.23°E, 142 m msl), India from April to July, 2011. Particle types broadly classified as (a) Cu-rich particles mixed with carbon and sulphur (b) dust and clays mixed with carbonaceous species (c) Fe-rich particles mixed with carbon and sulfur and (d) calcite (CaCO₃) particles aged with nitrate, were observed. The frequency distributions of aspect ratio (AR; indicator of extent of particle non-sphericity) of total 708 particles from April to June reveal that particles with aspect ratio range >1.2 to ≤1.4 were abundant throughout the experiment except during June when it was found to shift to high AR range, >1.4 to ≤1.6 (followed with another peak of AR i.e. >2 to ≤2.4) due to dust storm conditions enhancing the occurrence of more non-spherical particles over the sampling site. The spherical particles (and close to spherical shape; AR range, 1.0 to ≤1.2) were found to be <20% throughout the experiment with a minimum (11.5%) during June. Consideration of Homogeneous Equivalent Sphere Approximation (HESA) in the optical/radiative model over the study region is found to be irrelevant during the campaign.