A possibilistic clustering approach to novel fault detection and isolation

In this paper, a new approach for fault detection and isolation that is based on the possibilistic clustering algorithm is proposed. Fault detection and isolation (FDI) is shown here to be a pattern classification problem, which can be solved using clustering and classification techniques. A possibilistic clustering based approach is proposed here to address some of the shortcomings of the fuzzy c-means (FCM) algorithm. The probabilistic constraint imposed on the membership value in the FCM algorithm is relaxed in the possibilistic clustering algorithm. Because of this relaxation, the possibilistic approach is shown in this paper to give more consistent results in the context of the FDI tasks. The possibilistic clustering approach has also been used to detect novel fault scenarios, for which the data was not available while training. Fault signatures that change as a function of the fault intensities are represented as fault lines, which have been shown to be useful to classify faults that can manifest with different intensities. The proposed approach has been validated here through simulations involving a benchmark quadruple tank process and also through experimental case studies on the same setup. For large scale systems, it is proposed to use the possibilistic clustering based approach in the lower dimensional approximations generated by algorithms such as PCA. Towards this end, finally, we also demonstrate the key merits of the algorithm for plant wide monitoring study using a simulation of the benchmark Tennessee Eastman problem.     

Comparison of mass transfer efficiency in horizontal rotating packed beds and rotating biological contactors

In this study, the mass transfer efficiencies of a novel horizontal rotating packed (h‐RPB) bed and the conventional disc‐type rotating biological contactor (RBC) were studied at four speeds and seven submergences. Pall rings of two different sizes (25, 38 mm), superintalox saddles and a wiremesh spiral bundle were used as packings in the h‐RPB. Volumetric gas–liquid mass transfer coefficients were determined by unsteady state absorption of atmospheric oxygen in de‐aerated water. Power consumption per unit liquid volume has been found for all geometries tested. The oxygen transfer efficiency values for the h‐RPB were found to be 2–5 kg kWh^?1 and for the disc RBC were found to be 1–2 kg kWh^?1. The performance of the h‐RPB was also compared with other gas–liquid contactors such as surface aerators. The study proves that the h‐RPB is a energy efficient alternative to conventional contactors. Copyright © 2005 Society of Chemical Industry     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

CFD modeling of pilot-scale pump-mixer: Single-phase head and power characteristics

The present work involves single-phase computational fluid dynamics (CFD) simulations of continuous flow pump-mixer employing top-shrouded Rushton turbines with trapezoidal blades. Baffle—impeller interaction has been modeled using sliding mesh and multiple reference frame approaches. Standard k-ε model has been used for turbulence modeling. Several CFD runs representing different combinations of geometric and process parameters have been carried out. Results of CFD simulations have been used to find out two macroscopic performance parameters of pump-mixer—power consumption and head generated by the impeller. The simulation results have been compared with the experimental data obtained on a pilot-scale setup. Good agreement between CFD predictions and experimental results is observed. In most cases, sliding mesh approach is found to perform better than multiple reference frame approach. Details from CFD simulations have been used to have an insight into the pumping action of the impeller.     

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.     

Closed-loop identification using direct approach and high order ARX/GOBF-ARX models

Model accuracy plays a key role in the performance of advanced, model predictive control algorithms. Model fidelity is usually affected by routine operating condition changes, which necessitate reidentification. From several theoretical and practical considerations, it is recommended that such re-identification be performed under closed-loop conditions. The direct approach for closed-loop identification, owing to its simplicity, is better suited for MPC. In order to yield unbiased and consistent parameter estimates, however, this approach requires the noise model to be sufficiently parameterized. Towards this objective, high order ARX models are the most suitable candidates from the viewpoint of ease of parameter estimation. For multivariable systems, however, the identification of high order ARX models would require longer experiments to be performed. This being undesirable from a practical viewpoint, there is a need for a parsimonious parameterization that would retain the benefits of high order ARX models. In this work, we propose to use generalized orthonormal basis filters (GOBFs) to achieve this parsimonous parameterization. Further, we propose an approach to obtain reduced order models by emphasizing important frequencies so as to suitably shape the bias. We also show that the choice of the GOBF parameterization has another important merit, viz. their ability to perform well even with minimal perturbation data or short experiment times. The efficacy of the proposed approach is demonstrated via simulations on the benchmark Shell Control Problem and a laboratory quadruple tank setup.     

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.     

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.     

Transport of cobalt(II) through a hollow fiber supported liquid membrane containing di-(2-ethylhexyl) phosphoric acid (D2EHPA) as the carrier

This work presents experimental, modeling and simulation studies for Co²⁺ ion extraction using hollow fiber supported liquid membrane (HFSLM) operated in a recycling mode. Extractant di-(2-ethylhexyl) phosphoric acid (D2EHPA) diluted with kerosene has been used as the membrane phase. The Co²⁺ ion concentration in the aqueous feed phase was varied in the range of 1–3 mM. Also, D2EHPA concentration was varied in the range of 10–30% (v/v). A mass transfer model has been developed considering the complexation and de-complexation reactions to be fast and at equilibrium. Equations for extractant mass balance and counter-ion (H⁺) transport have also been incorporated in the model. Extraction equilibrium constant (K_ex) for cobalt–D2EHPA system has been estimated from equilibration experiments and found to be 3.48 × 10⁻⁶. It was observed that the model results are in good agreement with the experimental data when diffusivity of metal-complex (D_m) through the membrane phase is 1.5 × 10⁻¹⁰ m²/s. Feed phase pH and strip phase acidity had negligible effect on the extraction profiles of Co²⁺ ions. An increase in D2EHPA concentration increased extraction rates of Co²⁺ ions. The membrane phase diffusion step was found to be the controlling resistance to mass transfer.     

Growth studies of Azolla pinnata RBr. in a permanent pond

The growth pattern of Azolla pinnata in association with Spirodela polyrhiza was studied in a permanent pond. These two plants would provide a regular source of biomass. The suitability of integration of Azolla pinnata into other aquatic plants ‐ based wastewater treatment systems has been proposed. The favourable qualities offered by Azolla pinnata as a component in wastewater treatment systems has been emphasized.