A decision theoretic approach to parameter estimation

A decision theoretic approach to estimation of unknown random and nonrandom parameters from a linear measurements model is proposed, when the a priori statistics are incomplete and only a small number of data points are available. The unknown statistics are partially characterized by considering two regions in the measurement space, namely, good and bad data regions and constraining the partial probability, the partial covariance, or the combination thereof of the measurements. The random parameter is assumed to be Gaussian variable with known mean and known covariance. Choosing the minimum covariance criterion, the min-max estimator is found to be soft-limiter or tangent type nonlinear function depending upon the a priori statistic available. The estimator for the unknown nonrandom parameter is obtained from the root of some function of the residuals, the function being obtained by minimizing the error covariance. The estimator obtained is similar to a random parameter case.     

A novel narrow band digital filter and its application to multivariable system identification

A novel narrow band time-varying digital filter is proposed, which has desirable properties such as global asymptotic stability, asymptotic noise annihilation and asymptotic signal tracking. It is shown that the proposed filter is comparable to the Kalman filter in performance, but with substantial computational simplicity; no Ricatti equation is involved. It is basically a Fourier analysis method but the Fourier coefficients are found recursively. The application of the proposed filter for on-line identification of a linear multivariable system subject to both deterministic and stochastic disturbances is presented; simulation results are given.     

Robust Servomechanism Controller Design for Digital Implementation

A systematic design procedure is outlined for implementing a digital servomechanism controller. In the presence of a certain class of disturbances, the controlled process asymptotically tracks a class of reference commands. The design procedure takes account of analog-to-digital conversion, digital-to-analog conversion time, digital controller computation delay, and quantization effects.     

On facilitated computation of mesoscopic behavior of reaction‐diffusion systems

Various cellular and subcellular biological systems occur in the conditions where both reactions and diffusion take place. Since the concentration of species varies spatially, application of reaction‐diffusion master equation has served as an effective method to handle these complicated systems; yet solving these equation incurs a large CPU time penalty. Counter to the traditional technique of generating many sample paths, this article introduces a method which combines Grima's effective rate equation approach (Grima, J Chem Phys. 2010;133:3) with a linear operator formalism for diffusion to capture averaged species behaviors. The formulation also shows correct results at various choices of compartment sizes, which have been found to be an important factor that can affect accuracy of the final predictions (Erban, Chapman, Phys Biol. 2009;6:4). It is shown that the method presented allows the computation of the mesoscopic average of reaction‐diffusion systems at considerably accelerated rates (exceeding a thousand fold) over those based on sample path averages. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5258–5266, 2017     

Theoretical investigations of dynamic behavior of isothermal continuous stirred tank biological reactors

The dynamic behavior of an isothermal biological CSTR modelled by idealized cell and substrate balance equations has been investigated theoretically in terms of multiplicity and stability of steady states and existence and stability character of limit cycles. Various types of dynamic behavior have been classified in terms of a Damköhler number and two other system parameters. The predicted types of behavior have been illustrated by numerical computation of cell and substrate concentration trajectories.     

Effect of impeller design and power consumption on crystal size distribution

Crystallization processes in a 500 mL stirred tank crystallizer with computational fluid dynamics (CFD) and population balances toward estimating how crystal size distributions (CSDs) are influenced by flow inhomogeneities was explored. The flow pattern and CSD are presented here though extensive phase Doppler particle analyzer measurements and CFD predictions for three different impeller designs (disc turbine, pitched blade turbine, and Propeller) and each rotated at three different speeds (2.5, 5, and10 r/s). As crystallization processes in practice could involve break‐up and aggregation of crystals, some selected break‐up and aggregation kernels are incorporated. Extensive comparison of simulations with experimental data showed consistent trends in the proper quantitative range. An attempt has also been made to develop scaling laws: (a) mean particle size with average power consumption per unit mass and (b) particle‐size distribution with the turbulent energy dissipation distribution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3596–3613, 2014     

Response Surface Optimization of the Critical Media Components for the Production of Surfactin

Optimization of the fermentation media for maximization of surfactin production was carried out. The carbon source (glucose), the nitrogen source (ammonium nitrate) and the mineral salts ferrous and manganous sulphates were the critical components of the medium optimized. A 2⁴ full factorial central composite experimental design followed by multi-stage Monte-Carlo optimization was used in the design of experiments and in the analysis of results. This procedure limited the number of actual experiments performed while allowing for possible interactions between the four components. The optimum values for the tested variables for the maximal production of surfactin were (in g dm⁻³): glucose = 36·5; NH₄NO₃ = 4·5; FeSO₄ = 4×10⁻³ and MnSO₄ = 27·5 ×10⁻². Relative surfactant concentrations were expressed as the reciprocal of the critical micelle concentration (CMC⁻¹) and the maximum predicted yield of surfactin in terms of CMC⁻¹ was 45·5. © 1997 SCI.     

A discrete element implementation for concrete: particle generation,contact calculations,packing under gravity and modeling material response

A three-dimensional discrete element modelling capability for concrete based on rigid particles of arbitrary shape and size has been developed. The novel particle generation algorithm allows control of particle size, angularity and flakiness. General rigid body kinematics including finite rotations is accounted for, and an explicit time integration algorithm that conserves energy and momentum is implemented. An efficient contact algorithm with several features to increase the efficiency of the contact computations has been developed. This enables the gravity packing problem for arbitrary shaped particles to be solved in reasonable run time. The proposed procedure is used to generate assemblies of concrete specimens of various sizes that are homogeneous and isotropic in the bulk, and can capture the wall effect due to the formwork. The calibrated specimens are seen to be capable of accurately capturing experimentally observed macro stress strain response and failure patterns. The influence of aggregate shape on texture formation in the packed specimen, and on macro strength and failure patterns in hardened concrete, is demonstrated and is seen to be consistent with experimental results.