Predicting Uncertainty Propagation in a Highly Nonlinear System with a Stochastic Projection Method

Abstract With the recent success of using the time series to vast applications, one would expect its boundless adaptation to problems like nonlinear control and nonlinearity quantification. Though there exist many system identification methods, finding suitable method for identifying a given process is still cryptic. Moreover, to this notch, research on their usage to nonlinear system identification and classification of nonlinearity remains limited. This article hovers around the central idea of developing a ‘kSINDYc’ (key term based Sparse Identification of Nonlinear Dynamics with control) algorithm to capture the nonlinear dynamics of typical physical systems. Furthermore, existing two reliable identification methods namely NL2SQ (Nonlinear least square method) and N3ARX (Neural network based nonlinear auto regressive exogenous input scheme) are also considered for all the physical process-case studies. The primary spotlight of present research is to encapsulate the nonlinear dynamics identified for any process with its nonlinearity level through a mathematical measurement tool. The nonlinear metric Convergence Area based Nonlinear Measure (CANM) calculates the process nonlinearity in the dynamic physical systems and classifies them under mild, medium and highly nonlinear categories. Simulation studies are carried-out on five industrial systems with divergent nonlinear dynamics. The user can make a flawless choice of specific identification methods suitable for given process by finding the nonlinear metric (Δ0). Finally, parametric sensitivity on the measurement has been studied on CSTR and Bioreactor to evaluate the efficacy of kSINDYc on system identification.

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A Numerical Simulation of Silver–Water Nanofluid Flow with Impacts of Newtonian Heating and Homogeneous–Heterogeneous Reactions Past a Nonlinear Stretched Cylinder

Symmetry ◽

10.3390/sym11020295 ◽

2019 ◽

Vol 11 (2) ◽

pp. 295 ◽

Cited By ~ 26

Author(s):

Muhammad Suleman ◽

Muhammad Ramzan ◽

Shafiq Ahmad ◽

Dianchen Lu ◽

Taseer Muhammad ◽

...

Keyword(s):

Numerical Simulation ◽

Nonlinear System ◽

Thermal Radiation ◽

Concentration Field ◽

Heterogeneous Reactions ◽

Nonlinear Thermal Radiation ◽

Newtonian Heating ◽

Nanofluid Flow ◽

Shooting Technique ◽

Highly Nonlinear

The aim of the present study is to address the impacts of Newtonian heating and homogeneous–heterogeneous (h-h) reactions on the flow of Ag–H2O nanofluid over a cylinder which is stretched in a nonlinear way. The additional effects of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also added features of the problem under consideration. The Shooting technique is betrothed to obtain the numerical solution of the problem which is comprised of highly nonlinear system ordinary differential equations. The sketches of different parameters versus the involved distributions are given with requisite deliberations. The obtained numerical results are matched with an earlier published work and an excellent agreement exists between both. From our obtained results, it is gathered that the temperature profile is enriched with augmented values radiation and curvature parameters. Additionally, the concentration field is a declining function of the strength of h-h reactions.

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Model Predictive Control-Based Path-Following for Tail-Actuated Robotic Fish

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4043152 ◽

2019 ◽

Vol 141 (7) ◽

Cited By ~ 6

Author(s):

Maria L. Castaño ◽

Xiaobo Tan

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Projection Method ◽

Beat Frequency ◽

Path Following ◽

Robotic Fish ◽

Model Parameters ◽

Underwater Robots ◽

Control Effort ◽

Highly Nonlinear

There has been an increasing interest in the use of autonomous underwater robots to monitor freshwater and marine environments. In particular, robots that propel and maneuver themselves like fish, often known as robotic fish, have emerged as mobile sensing platforms for aquatic environments. Highly nonlinear and often under-actuated dynamics of robotic fish present significant challenges in control of these robots. In this work, we propose a nonlinear model predictive control (NMPC) approach to path-following of a tail-actuated robotic fish that accommodates the nonlinear dynamics and actuation constraints while minimizing the control effort. Considering the cyclic nature of tail actuation, the control design is based on an averaged dynamic model, where the hydrodynamic force generated by tail beating is captured using Lighthill's large-amplitude elongated-body theory. A computationally efficient approach is developed to identify the model parameters based on the measured swimming and turning data for the robot. With the tail beat frequency fixed, the bias and amplitude of the tail oscillation are treated as physical variables to be manipulated, which are related to the control inputs via a nonlinear map. A control projection method is introduced to accommodate the sector-shaped constraints of the control inputs while minimizing the optimization complexity in solving the NMPC problem. Both simulation and experimental results support the efficacy of the proposed approach. In particular, the advantages of the control projection method are shown via comparison with alternative approaches.

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On Mixed Convection Squeezing Flow of Nanofluids

Energies ◽

10.3390/en13123138 ◽

2020 ◽

Vol 13 (12) ◽

pp. 3138 ◽

Cited By ~ 1

Author(s):

Sheikh Irfan Ullah Khan ◽

Ebraheem Alzahrani ◽

Umar Khan ◽

Noreena Zeb ◽

Anwar Zeb

Keyword(s):

Nonlinear System ◽

Differential Equations ◽

Mixed Convection ◽

Ordinary Differential Equations ◽

Volume Fraction ◽

Squeezing Flow ◽

Physical Parameters ◽

Gamma Alumina ◽

Highly Nonlinear ◽

The Impact

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

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Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2019.2.00052 ◽

2019 ◽

Vol 4 (2) ◽

pp. 551-558

Author(s):

Youcef Belgaid ◽

Mohamed Helal ◽

Ezio Venturino

Keyword(s):

Immune Response ◽

Chronic Lymphocytic Leukemia ◽

Nonlinear System ◽

Differential Equations ◽

B Cell ◽

Mathematical Analysis ◽

Lymphocytic Leukemia ◽

Highly Nonlinear ◽

Theoretical Question ◽

Cell Chronic Lymphocytic Leukemia

AbstractA B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important theoretical question of the equilibria existence. Under suitable assumptions all model populations are shown to coexist.

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