Linearized Research Articles

Numerical computation of magnetized bioconvection nanofluid flow with temperature-dependent viscosity and Arrhenius kinetic

The current study focused on the impact of activation energy and magnetic field on immiscible steady nanofluid moving over an elastic stretched surface containing motile gyrotactic microorganisms. We use the Reynolds exponential model to develop the mathematical modeling since the viscosity of the fluid is temperature-dependent. Under the presence of uniformly disseminated nanoparticles, the base fluid is electrically conductive. The Buongiorno model, which incorporates thermophoretic forces and Brownian motion, has been used. Using the spectral local linearization approach (SLLM), the looming nonlinear, coupled differential equations are numerically addressed. Because it is based on a smooth Uni-variant linearization of non-linear functions, the SLLM method is simple to construct and use. The numerical performance of SLLM is even better since it grows a collection of equations that are solved sequentially by operating the findings from one equation into the next. The successive over-relaxation technique was used to accelerate and enhance the convergence of the SLLM system. The reliability of the SLLM will be verified through the use of well-known techniques and comparisons with other data We have illustrated and analyzed in detail the graphical behavior of all emergent variables for temperature, velocity, and concentration distributions, and also the Nusselt number, Sherwood number, skin friction, and density number of motile microorganisms. It is significant to claim that the spectral local linearization approach has been demonstrated to be extremely stable and adaptive for the solution of non-linear differential equations.

An efficient solver of predictive control methods for motion control of autonomous vehicles with experimental verification

Real-time performance is one of the major challenges for optimal control and MPC control. In this paper, a novel general open-source C++ MPC solver based on state-of-the-art sparse QP solver OSQP is designed to solve the motion control problem of autonomous vehicles efficiently. A new linear dynamic model is proposed by replacing heading angle error with planning lateral projection speed, whose measurement is independent of the measurement of heading angle. A general local linearization method for the nonlinear tire model is proposed. Through the theory of offset-free MPC control, the steady-state value problem is solved caused by a disturbance in the time domain systematically. The algorithm in this paper is implemented in ROS, which means that the algorithm can be directly used in the prototype development of autonomous vehicles. The proposed MPC solver can solve a linear time-varying or time-invariant system, with or without disturbances. It is very efficient and can handle different kinds of hard and soft constraints. A real-time simulation platform based on Unreal Engine 4 and CarSim is designed to verify the algorithm’s effectiveness. Real-time simulations and real vehicle experiments verify the efficiency of the algorithm.

RETRACTED: Input design for integrated active fault diagnosis and output tracking control

The fault diagnosis module is a key component integrated in active fault-tolerant control systems. However, the classical methods usually design fault diagnosis and control modules, separately, which ignore the existing interactions between the two key modules in active fault-tolerant control systems. In order to deal with this problem, this paper establishes a framework for integrated design of active fault diagnosis (AFD) and control while ensuring the performance of tracking control. In particular, the input is designed to balance the goal of AFD with the reference output tracking performance. The design of inputs is formulated to minimize the sum of a quadratic function and a non-convex quadratic fractional function at each step, whose global optimality can be obtained under the tight condition of convex relaxation. Furthermore, despite the global optimal condition is not achieved, a locally optimal solution could still be obtained by using our proposed local linearization search algorithm, whose suboptimality can be strictly guaranteed theoretically. At the end, a practical four-tank system example is used to verify the effectiveness of our proposed method.

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

AbstractThe thermodynamics modeling of a Reiner–Philippoff‐type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear‐thinning, Newtonian, or shear‐thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature‐ and concentration‐induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral‐based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature‐dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.

Statistical inference for stochastic differential equations

AbstractMany scientific fields have experienced growth in the use of stochastic differential equations (SDEs), also known as diffusion processes, to model scientific phenomena over time. SDEs can simultaneously capture the known deterministic dynamics of underlying variables of interest (e.g., ocean flow, chemical and physical characteristics of a body of water, presence, absence, and spread of a disease), while enabling a modeler to capture the unknown random dynamics in a stochastic setting. We focus on reviewing a wide range of statistical inference methods for likelihood‐based frequentist and Bayesian parametric inference based on discretely‐sampled diffusions. Exact parametric inference is not usually possible because the transition density is not available in closed form. Thus, we review the literature on approximate numerical methods (e.g., Euler, Milstein, local linearization, and Aït‐Sahalia) and simulation‐based approaches (e.g., data augmentation and exact sampling) that are used to carry out parametric statistical inference on SDE processes. We close with a brief discussion of other methods of inference for SDEs and more complex SDE processes such as spatio‐temporal SDEs.This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Algorithms and Computational Methods > Maximum Likelihood Methods Statistical Models > Fitting Models

The Design and Experimental Analysis of Excavator with Rotor

Abstract In this paper deriving of dynamical model of the load-bearing structure in form of a Trusses of the excavator with rotor is elaborated. Finite Element Methods and real working conditions are used to derive the dynamical model and to perform the local linearization of the dynamic elastic line for the structure of the load-bearing of the excavator with rotor. As carriers with continuous masses were treated the upper bearing structure of the Dynamical model and the truss levels. Finally, in accordance with the requirements of the problem, the degrees of freedom and the reference nodes are selected. The second stage of reduction, represents the final formation of the dynamical model of the load-bearing infrastructure, which however must be more accurate during the dynamic behaviour of the excavator with the rotor. The exposed work with the formation of the dynamic model of the Truss bearing structure, enables the concrete solution of the oscillations of the excavator with rotor. In addition, the model is of a universal character, respectively, can also be used during the formation of the dynamical model of truss carriers in general.

On several local asymptotic properties for fractional autoregressive models with strong mixing noises

This paper is devoted to study several local asymptotic properties for fractional autoregressive models with strong mixing noises, we treat local asymptotic normality using Swensen’s lemma, then we deal with local asymptotic minimaxity and local asymptotic linearity, these properties are fundamental and prepare the way for the construction of adaptive estimator. In order to measure the performance of our approach we deal with simulation study, it allows us to check the validity of the theoretical results.

Effects of yield stress and chemical reaction on magnetic two-phase nanofluid flow in a porous regime with thermal ray

This study investigates consequences of the steady flow of nanofluid via contracting cylinder utilizing the mathematical Buongiorno's model of nanofluid. Herein, the influence of magnetic field and porous materials are discussed in this paper. The parameters of heat sink/source and radiation are taken into respect. Furthermore, the react of chemical and the yield stress within the nanoingredients too, take up a new niche in this research. The transformations of similarity facilitate the paradigm of partial differential equations into ordinary differential equations. To hit the solutions of the nonlinear equations, the spectral local linearization method has been utilized. Consequences are discussed with diagrams and discussions. The physical consignments as a local Sherwood number, local Nusselt number and drag force are displayed. Excellent advancement in transmit of mass and heat is spotted, which can be conceived through graphs. Results elucidate that the transport of heat increased by increasing the porous medium permeability, thermal radiation, chemical reaction and magnetic field, but raising the heat sink/source and yield stress reduce the heat transfer, whereas the adverse behavior is noticed with the transmit of mass for these parameters.

Hall Effect on MHD Flow and Heat Transfer Over an Unsteady Stretching Permeable Surface In the Presence of Thermal Radiation and a Heat Source/sink

This paper employs the computational iterative approach known as Spectral Local Linearization Method (SLLM) to analyze Hall effect on MHD flow and heat transfer over an unsteady stretching permeable surface in the presence of thermal radiation and heat source/sink. To demonstrate the reliability of our proposed method, we made comparison with Matlab bvp4c routine technique and excellent agreement was observed. The governing partial equations are transformed into a system of ordinary differential equations by using suitable similarity transformations. The results are obtained for velocity, temperature, skin friction and Nusselt number.

Numerical experiment to examine activation energy and bi-convection Carreau nanofluid flow on an upper paraboloid porous surface: Application in solar energy

The current article examines the physical features of magneto-hydrodynamics (MHD) Carreau nanofluid bi-convection flow past an upper paraboloid porous surface. The presence of activation energy and chemical reaction are also examined. The notion of the Carreau nanofluid was established with recent parametric quantities to accomplish the momentum governing equation.The momentum equation is furthermore reformed by applying Darcy law. The governing partial differential equations are reconstructed into ordinary differential equations by making use of similarity transforms. The reformed non-linear coupled differential equations are solved by implementing the spectral local linearization technique (SLLM). The SLLM technique is forthright to grow and employing since this algorithm relies upon a smoothly Uni-variant linearizing of non-linear functions. The numerical interpretation of SLLM is admirable cause it establishes a system of equations, which consecutively resolve by functioning the outcomes through the first equation into the subsequent equation. To advance and strengthen the converged solutions for the SLLM algorithm, the SOR method is also implemented. The numerical outcomes of temperature, velocity, and concentration profiles, even though the skin friction, Sherwood number, and Nusselt number are adorned via graphical curves for all the arising parametric quantities and analyzed in detail.

Ultrasound Computed Tomography.

This chapter presents theoretical, numerical, and experimental frameworks for the use of Ultrasound Computed Tomography (USCT) for cortical bone tissue imaging. Most of the research conducted on this topic concerns adult bone, although some work presented in this chapter is specific to the study of child bone. USCT is recognized as a powerful method for soft tissue imaging. In bone imaging, the difficulties arise from the very high impedance contrast between tissues which alters the propagation of the ultrasonic waves and limits the linear inversion algorithms used. Solutions consist in optimally assessing non-linear effects in an iterative approach aiming at local linearization. When the problem can be reduced to the study of a fluid-like cavity buried in an elastic cylinder surrounded by water, the signal processing and/or compound algorithms can be added as an extension to the linear algorithms. The main limitation of these methods is the heavy experimental costs involved. We have then suggested the introduction of purely numerical non-linear full-waveform inversion algorithms. The performances and the limitations of these linear and non-linear methods applied to cortical bone tissue imaging problems are overviewed and discussed.

A predictive control based on decentralized fuzzy inference for a pH neutralization process

In this paper a predictive control method based on decentralized fuzzy inference (DFIPC) is proposed to deal with the problems of strong nonlinearity, large hysteresis and uncertainty in pH neutralization process. Firstly, the localized linearization of the non-linear object model is performed, and the future output of the control object is predicted based on the step response models of the linearized objects. Secondly, a decentralized fuzzy inference structure is designed, which is based on the deviation information between the expected value and the predicted value in a future time, and the control output of the system is generated by the weighted synthesis of the decentralized inference results. Finally, to verify the effectiveness, the proposed scheme is applied to the pH neutralization process. The results indicate that the proposed scheme not only possesses good tracking and anti-disturbance ability, but also shows better robustness and performance than the conventional model predictive control.

Local Linearization Based Subvector Inference in Moment Inequality Models

Local Linearization Based Subvector Inference in Moment Inequality Models

Lightweight Neural Network for Real-Time Crack Detection on Concrete Surface in Fog

Cracks are one of the most common factors that affect the quality of concrete surfaces, so it is necessary to detect concrete surface cracks. However, the current method of manual crack detection is labor-intensive and time-consuming. This study implements a novel lightweight neural network based on the YOLOv4 algorithm to detect cracks on a concrete surface in fog. Using the computer vision algorithm and the GhostNet Module concept for reference, the backbone network architecture of YOLOv4 is improved. The feature redundancy between networks is reduced and the entire network is compressed. The multi-scale fusion method is adopted to effectively detect cracks on concrete surfaces. In addition, the detection of concrete surface cracks is seriously affected by the frequent occurrence of fog. In view of a series of degradation phenomena in image acquisition in fog and the low accuracy of crack detection, the network model is integrated with the dark channel prior concept and the Inception module. The image crack features are extracted at multiple scales, and BReLU bilateral constraints are adopted to maintain local linearity. The improved model for crack detection in fog achieved an mAP of 96.50% with 132 M and 2.24 GMacs. The experimental results show that the detection performance of the proposed model has been improved in both subjective vision and objective evaluation metrics. This performs better in terms of detecting concrete surface cracks in fog.

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem arises in, for example, corrosion detection, and thermal parameter estimation. We carry out both linearised uncertainty quantification, based on a local Gaussian approximation, and full exploration of the joint posterior using Markov chain Monte Carlo sampling. By exploiting a known invariance property of the Poisson problem, we are able to circumvent the need to re-mesh as the shape of the boundary changes. The linearised uncertainty analysis presented here relies on a local linearisation of the parameter-to-observable map, with respect to both the Robin coefficient and the boundary shape, evaluated at the maximum a posteriori (MAP) estimates. Computation of the MAP estimate is carried out using the Gauss–Newton method. On the other hand, to explore the full joint posterior we use the Metropolis-adjusted Langevin algorithm, which requires the gradient of the log-posterior. We thus derive both the Fréchet derivative of the solution to the Poisson problem with respect to the Robin coefficient and the boundary shape, and the gradient of the log-posterior, which is efficiently computed using the so-called adjoint approach. The performance of the approach is demonstrated via several numerical experiments with simulated data.

Full-Field Strain Determination for Additively Manufactured Parts Using Radial Basis Functions

Additively manufactured components, especially those produced in deposition welding processes, have a rough curvilinear surface. Strain and surface deformation analysis of such components is increasingly performed using digital image correlation (DIC) methods, which raises questions regarding interpretability of the results. Furthermore, in triangulation or local tangential plane based DIC strain analysis, the principal strain directions are difficult to be calculated at any point, which is due to the non-continuity of the approach. Thus, both questions will be addressed in this article. Apart from classical local strain analysis based on triangulation or local linearization concepts, the application of globally formulated radial basis functions (RBF) is investigated for the first time, with the advantage that it is possible to evaluate all interesting quantities at arbitrary points. This is performed for both interpolation and regression. Both approaches are studied at three-dimensional, curvilinear verification examples and real additively manufactured cylindrical specimens. It is found out that, if real applications are investigated, the RBF-approach based on interpolation and regression has to be considered carefully due to so-called boundary effects. This can be circumvented by only considering the region that has a certain distance to the edges of the evaluation domain. Independent of the evaluation scheme, the error of the maximum principal strains increases with increasing surface roughness, which has to be kept in mind for such applications when interpreting or evaluating the results of manufactured parts. However, the entire scheme offers interesting properties for the treatment of DIC-data.

Transmission line surface defect detection method based on uav autonomous inspection

The existing transmission line surface defect detection methods have the problem of incomplete image data set, resulting in a low recognition success rate. A transmission line surface defect detection method based on uav autonomous inspection is designed. The safety of power grid operation is evaluated, the local linearization process is transformed into linear equation expression, the image data set is obtained by uav autonomous inspection, the transmission line state is judged, the corresponding constraint conditions are set, the type of transmission line surface defects are identified, the number of image poles and towers is matched, and the detection mode is optimized by edge detection algorithm. Experimental results: The average recognition success rate of the transmission line surface defect detection method in this paper and the other two detection methods is 59.89%, 51.89% and 52.03%, proving that the transmission line surface defect detection method integrating UAV technology inspection has a wider application space.

Rheological Analysis of Suspended Single-Walled Carbon Nanotubes in a Walters' B fluid

Objective: In this paper, we present a rheological analysis of suspended single-walled Carbon nanotubes in a Walters' B fluid. Methods: We assume that the viscosity varies exponentially as a function of the temperature use the Reynolds model of viscosity for the study. A variable thermal conductivity is also assumed along with buoyancy, magnetic field, viscous dissipation and a convective boundary condition. The system of nonlinear coupled equations is solved using the spectral local linearization method. Results: Our solutions are validated using through comparison with previously published results for a given set of conditions. Conclusion: The study finds that good agreement is achieved.

Spectral methods to solve nonlinear problems: A review

The study is intended to give a brief overview of recent papers on spectral methods in different types of fluid flow especially nanofluid flow. The survey does not presume to be exhaustive; hence some selection is necessary. The papers reviewed herein relate to the recent use of some spectral based algorithms, notably the spectral relaxation method, the spectral local linearization method, the spectral quasi-linearization method, the successive linearization method, the piecewise successive linearization method and the spectral homotopy analysis method, etc. We review the important papers and problems where these methods have been used. The paper is divided into sections related to the use of each method. In addition to reviewing the journal articles in the main body of the paper, we also give details of important books published on spectral methods in fluid dynamics.

EEG fading data classification based on improved manifold learning with adaptive neighborhood selection

In electroencephalogram (EEG) signal analysis, data fading problem exists from signal production to collection by brain-computer interface (BCI) device, which can be raised by BCI device deficiency, dynamic network limitation and subject issue. EEG data fading problem changes the distribution of data, which results in the movement of the cluster center and fuzzy class boundary after feature extraction with negative effects in EEG classification results. To decrease the adverse influence of data fading, a novel fading data classification method based on manifold learning and adaptive neighborhood selection is proposed in this paper to mitigate this adverse effect of data fading. In the proposed method, after neighborhood selection according to local linearity, data are mapped into manifold space through local tangent space alignment (LTSA) for dimensionality reduction. The method is carried out on BCI Competition 2008 – Graz data set A of four-class EEG data of motor imagery (MI) experiments. The experimental results are compared with conventional LTSA and indicate that the proposed method effectively improves the classification accuracy of fading data.