Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

The current investigations are presented to solve the fractional order HBV differential infection system (FO-HBV-DIS) with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMBNNs. The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics, healthy hepatocytes (H), capsids (D), infected hepatocytes (I), free virus (V) and antibodies (W). The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS. The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with the response of antibody immune. The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach. To authenticate the validity, competence, consistency, capability and exactness of the LMBNNs, the numerical presentations using the mean square error (MSE), error histograms (EHs), state transitions (STs), correlation and regression are accomplished.     

An Intelligence Computational Approach for the Fractional 4D Chaotic Financial Model

The main purpose of the study is to present a numerical approach to investigate the numerical performances of the fractional 4-D chaotic financial system using a stochastic procedure. The stochastic procedures mainly depend on the combination of the artificial neural network (ANNs) along with the Levenberg-Marquardt Backpropagation (LMB) i.e., ANNs-LMB technique. The fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional order α. The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and 1. The data proportion is applied as 73%, 15%, and 12% for training, testing, and certification to solve the chaotic fractional system. The acquired results are verified through the comparison of the reference solution, which indicates the proposed technique is efficient and robust. The 4-D chaotic model is numerically solved by using the ANNs-LMB technique to reduce the mean square error (MSE). To authenticate the exactness, and consistency of the technique, the obtained performances are plotted in the figures of correlation measures, error histograms, and regressions. From these figures, it can be witnessed that the provided technique is effective for solving such models to give some new insight into the physical behavior of the model.     

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries. Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation. Because of little maintenance, the heat exchanger of such type is extensively used. Here, we generate simulation of flow and heat transfer using non-isothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation (RANS) model of the turbulent flow together with heat equation. Simulation is tested with Prandtl number (Pr = 0.7) with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2 × 10⁵ to 4.4 × 10⁵ with turbulence kinetic energy and the dissipation rate in ranges (3.75 × 10⁻³ to 1.5 × 10⁻²) and (3.73 × 10⁻³−3 × 10⁻²) respectively. Two correlations available in the literature are used in order to check validity. The results are displayed through streamlines, surface plots, contour plots, isothermal lines, and graphs. It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15% to a maximum of 514%. The temperature at the middle shows the consistency in value but declines immediately at the end. This process becomes faster with the decrease in inlet velocity magnitude.     

Age-structured predator–prey model with habitat complexity: oscillations and control

In this article, we study a predator–prey interaction in a homogeneously complex habitat where predator takes a fixed time to develop from immature to its mature stage. The age-structure of the predator and its interaction with the prey is framed in a system of delay differential equations. The objective is to study the role of habitat complexity and the maturation delay of the predator on the overall dynamics of the model system. Different interesting dynamical behaviours can be obtained by regulating two key parameters, namely the degree of habitat complexity and the maturation delay. It is observed that the system becomes unstable from its stable condition when the maturation delay crosses some critical value. The periodic solutions bifurcated from the interior equilibrium is found to be supercritical and stable. Synchronization of population fluctuations is, however, possible by increasing the strength of habitat complexity. The predator population goes to extinction and the prey population reaches to its maximum, irrespective of the length of maturation delay, when the habitat complexity crosses some upper critical value. The qualitative dynamical behaviours of the model system are verified with the data of Paramecium aurelia (prey) and Didinium nasutum (predator) interaction.     

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans , infected humans , recovered humans , infected vectors , and susceptible vector based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.     

基于忆阻器的随机神经网络的稳定性

与传统的神经网络相比，基于忆阻器的神经网络能够更好地反映突触的强度可变的这一特性，从而更好地模拟人脑的神经系统。在 Filippov 解的框架下，通过构造恰当的 Lyapunov 泛函，利用 It$\hat{\rm o}$ 微分公式、微分包含和集值映射理论，研究了一类基于忆阻器的随机神经网络的动力学行为，获得了确保该系统均方指数稳定的充分判别条件。最后，通过给出两个数值仿真的例子验证了结论的有效性。     

Infrared Spectroscopy-Based Chemometric Analysis for Lard Differentiation in Meat Samples

One of the most pressing concerns for the consumer market is the detection of adulteration in meat products due to their preciousness. The rapid and accurate identification mechanism for lard adulteration in meat products is highly necessary, for developing a mechanism trusted by consumers and that can be used to make a definitive diagnosis. Fourier Transform Infrared Spectroscopy (FTIR) is used in this work to identify lard adulteration in cow, lamb, and chicken samples. A simplified extraction method was implied to obtain the lipids from pure and adulterated meat. Adulterated samples were obtained by mixing lard with chicken, lamb, and beef with different concentrations (10%–50% v/v). Principal component analysis (PCA) and partial least square (PLS) were used to develop a calibration model at 800–3500 cm⁻¹. Three-dimension PCA was successfully used by dividing the spectrum in three regions to classify lard meat adulteration in chicken, lamb, and beef samples. The corresponding FTIR peaks for the lard have been observed at 1159.6, 1743.4, 2853.1, and 2922.5 cm⁻¹, which differentiate chicken, lamb, and beef samples. The wavenumbers offer the highest determination coefficient R² value of 0.846 and lowest root mean square error of calibration (RMSEC) and root mean square error prediction (RMSEP) with an accuracy of 84.6%. Even the tiniest fat adulteration up to 10% can be reliably discovered using this methodology.     

水下稳态涡流场声传播的数值模拟和实验研究

声波穿过涡流场时声传播特性会发生改变,可由此判断涡流场的存在及其特征参数。文章首先推导了二维稳态涡流场的射线微分方程组,实现了声波通过涡流场的声线轨迹模拟。然后开展水池超声传感器实验,采用现代计算流体力学(Computational Fluid Dynamics,CFD)仿真方法获取涡流场参数。最后将通过涡流场声信号的时延结果,与实验测量值进行对比分析。结果表明,对于涡核半径为30 mm,最大切向速度为1.2 m·s^-1的涡流场,数值模拟误差小于10%,验证了基于射线声学的水下稳态涡流场声传播数值模拟的有效性。     

Development and analyses of data-driven models for predicting the bed depth profile of solids flowing in a rotary kiln

Soft computing data-driven modeling (DDM) techniques have attracted the attention of many researchers across the globe as they do not require deep knowledge of the complex physical process. In the present research, data-driven based models have been developed using support vector regression (SVR), multilayer perceptron neural network (MLP), radial basis function neural network (RBFNN) and general regression neural networks (GRNN) techniques for predicting the bed depth profile of solids flowing in a rotary kiln. The performances of the developed models were compared and evaluated against the experimental results in terms of statistical measures such as coefficient of determination (R²), and average absolute relative error (AARE). The obtained results and findings from this research have revealed that data-driven models can predict the bed depth profile of solids flowing in a rotary kiln quite accurately. The SVR-based model exhibited the lowest AARE value of 1.72% and highest R² value of 0.9981 while GRNN, RBFNN, and MLP models gave corresponding values of AARE as 3.69%, 55.13%, 98.15% and those of R² as 0.9898, 0.0052 and 0.0081, respectively. Moreover, the developed DDM-based models i.e. GRNN, RBFNN, and MLP models overcame the limitations of the existing solutions which involved iterative numerical procedure entailing high degree of computational complexity.     

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

The purpose of this paper is to present a numerical approach based on the artificial neural networks (ANNs) for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system. The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation (LMB), named the ANNs-LMB. This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution. Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model. The selection of the data to solve the fractional-order chaotic financial model are selected as 75% for training, 10% for testing, and 15% for certification. The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise. The obtained results are testified to reduce the mean square error (MSE) for solving the fractional model and verified through the various measures including correlation, MSE, regression histogram of the errors, and state transition (ST).     

基于钟差建模的水下定位时延修正算法

针对同步定位模式中存在的钟差影响定位精度的问题,提出了一种适用于水声定位系统的同步时钟修正算法。对单个水下固定潜标的时延进行长时间观测,测量定位时延的变化量,建立了钟差修正模型,定位精度得到明显提高。此模型在海试试验数据中得到了验证,两个潜标的相对定位精度分别提高了31.1%和64.6%,且解算钟差模型系数与设备精度吻合,证明了算法的有效性与准确性。此修正算法对于水下固定节点标定精度的提高具有重要意义。     

Adaptive reduced order modeling for nonlinear dynamical systems through a new a posteriori error estimator: Application to uncertainty quantification

Multiquery problems such as uncertainty quantification (UQ), optimization of a dynamical system require solving a differential equation at multiple parameter values. Therefore, for large systems, the computational cost becomes prohibitive. This issue can be addressed by using a cheaper reduced order model (ROM) instead. However, the ROM entails error in the solution due to approximation in a lower dimensional subspace. Moreover, the ROM lacks robustness over a wide range of parameter values. To address these issues, first, an upper bound on the norm of the state transition matrix is derived. This bound, along with the residual in the governing equation, are then used to develop an error estimator for general nonlinear dynamical systems. Furthermore, this error estimator is used in conjunction with the modified greedy search algorithm proposed by Hossain and Ghosh (Int J Numer Methods Eng, 2018;116(12-13): 741-758) to adaptively construct a robust proper orthogonal decomposition-based ROM. This adaptive ROM is subsequently deployed for UQ by invoking it in a statistical simulation. Two numerical studies: (i) viscous Burgers' equation and (ii) beam on nonlinear Winkler foundation, showed an improved accuracy of the error estimator compared to the current literature. A significant computational speed-up in UQ is achieved.     

带挤压油膜阻尼器双盘转子的动力学响应与支承优化

本文研究模拟低压转子的动力学响应及支承优化问题。首先基于发动机模拟低压转子,建立了弹性支承-两端带挤压油膜阻尼器的双盘转子动力学模型,推导了其运动微分方程。对于这个12维的动力学方程组,采用数值方法进行了求解,得到了其响应。转子系统的支承刚度对于其动力学响应影响很大,为了减小振动,采用多岛遗传算法与序列二次规划算法对转子系统的支承进行了多目标优化,得到了在工作转速下支承的最佳刚度。     

Prediction of mechanical properties of a warm compacted molybdenum prealloy using artificial neural network and adaptive neuro-fuzzy models

Predictive models using artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were successfully developed to predict yield strength and ultimate tensile strength of warm compacted 0.85 wt.% molybdenum prealloy samples. To construct these models, 48 different experimental data were gathered from the literature. A portion of the data set was randomly chosen to train both ANN with back propagation (BP) learning algorithm and ANFIS model with Gaussian membership function and the rest was implemented to verify the performance of the trained network against the unseen data. The generalization capability of the networks was also evaluated by applying new input data within the domain covered by the training pattern. To compare the obtained results, coefficient of determination (R²), root mean squared error (RMSE) and average absolute error (AAE) indexes were chosen and calculated for both of the models. The results showed that artificial neural network and adaptive neuro-fuzzy system were both potentially strong for prediction of the mechanical properties of warm compacted 0.85 wt.% molybdenum prealloy; however, the proposed ANFIS showed better performance than the ANN model. Also, the ANFIS model was subjected to a sensitivity analysis to find the significant inputs affecting mechanical properties of the samples.     

A Robust Numerical Scheme for Singularly Perturbed Delay Differential Equations with Turning Point

Abstract

In this article, we propose a parameter uniform numerical method for singularly perturbed delay differential equations with turning point. Using interpolation, a new algorithm is developed to tackle the retarded term. A fitted operator finite difference scheme using Il’in Allen Southwell fitting factor is used for numerical discretization. Bounds on the analytical solution and its derivatives are obtained. The efficiency of the proposed numerical method is illustrated via applying the proposed method on some test problems. The solution is proved to be stable and ε-uniform error estimates are derived. It is shown that the delay argument has significant effect on the solution behavior.     

Electronic expansion valve mass flow rate prediction based on dimensionless correlation and ANN model

Refrigerant mass flow rate through electronic expansion valve (EEV) makes significant sense for refrigeration system intelligent control and energy conservation. Objectives of this study were to present experimental data of R134a mass flow rate through EEV and to develop models for EEV mass flow rate prediction via two approaches: dimensionless correlation based on Buckingham π-theorem and artificial neural network (ANN) model based on dimensionless parameters. The database utilized for model training and test was comprised of our experimental data and data available in open literatures including R22, R407C, R410A and R134a. Compared with three existing dimensionless correlations, the proposed dimensionless correlation and ANN model demonstrated higher accuracy. The proposed dimensionless correlation gave mean relative error (MRE) of 6.60%, relative mean square error of (RMSE) 12.05 kg h⁻¹ and correlation coefficient (R²) of 0.9810. The ANN model with the configuration of 8-6-1 showed MRE, RMSE and R² of 3.97%, 7.59 kg h⁻¹ and 0.9924, respectively.     

步行器精密测力系统中的人工神经网络标定新技术

设计了一种可用于步行器精密测力系统标定的3层反向传播人工神经网络模型,以测力系统12导联应变片电桥输出电压作为网络输入向量,6个负载分量力作为网络输出向量,并通过目标误差下的绝对误差和对比确定出模型隐含层的最优神经元数.有关误差校验结果表明,使用该神经网络技术标定后的系统最大单向力精度误差为7.78%,最大交叉干扰为7.49%,与传统的线性标定方法相比,能够有效提高步行器受载力的测量精度并大大降低干扰误差,未来有望为步行器助行康复训练效果的准确监控和评估提供帮助.     

On the design of human immunodeficiency virus treatment based on a non‐linear time‐delay model

Mathematical modelling and methods from control theory can be employed to find appropriate drug regimens in human immunodeficiency virus (HIV) treatment. In this study, using a non‐linear time‐delay model, the authors design some suboptimal highly active antiretroviral therapy (HAART) [http://www.en.wikipedia.org/wiki/Protease_inhibitor_%28pharmacology%29] regimens for patients with HIV. The non‐linear delayed model is used to describe the dynamical interactions between HIV and human immune system in the presence of HAART. Based on the model, a set point tracking problem is defined in order to set the number of susceptible CD4⁺ T cells to a desired value. To solve this set point tracking problem in a suboptimal way, the authors introduce a new method which is able to consider constraints on the amount of drug dosage. It is proved that the proposed method is able to set the number of susceptible CD4⁺ T cells to the desired value. Simulation results confirm that the method is efficient even in the presence of parametric uncertainties.Inspec keywords: control theory, delays, diseases, patient treatmentOther keywords: human immunodeficiency virus treatment design, nonlinear time delay model, control theory, HIV treatment, suboptimal highly active antiretroviral therapy, suboptimal HAART, human immune system, set point tracking problem, CD4+T cells, drug dosage     

Dynamical micromagnetics by the finite element method

We developed a new numerical procedure to study dynamical behavior in micromagnetic systems. This procedure solves the damped Gilbert equation for a continuous magnetic medium, including all interactions in standard micromagnetic theory in three-dimensional regions of arbitrary geometry and physical properties. The magnetization is linearly interpolated in each tetrahedral element in a finite element mesh from its value on the nodes, and the Galerkin method is used to discretize the dynamic equation. We compute the demagnetizing field by solution of Poisson's equation and treat the external region by means of an asymptotic boundary condition. The procedure is implemented in the general purpose dynamical micromagnetic code (GDM). GDM uses a backward differential formula to solve the stiff ordinary differential equations system and the generalized minimum residual method with an incomplete Cholesky conjugate gradient preconditioner to solve the linear equations. GDM is fully parallelized using MPI and runs on massively parallel processor supercomputers, clusters of workstations, and single processor computers. We have successfully applied GDM to studies of the switching processes in isolated prolate ellipsoidal particles and in a system of multiple particles