ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

Parameters analysis and application of the differential excitation detection technology

A differential excitation probe based on eddy current testing technology was designed. Sheet specimens of Q 235 steel with prefabricated micro-cracks of different widths and of aluminum with prefabricated micro-cracks of different depths were detected through the designed detection system. The characteristics of micro-cracks can be clearly showed after signals processing through the short-time Fourier transform（ STFT）. By changing the parameter and its value in detecting process,the factors including the excitation frequency and amplitude,the lift-off effect and the scanning direction were discussed,respectively. The results showed that the differential excitation probe was insensitive to dimension and surface state of the tested specimen,while it had a high degree of recognition for micro-crack detection. Therefore,when the differential excitation detection technology was used for inspecting micro-crack of turbine blade in aero-engine,and smoothed pseudo Wigner-Ville distribution was used for signal processing,micro-cracks of 0. 3 mm depth and 0. 1 mm width could be identified. The experimental results might be useful for further research on engineering test of turbine blades of aero-engine.

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems(DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator(RMO) is presented to enhance the previous differential evolution(DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Recast combination functions of coordinate and momentum operators into their ordered product forms

By using the parameter differential method of operators,we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings,which is more ecumenical,simpler,and neater than the existing ways.These products are very useful in obtaining some new differential relations and useful mathematical integral formulas.Further,we derive the normally ordered form of the operator(fQ+gP)^-n with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate-momentum representation.In addition,general mutual transformation rules of the normal and anti-normal orderings,which have good universality,are derived and hence the anti-normal ordering of(fQ+gP)^-n is also obtained.Finally,the application of some new identities is given.

Robust Estimation of Parameters in Nonlinear Ordinary Differential Equation Models

Ordinary differential equation(ODE) models are widely used to model dynamic processes in many scientific fields.Parameter estimation is usually a challenging problem,especially in nonlinear ODE models.The most popular method,nonlinear least square estimation,is shown to be strongly sensitive to outliers.In this paper,robust estimation of parameters using M-estimators is proposed,and their asymptotic properties are obtained under some regular conditions.The authors also provide a method to adjust Huber parameter automatically according to the observations.Moreover,a method is presented to estimate the initial values of parameters and state variables.The efficiency and robustness are well balanced in Huber estimators,which is demonstrated via numerical simulations and chlorides data analysis.

The hydrodynamics of self-rolling locomotion driven by the flexible pectoral fins of 3-D bionic dolphin

The novel autonomous rolling performance is realized by the pair of pectoral fins of a three-dimensional(3-D)bionic dolphin in this paper numerically.3-D Navier-Stokes equations are employed to simulate the viscous fluid around the bionic dolphin.The effect of self-rolling manoeuvrability is ex-plored using the dynamic mesh technology and user-defined function(UDF).By varying the parameter ratios,the interaction of flexible pectoral fins is divided into two motion modes,amplitude differential and frequency differential mode.As the primary driving source,the differential motion of a pair of pec-toral fins can effectively provide the rolling torque,and the trajectory of the entire rolling process is approximately the clockwise spiral.The results demonstrate that the rolling angular velocity and driving torque in the steady state can be improved by increasing parameter ratios,and the rolling efficiency can reach the maximum under the optimal parameter ratio.Meanwhile,different parameter ratios do not af-fect the rolling radius of the self-rolling dolphin.The evolution process around the pair of pectoral fins is shown by the flow structures in self-rolling swimming,reasonably revealing that self-rolling locomotion is produced by the pressure and wake vortices surrounding the pair of pectoral fins,and the wake struc-tures depend primarily on the variation of parameter ratio.It properly turns out that the application of the pair of pectoral fins can realize the self-rolling performance through parameter differential modes.