sensor fault detection observer design for nonlinear systems in Takagi–Sugeno’s form

This paper addresses sensor fault detection observer design problems for discrete- and continuous-time nonlinear systems in Takagi–Sugeno’s (T–S) form. It is desired that the fault detection observer is as sensitive to fault and robust against disturbance as possible. To this end, sufficient conditions for stable T–S fuzzy model-based observer design with performance are derived in terms of linear matrix inequalities in both cases. An example on the backing-up problem of a truck-trailer is provided to illustrate the effectiveness of the proposed methodology.     

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5]. The Project supported by the National Natural Science Foundation of China.     

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.     

Study of Hydraulic Properties of Uncoated Paper: Image Analysis and Pore-Scale Modeling

In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution \((0.9~\upmu \hbox {m})\). Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of \(400\times 400\times 150\,\upmu \hbox {m}^{3}\) and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure–saturation Open image in new window imbibition curves for various domain sizes. We studied the directional dependence of Open image in new window curves by simulating water penetration into the layer from various directions. We did not find any significant difference between Open image in new window curves in different directions. We studied the effect of compression of paper on Open image in new window curves. We found that up to 30% compression of the paper layer had very small effect on the Open image in new window curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them.     

Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel

Unsteady momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel is numerically investigated using FLUENT for the ranges of Reynolds numbers as 10≤Re≤500, of the blockage ratio as 0.1≤β≤0.4, and of the gap ratio as 0.125≤γ≤1 for a constant value of the Prandtl number of 0.744. The transition of the flow from steady to unsteady (characterized by critical Re) is determined as a function of γ and β. The effect of γ on the mean drag and lift coefficients, Strouhal number (St), and Nusselt number (Nu _w ) is studied. Critical Re was found to increase with decreasing γ for all values of β. and St were found to increase with decreasing values of γ for fixed β and Re. The effect of decrease in γ on was found to be negligible for all blockage ratios investigated.     

Determining Modes, Nodes and Volume Elements for Stationary Solutions of the Navier-Stokes Problem Past a Three-Dimensional Body

In this paper we show that every solution of the three-dimensional exterior Navier-Stokes boundary-value problem, corresponding to a given non-zero, constant velocity at infinity (flow past a body) and belonging to a very general functional class, , can be determined by a finite number of parameters. Our results extend the analogous classical results by Foiaş & Temam [6, 7], and by Jones & Titi [14] for the interior problem. This extension is by no means trivial, in that all fundamental tools used in the case of the interior problem – such as compactness of the Sobolev embeddings, Poincaré's inequality, and the special basis constituted by eigenfunctions of the Stokes operator – are no longer available for the exterior problem. An important consequence of our results is that any solution in is uniquely determined by the knowledge of the associated velocity field only ``near' the boundary. Just how ``near' it has to be depends only on the Reynolds number and on the body. Dedicated to John Heywood on the occasion of his 65th birthday     

On the validity of the Boltzmann–BGK model through relaxation evaluation

The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.     

A cellular scale numerical study of the effect of mechanical properties of erythrocytes on the near-wall motion of platelets

The effect of mechanical properties of erythrocytes on the near-wall motion of platelets was numerically studied with the immersed boundary method. Cells were modeled as viscous-fluid-filled capsules surrounded by hyper-elastic membranes with negligible thickness. The numerical results show that with the increase of hematocrit, the near-wall approaching of platelets is enhanced, with which platelets exhibit larger deformation and orientation angle of its near-wall tank-treading motion, and the lateral force pushing platelets to the wall is increased with larger fluctuation amplitude. Meanwhile the near-wall approaching is reduced by increasing the stiffness of erythrocytes.     

Mechanical properties of double-stranded DNA biofilm with Gaussian distribution简

In microcantilever-based label-free biodetection technologies, deflection changes induced by adsorptions of double-stranded DNA （dsDNA） molecules on Au-layer surface are greatly affected by the mechanical, thermal and electrical properties of DNA biofilm. In this paper, the elastic properties of dsDNA biofilm are studied. First, the Parsegian＇s empirical potential based on a mesoscopic liq- uid crystal theory is employed to describe the interaction energy among coarse-grained DNA cylinders. Then, con- sidering a Gaussian distribution of DNA interaxial distance, the thought experiment method is used to derive an analyti- cal expression for Young＇s modulus of DNA biofilm with a stochastic packing pattern for the first time. Results show that Young＇s modulus of DNA biofilm is on the order of 10 MPa. These findings could provide a simple and effective method to evaluate the mechanical properties of soft biofilm on snbstrate.     

The application of three-dimensional hydroelastic analysis of ship structures in Pekeris hydro-acoustic waveguide environment简

The hydroelastic analysis and sonoelastic analysis methods are incorporated with the Green＇s function of the Pekeris ocean hydro-acoustic waveguide model to produce a three-dimensional sonoelastic analysis method for ships in the ocean hydro-acoustic environment. The seabed condition is represented by a penetrable boundary of prescribed density and sound speed. This method is employed in this paper to predict the vibration and acoustic radiation of a 1 500 t Small Water Area Twin Hull （SWATH） ship in shallow sea acoustic environment. The wet resonant frequencies and radiation sound source levels are predicted and compared with the measured results of the ship in trial.     

Frequency domain fundamental solutions for a poroelastic half-space

In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot＇s theory. Based on Biot＇s theory, the governing field equations for the dynamic poroelasicity are established in terms of solid displacement and pore pressure. A method of potentials in cylindrical coordinate system is proposed to decouple the homogeneous Biot＇s wave equations into four scalar Helmholtz equations, and the general solutions to these scalar wave equations are obtained. After that, spectral Green＇s functions for a poroelastic full-space are found through a decomposition of solid displacement, pore pressure, and body force fields. Mirror-image technique is then applied to construct the half-space fundamental solutions.Finally, transient responses of the half-space to buried point forces are examined.     

Stability analysis of a thin-walled cylinder in turning operation using the semi-discretization method

In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.     

INITIAL BOUNDARY VALUE PROBLEMS FOR A CLASS OF NONLINEAR INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣｕｉＳｈａｎｇ－ｂｉｎ（崔尚斌）（Ｄｅｐｔ．ｏｆＭａｔｈ．,ＬａｎｚｈｏｕＵｎｉ...     

Analytical solution of a double moving boundary problem for nonlinear flows in one-dimensional semi-infinite long porous media with low permeability简

Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.     

Coupled extension and thickness-twist vibrations of lateral field excited AT-cut quartz plates简

In this paper, the coupled extension and thickness- twist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation （LFE） with variations along the x1- direction. Mindlin＇s two-dimensional equations are used for anisotropic crystal plates. Both free and electrically forced vibrations are considered. Important vibration characteristics are obtained, including dispersion relations, frequency spectra, and motional capacitances. It is shown that, to avoid the effects of the couplings between extension and thickness-twist vibrations, a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded. The results are of fundamental significance for the design of LFE resonators and sensors.     

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters简

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.     

Vibration analysis of axisymmetric functionally graded viscothermoelastic spheres简

The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial di- rection with a simple power law. Matrix Frrbenious method of extended power series is employed to derive the analytical solutions for displacement, temperature, and stresses. The dispersion relations for the existence of various types of pos- sible modes of vibrations in the considered hollow sphere are derived in a compact form. In order to explore the character- istics of vibrations, the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software. The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies, frequency shift, inverse quality factor, displacement, temperature change, and radial stress.     

The Life and Work of Robin A. Wooding

Robin A. Wooding (1926–2007) made many outstanding and original contributions to the field of convection in porous media throughout his research career. He was an applied mathematician who also worked on a wide variety of other important hydrological, meteorological, earth science and physical science problems. Important contributions included (i) the discovery of the occurrence of fingers in the context of mono-diffusive convection in a porous medium and an early body of associated papers on convection in porous media, (ii) the development of a novel hydraulic model for the catchment-stream problem and (iii) the mathematical solution to the problem of steady infiltration from a shallow circular pond that formed the basis for the disc permeameter method. This note documents biographical matters and assesses the importance of his scientific work. Robin A. Wooding 6 March 1926–19 November 2007 (Photograph circa 1975)

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