Implementation of higher-order asymptotics to S-plus

Higher-order asymptotics is an active area of development in theoretical statistics. However, most existing work in higher-order asymptotics is directed to the theoretical aspects. This paper attempts to incorporate higher-order inference procedures to S-plus, a widely used software in statistics. Algorithm is developed in the settings of generalized linear models and nonlinear regression models. The proposed algorithm generalizes the standard S-plus functions “glim” and “nls” in the sense that both the first-order and higher-order p-values are provided, and its manipulation is straightforward.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.     

Towards mesoscopic thermodynamics: Small systems in higher-order states

A higher-order generalization of the usual thermodynamic formalism is presented for systems with the number of particlesN large in comparison with 1, but sufficiently small that one or many higher-order fluctuations of energy (or other observables) are measurable, directly or indirectly. Then 1 «N «N _A , whereN _A is the Avogadro number, andn2, wheren is the highest order of fluctuations (central statistical moments). The systems are then open, finite and compact, and they have compact boundary surfaces, so that the energy is non-additive and temperatures are non-intensive, in general. Such systems will be called comesoscopic, while a finite or infinite super-system of such systems will be called mesoscopic. Three ideal models of comesoscopic systems are discussed in detail with one or two higher-order temperatures. General conclusions concerning hierarchical composite systems are drawn afterwards.

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A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations

A three-step wavelet Galerkin method based on Taylor series expansion in time is proposed. The scheme is third-order accurate in time and O(2^?jp ) accurate in space. Unlike Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving non-linear problems. The compactly supported orthogonal wavelet bases D6 developed by Daubechies are used in the Galerkin scheme. The proposed scheme is tested with both parabolic and hyperbolic partial differential equations. The numerical results indicate the versatility and effectiveness of the proposed scheme.     

Real and complex-exponential describing functions for transient analysis of non-linear control systems†

A real exponential describing function as an analysis tool for studying the transient response of a class of non-linear feedback systems was developed by Bickart (1966). In this paper describing functions are developed for similar analysis more suitable to higher-order non-linear feedback systems. The two classes of describing functions developed are identified as real exponential or complex exponential.

Here, signals in ?₂ ( ? ∞, t] a space of the space of square integrable signals defined on (?∞, t ], are approximated by the sum of n signals in ?₂ ^{1, m} (?∞, t)one-dimensional sub-spaccs of ?₂ ( ? ∞, t] having the mth function from the set of reversed time orthogonalized real or eponential functions as a basis. A system mapping ?₂ ^{1, m}(?∞, t] into itself is associated with a system mapping ?₂ ^{1, m}(?∞, t] into itself; the latter system is characterized by a gain—real or exponential describing function. These multiple one-dimensional system mappings give rise to approximation components of the response whoso addition will represent a better approximation to the actual response than each component by itself. The contraction-mapping fixed point theorem is also used to determine conditions for the existence of a solution prior to the use of the exponential describing functions for obtaining on approximate response.     

Models of branching walks and their use in the reliability theory

Application of the branching walk models in the reliability theory was discussed. The results obtained for the models of a symmetric continuous-time branching random walk on Z ^d with the source of particle birth and death at one of the lattice points were reviewed. Emphasis was made on the survival analysis and study of the branching walk properties depending on the source intensity. It was shown that if d ≥ 3, then under the supercritical branching process at the source the supercritical, critical and even subcritical branching random walk may arise on Z ^d . A classification relying on the asymptotic behavior of the number of particles at an arbitrary lattice point which specifies the phase transitions on lattice dimension for the critical and subcritical branching random walk was presented.     

Damping optimization of viscoelastic laminated sandwich composite structures

Recent developments on the optimization of passive damping for vibration reduction in sandwich structures are presented in this paper, showing the importance of appropriate finite element models associated with gradient based optimizers for computationally efficient damping maximization programs. A new finite element model for anisotropic laminated plate structures with viscoelastic core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach. The complex modulus approach is used for the viscoelastic material behavior, and the dynamic problem is solved in the frequency domain. Constrained optimization is conducted for the maximization of modal loss factors, using gradient based optimization associated with the developed model, and single and multiobjective optimization based on genetic algorithms using an alternative ABAQUS finite element model. The model has been applied successfully and comparative optimal design applications in sandwich structures are presented and discussed.     

Solid-to-shell transition elements for the computation of interlaminar stresses

This paper presents an accurate and practical technique for coupling shell element models to three-dimensional continuum finite element models. The compatibility between these two types of formulations is enforced by degenerating a continuum element through kinematic constraints compatible with shell deformations. Two formulations of two-dimensional/three-dimensional transition elements are presented. The first and simplest formulation is based on the Mindlin-Reissner plate assumptions, and is found to perform well in a variety of problems involving the analysis of geometrically linear/non-linear laminated structures. The second formulation is based on a higher-order shell theory that allows stretching in the through-the-thickness direction. This additional freedom virtually eliminates the interlaminar normal stress boundary layer that can form in lower-order transition elements. Finally, the coupling of two-dimensional to three-dimensional subdomains is enriched with the use of an interface element, which can be used in conjunction with either transition formulation. The interface element improves the efficiency of the solid-to-shell transition modeling scheme by allowing the independent selection of optimal mesh sizes in the shell and the three-dimensional regions of the model.     

The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches

In this paper we present an isogeometric formulation for rotation-free thin shell analysis of structures comprised of multiple patches. The structural patches are C¹- or higher-order continuous in the interior, and are joined with C⁰-continuity. The Kirchhoff–Love shell theory that relies on higher-order continuity of the basis functions is employed in the patch interior as presented in Kiendl et al. [36]. For the treatment of patch boundaries, a method is developed in which strips of fictitious material with unidirectional bending stiffness and zero membrane stiffness are added at patch interfaces. The direction of bending stiffness is chosen to be transverse to the patch interface. This choice leads to an approximate satisfaction of the appropriate kinematic constraints at patch interfaces without introducing additional stiffness to the shell structure. The attractive features of the method include simplicity of implementation and direct applicability to complex, multi-patch shell structures. The good performance of the bending strip method is demonstrated on a set of benchmark examples. Application to a wind turbine rotor subjected to realistic wind loads is also shown. Extension of the bending strip approach to the coupling of solids and shells is proposed and demonstrated numerically.     

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C⁰ finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.     

Linearized dynamic models of robot manipulators in cartesian space

This article presents development of the linearized dynamic models of robot manipulators in Cartesian space. A clever method is proposed to formulate the linearized dynamic models of robot manipulators in Cartesian space. Efficient methods are developed to compute various matrices involved in the models (or the manipulator sensitivity matrices in Cartesian space), such as the Jacobian matrix and the first and second derivatives of it with respect to time as well as the manipulator sensitivity matrices in joint space. The proposed methods are simple and systematic and have computational complexity of the order O(n²) only, where n is the number of degrees-of-freedom of the manipulator.     

Free vibration of laminated plates using a finite strip method based on a higher-order plate theory

The finite strip method based on the higher-order plate theory is developed for determining the natural frequencies of laminated plates. This method can accurately predict the through thickness effect of transverse shear deformation. Furthermore, only a few degress of freedom are required in the finite strip method. Some numerical results for various span-to-thickness ratios, material properties and stack sequences are presented for illustrative purposes. The present model provides a better way to obtain more accurate natural frequency results.     

THE LOGIC OF AUTOMATA

Automata are the prime example of general systems over discrete spaces, and yet the theory of automata is fragmentary and it is not clear what makes a general structure an automaton. This paper investigates the logical foundations of automata relating it to the semantics of our notions of uncertainty, state and state-determined. A single framework is established for the conventional spectrum of automata: deterministic, probabilistic, fuzzy, and non-deterministic, which shows this set to be, in some sense, complete. Counter-examples are then developed to show that this spectrum alone is inadequate to describe the behaviour of certain forms of uncertain system. Finally a general formulation is developed based on the fundamental semantics of our notion of a state that shows that the logical Structure of an automaton must be at least a positive ordered semiring. The role of probability logic, its relationship to fuzzy logic, the rotes of topological models of automata, and the symmetry between inputs and outputs in hyperstate/hyperinput-determinedsystems are also discussed.     

Feasibility of imperialist competitive algorithm to predict the surface settlement induced by tunneling

Surface settlement is considered as an adverse effect induced by tunneling in the civil projects. This paper proposes the use of the imperialist competitive algorithm (ICA) for predicting the maximum surface settlement (MMS) resulting from the tunneling. For this work, three forms of equations, i.e., linear, quadratic and power are developed and their weights are then optimized/updated with the ICA. The requirement datasets were collected from the line No. 2 of Karaj urban railway, in Iran. In the ICA models, vertical to horizontal stress ratio, cohesion and Young’s modulus, as the effective parameters on the MSS, are adopted as the inputs. The statistical performance parameters such as root mean square error (RMSE), mean bias error (MBE), and square correlation coefficient (R²) are presented and compared to validate the performance. The findings indicate that the developed ICA-based models with the R² of 0.979, 0.948 and 0.941, obtained from ICA power, ICA quadratic and ICA linear models, respectively, are the acceptable and accurate tools to estimate MSS, and furthermore prove their prediction capability for future research works in this field.

     

THE LOGIC OF AUTOMATA

Automata are the prime example of general systems over discrete spaces, and yet the theory of automata is fragmentary and it is not clear what makes a general structure an automaton. This paper investigates the logical foundations of automata relating it to the semantics of our notions of uncertainty, state and state-determined. A single framework is established for the conventional spectrum of automata: deterministic, probabilistic, fuzzy, and non-deterministic, which shows this set to be, in some sense, complete. Counter-examples are then developed to show that this spectrum alone is inadequate to describe the behaviour of certain forms of uncertain system. Finally a general formulation is developed based on the fundamental semantics of our notion of a state that shows that the logical structure of an automaton must be at least a positive ordered semiring. The role of probability logic, its relationship to fuzzy logic, the roles of topological models of automata, and the symmetry between inputs and outputs in hyperstate/hyperinput-determined systems are also discussed.     

Shape optimization of axisymmetric shells using a higher-order shear deformation theory

In this paper structural and sensitivity analysis for the optimization of laminated axisymmetric shells subjected to static constraints and arbitrary loading is presented. The shell thickness, radial coordinate of a nodal point, lamina thickness and the angle of orientation of the fibers are the design variables. The objective of the design optimization is the minimization of the volume of the shell or the strain energy. The model is based on a three-node axisymmetric finite element with 24 degrees of freedom. A higher-order theory is developed for the nonlinear distribution of the meridional displacement component through the thickness of the shell. The sensitivities of the discrete model developed are evaluated analytically using a symbolic manipulator. The efficiency and accuracy of the proposed model is discussed with reference to the applications.     

Modelling cross-ply laminated elastic shells by a higher-order theory and multiquadrics

The higher-order shear-deformation theory of laminated orthotropic elastic shells of Vlasov–Reddy is a modification of Sanders’ theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the shell. The Vlasov–Reddy shell theory allows the fulfillment of homogeneous conditions (zero values) at the top and bottom surfaces of the shell. This paper deals with a meshless solution of the Vlasov–Reddy higher-order shell theory. The meshless technique is based on the asymmetric global multiquadric radial basis function method proposed by Hardy and Kansa. This paper demonstrates that this truly meshless method is successful in the analysis of laminated composite shells.     

Improvements in the estimation of daily minimum air temperature in peninsular Spain using MODIS land surface temperature

Air temperature (T_a) is a key variable in many environmental risk models and plays a very important role in climate change research. In previous studies we developed models for estimating the daily maximum (T_max), mean (T_mean), and minimum air temperature (T_min) in peninsular Spain over cloud-free land areas using Moderate Resolution Imaging Spectroradiometer (MODIS) data. Those models were obtained empirically through linear regressions between daily T_a and daytime Terra-MODIS land surface temperature (LST), and then optimized by including spatio-temporal variables. The best T_mean and T_max models were satisfactory (coefficient of determination (R²) of 0.91–0.93; and residual standard error (RSE) of 1.88–2.25 K), but not the T_min models (R² = 0.80–0.81 and RSE = 2.83–3.00 K). In this article T_min models are improved using night-time Aqua LST instead of daytime Terra LST, and then refined including total precipitable water (W) retrieved from daytime Terra-MODIS data and the spatio-temporal variables curvature (c), longitude (λ), Julian day of the year (JD) and elevation (h). The best T_min models are based on the National Aeronautics and Space Administration (NASA) standard product MYD11 LST; and on the direct broadcast version of this product, the International MODIS/AIRS Processing Package (IMAPP) LST product. Models based on Sobrino’s LST1 algorithm were also tested, with worse results. The improved T_min models yield R² = 0.91–0.92 and RSE = 1.75 K and model validations obtain similar R² and RSE values, root mean square error of the differences (RMSD) of 1.87–1.88 K and bias = 0.11 K. The main advantage of the T_min models based on the IMAPP LST product is that they can be generated in nearly real-time using the MODIS direct broadcast system at the University of Oviedo.     

A generalized unconstrained theory and isogeometric finite element analysis based on Bézier extraction for laminated composite plates

This work presents an isogeometric finite element formulation based on Bézier extraction of the non-uniform rational B-splines (NURBS) in combination with a generalized unconstrained higher-order shear deformation theory (UHSDT) for laminated composite plates. The proposed approach relaxes zero-shear stresses at the top and bottom surfaces of the plates and no shear correction factors are required. A weak form of static, free vibration and transient response analyses for laminated composite plates is then established and is numerically solved using isogeometric Bézier finite elements. NURBS can be written in terms of Bernstein polynomials and the Bézier extraction operator. IGA is implemented with the presence of C°-continuous Bézier elements which allow to easily incorporate into existing finite element codes without adding many changes as the former IGA. As a result, all computations can be performed based on the basis functions defined previously as the same way in finite element method (FEM). Numerical results performed over static, vibration and transient analysis show high efficiency of the present method.