火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade

Non-linear static and dynamic analysis is presented for composite laminated anti-symmetric square plates supported on non-linear elastic foundation subjected to uniformly distributed transverse and step loading, respectively. The formulation is based on first order shear deformation theory (FSDT) and Von-Karman non-linearity, subgrade interaction is modeled as shear deformable with cubic nonlinearity. The methodology of solution is based on the Chebyshev series technique. The coupled non-linear partial differential equations are linearized using quadratic extrapolation technique. Houbolt time marching scheme is employed for temporal discretisation. An incremental iterative approach is employed for the solution. The effects of foundation stiffness parameters and boundary conditions on the non-linear static and dynamic analysis on the central response are studied.     

Evolution of near-soliton initial conditions in non-linear wave equations through their Bäcklund transforms

A novel analytic technique for determining the evolution of near-soliton initial conditions in non-linear wave equations is introduced. It is based on the Bäcklund transform connecting soliton solutions of successive order. This transformation lowers the order of the initial condition rendering the determination of the evolution easier. The result of the evolution in this order is transformed to the higher order using again the Bäcklund transform. As a demonstration, the proposed technique is applied to the non-linear Schrödinger (NLS) and Korteweg–de Vries (KdV) equations. The results are in very good agreement with those obtained by other approaches based on the inverse scattering method. Finally, numerical simulations verify the validity of the proposed technique.     

The stable manifold theorem for non-linear stochastic systems with memory. I. Existence of the semiflow

We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows and a non-linear variational technique. In Part II of this article, the above result will be used to prove a stable manifold theorem for non-linear sfde's.     

随机激励下结构的非线性分析

针对随机时间序列载荷激励下的非线性系统,提出一种基于Z变换的递归方法．对于所获得的响应时间序列的识别,建议了一种离散小波变换（DWT）的技术．     

On the existence of non-linear Beltrami fields

We prove an existence result of non-linear force-free (or Beltrami) fields in a threedimensional domain simply or multiply connected. The proof is based on a fixed point procedure and a singular perturbation technique.     

Profiling effects in industrial data mining by non-parametric DOE methods: An application on screening checkweighing systems in packaging operations

There is a growing interest in applying robust techniques for profiling complex processes in industry. In this work, we present an approach for analyzing fractional-factorial data by building distribution-free models suitable for dealing with replicated trials in search of non-linear effects. The technique outlined in this article is synthesized by implementing four key elements: (1) the data collection efficiency of non-linear fractional factorial designs, (2) the data compression capabilities of rank-sums for repetitive sampling schemes, (3) the rank-ordering as a means to transform data, and (4) the non-parametric screening for prominent effects where the normality and sparsity assumptions are waived. The technique is tested on four controlling factors for profiling the packaging weighing operations of a pharmaceutical enterprise. The robust data mining of repeated trials based on an L₉(3⁴) orthogonal array scheme with embedded uncontrolled noise is discussed extensively. The technique has been subjected to quality control as it is tested with well-defined artificial data. Concluding remarks involve contrasting this new technique with mainstream competing schemes.     

Nonlinear dynamic response of laminated composite plates subjected to pulse loading

An analytical solution methodology for the non-linear dynamic displacement response of laminated composite plates subjected to different types of pulse loading is presented. The mathematical formulation is based on third-order shear deformation plate theory and von-Karman non-linear kinematics. Fast-converging finite double Chebyshev series is employed for evaluating the displacement response. Houbolt time marching scheme is used for temporal discretization and quadratic extrapolation technique is used for linearization. The effects of magnitude and duration of the pulse load, boundary conditions and plate parameters on the central displacement and bending moment responses are studied.     

Smoothed particle hydrodynamics modeling of the thermal behavior of double skin facades in fires considering the effects of venetian blinds

At present, the fire safety of double skin facades (DSFs) is an important research area due to recent spikes in fires in high rise buildings involving glass DSF systems, and also due to our limited understanding of the thermal behavior of these systems. To overcome this lack of knowledge, a numerical framework is proposed for simulating the thermal performance of DSFs under fire conditions. The framework is based on the smoothed particle hydrodynamics technique and it can be used to compute numerical solutions and simulate the thermal degradation of DSFs under fire conditions. The numerical model was validated by comparing the predicted response parameters in a fire exposed DSF system with those measured in fire experiments. The validated numerical model was then employed to derive empirical equations linking temperature with both the time and location along the interior and exterior glass panes of DSFs. Finally, numerical simulations were conducted for the same DSF configuration but equipped with venetian blinds in order to examine the influence of the blinds on the fire performance of glass DSFs. An in-house MATLAB code was developed and implemented to conduct these numerical simulations. The results obtained from these numerical simulations clearly indicated that the “blind tilt angle” can significantly affect the fire spread characteristics and temperature distribution in DSFs, and thus it should be considered in the design of DSF systems for high rise buildings.     

A continuous model of the dynamical systems capable to memorise multiple shapes

This paper proposes the novel approach to the mathematical synthesis of continuous self-organising systems capable to memorise and restore own multiple shapes defined by means of functions of single spatial variable or parametric models in two-dimensional space. The model is based on the certain universal form of the integral operator with the kernel representing the system memory. The technique for memorising shapes uses the composition of singular kernels of integral operators. The whole system is described by the potential function, whose minimisation leads to the non-linear dynamics of shape reconstruction by integro-differential non-linear equations with partial derivatives. The corresponding models are proposed and analysed for both parametric and non-parametric shape definitions. Main features of the proposed model are considered, and the results of numerical simulation are shown in case of three shapes memorising and retrieval. The proposed model can be used in theory of smart materials, artificial intelligence and some other branches of non-linear sciences where the effect of multiple shapes memorising and retrieval appears as the core feature.     

Application of differential transform method to non-linear oscillatory systems

In this paper, the differential transform method is proposed for solving non-linear oscillatory systems. These solutions do not exhibit periodicity, which is the characteristic of oscillatory systems. A modification of the differential transform method, based on the use of Padé approximants, is proposed. We use alternative technique by which the solution obtained by the differential transform method is made periodic. The method is described and illustrated with examples. The results reveal that the method is very effective and convenient.     

An extended tube model for thermo-viscoelasticity of rubberlike materials: Parameter identification and examples

The extended tube-model was presented by KALISKE & HEINRICH (RCT 72, 602-632) in 1999 as a novel approach for isothermal hyperelasticity of rubberlike materials. This contribution is dedicated to its further development to finite non-linear thermo-viscoelasticity. A non-linear evolution law and a thermo-mechanical coupled free energy formulation are the kernel of the phenomenological approach where the elastic material response is inspired by statistical-mechanical theory. The representation of viscoelasticity is based on a multiplicative decomposition of the deformation gradient. The Helmholtz free energy of the material is formulated in terms of isothermal free energy functions multiplicatively coupled with non-linear temperature evolution functions. The non-linear evolution law for the viscous material branch is solved by applying a predictor-corrector algorithm with an exponential mapping scheme. In today's literature, several sophisticated thermo-mechanical material models are available. However, they are built upon a considerable number of material parameters governing the mechanical and thermal material response which need to be identified for practical application. Therefore, particular emphasis is given to an appropriate parameter identification technique for the thermal field. For the latter, a uniaxial extension test is carried out where the recorded data of the temperature field of the rubber specimen under cyclic loading is used for parameter identification. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Restoration of efficiency in a goal programming problem with linear fractional criteria

The problem resulting from a goal programming problem with linear fractional criteria is not easy to solve due to the non-linear constraints inherent in its formulation. This paper introduces a simple and reliable test to establish whether a linear fractional goal programming problem has solutions that verify all goals and, if so, how to find them by solving a linear programming problem. This paper also outlines a new technique for restoring efficiency based on a minimax philosophy. An example is presented.     

On the approximate solutions for system of fractional integro-differential equations using Chebyshev pseudo-spectral method

In this paper, we implement Chebyshev pseudo-spectral method for solving numerically system of linear and non-linear fractional integro-differential equations of Volterra type. The proposed technique is based on the new derived formula of the Caputo fractional derivative. The suggested method reduces this type of systems to the solution of system of linear or non-linear algebraic equations. We give the convergence analysis and derive an upper bound of the error for the derived formula. To demonstrate the validity and applicability of the suggested method, some test examples are given. Also, we present a comparison with the previous work using the homotopy perturbation method.     

Numerical Solution of the Fokker-Planck Equation with Time-Discontinuous Galerkin Methods

The response of non-linear dynamic systems under white noise excitation possesses Markov characteristics. The evolution of the probability density of the system response is represented by the Fokker-Planck equation, which characterizes advection and diffusion. The solution probability density distribution often possesses high gradients. Therefore an efficient numerical solution technique based on a discontinuous Galerkin approximation in the time domain is proposed for the solution of the Fokker-Planck equation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Implementation of sparse matrix algorithms in an advection-diffusion-chemistry module

A two-dimensional advection-diffusion-chemistry module of a large-scale environmental model is taken. The module is described mathematically by a system of partial differential equations. Sequential splitting is used in the numerical treatment. The non-linear chemistry is most time-consuming part and it is handled by six implicit algorithms for solving ordinary differential equations. This leads to the solution of very long sequences of systems of linear algebraic equations. It is crucial to solve these systems efficiently. This is achieved by applying four different algorithms. The numerical results indicate that the algorithms based on a preconditioned sparse matrix technique and on a specially designed algorithm for the particular problem under consideration perform best.     

Large dynamics of Yang–Mills theory: mean dimension formula

We study the Yang–Mills anti-self-dual (ASD) equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and moreover becomes an infinite dimensional and infinite entropy system. We study the mean dimension of this huge dynamical system. Mean dimension is a topological invariant of dynamical systems introduced by Gromov. We prove the exact formula of the mean dimension by developing a new technique based on the metric mean dimension theory of Lindenstrauss–Weiss.     

Use of digital terrain data for calculating fire rates of spread with the PREPLAN computer system

This study reports a new technique for predicting fire rates-of-spread with the PREPLAN computer system used by the NSW National Parks and Wildlife Service. Accurate data on slope and topographic geometry produced by new digital terrain modelling packages are used to generate slope vectors in four directions for the McArthur equations. Rates-of-spread predicted using these new techniques are compared to those predicted using an existing technique that requires a calibration constant to avoid a tendency to overestimate. Data from a real fire in Kosciusko National Park are used, and suggest that almost all need for the calibration constant can be accounted for. The results suggest a way to significantly improve the accuracy of fire behaviour predictions.     

The Siting of Fire Stations

Perhaps the most important decision facing any Chief Fire Officer is how many fire stations to have and on which sites to build them. It is appreciated that the optimum solution is that which minimizes the sum of the financial loss from fire and the cost of providing the fire brigade. Financial loss data are not as yet available so the criteria for optimization have had to be altered.A technique has been evolved which minimizes the total number of fire appliance journey times to fires for any given number of fire stations. A set of solutions is obtained giving the best combination of r station sites from a set of n alternative sites, where r varies from n-1 to 1. This technique has been applied to the area covered by Bristol Fire Brigade and the results are discussed.Although the criterion adopted for optimization was necessarily unsatisfactory a near valid set of answers appears to have been obtained. Suggestions for future work are also made.     

Profitability of online order fulfillment in multi-channel retailing

Store-based retailers have been concerned about the high fulfillment costs and low gross margins of their online sales. This paper incorporates such issues in a non-linear mixed-integer profit maximization model of the online order fulfillment process for multi-channel retailers. A solution approach based on an iterative outer-approximation technique is developed. Using empirical data from a large U.S. retailer, the profitability of different options used by multi-channel retailers to fill online orders is evaluated. Managerial insights are developed through a factorial research design that highlights the effect of relevant logistics processes and fulfillment methods on the profitability of online sales for retailers.