面向污水处理的动态变分贝叶斯混合因子故障诊断

在污水生化处理过程中,存在着多变量耦合、强非线性、参数时变、大滞后等特点,面对这些特点,传感器故障频发,从而导致生化过程无法得到有效优化和诊断.为此,本文在结合动态数据特性的基础上提出了一种基于变分贝叶斯混合因子的动态故障诊断方法,同时,利用混合因子的在线调整实现了诊断模型的半自适应化.该方法能够捕捉到污水处理过程的强非线性和动态性,从而可有效降低故障诊断的误报率和漏报率.通过在国际水协会的BSM1模型上的模拟研究,充分表明所提出的策略可以显著提高故障诊断能力,精确地检测传感器的突变和漂移故障,甚至定位故障所发生的根本原因.     

基于修正变分法开孔板和加强板结构的自由振动分析

为研究船舶开孔板和加强板结构的振动特性,用1阶剪切变形板理论描述各向同性板的位移场,并采用修正变分原理和区域分解方法建立板的离散动力学模型.每一块子域板的位移和转角分量通过第一类切比雪夫正交多项式展开.针对加强板模型,将该方法获得的结果与已经发表的文献和有限元商用软件计算结果进行对比,验证该方法的收敛性和正确性.基于修正变分法探讨多种开孔和加强板模型的自由振动特性,充分说明该数理模型和半解析方法是一种适合处理复杂板结构问题的数值工具.     

基于Cosserat连续体理论的疲劳寿命概率可靠性分析

基于Cosserat连续体理论建立考虑应变梯度效应的粉末高温合金弹塑性模型.该模型考虑微尺度长度效应,并能消除缺陷局部化问题求解时的网格依赖性.基于参变量变分原理提出一种高效的求解方法,该方法将原非线性问题转化为互补问题求解,可大大提高求解效率和收敛性.针对一种假想涡轮盘模型,将Cosserat尺度参数和Basquin斜率作为随机变量,分别采用蒙特卡洛法与二阶矩法进行疲劳寿命概率可靠度计算.结果表明二阶矩法在保证精度的情况下具有较高的效率.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

Numerical Schemes for Variational Inequalities Arising in International Asset Pricing

This paper introduces a valuation model of international pricing in the presence of political risk. Shipments between countries are charged with shipping costs and the country specific production processes are modelled as diffusion processes. The political risk is modelled as a continous time jump process that affects the drift of the returns in the politically unstable countries. The valuation model gives rise to a singular stochastic control problem that is analyzed numerically. The fundamental tools come from the theory of viscosity solutions of the associated Hamilton–Jacobi–Bellman equation which turns out to be a system of integral-differential Variational Inequalities with gradient constraints.     

The optimal retrieval of ocean color constituent concentrations based on the variational method

In this paper, a new approach to the optimal retrieval of the ocean color based on the variational method is developed by setting up a rational target functional combining with the Broydor Fletcher, Goldfarb, Shanno (BFGS) optimal algorithm. The numerical tests and the exemplary retrievals are carried out and compared with the statistical retrievals and the optimal retrievals based on the genetic algorithm. The results show that this approach enjoys a higher accuracy as compared to the statistical method and a higher efficiency as compared to the genetic algorithm. The optimal retrieval method presented in this paper provides a new idea for the ocean color inversion and could also be used as a reference for the direct assimilation of the satellite data into the ecological models.     

Pseudospectral methods based on nonclassical orthogonal polynomials for solving nonlinear variational problems

Two direct pseudospectral methods based on nonclassical orthogonal polynomials are proposed for solving finite-horizon and infinite-horizon variational problems. In the proposed finite-horizon and infinite-horizon methods, the rate variables are approximated by the Nth degree weighted interpolant, using nonclassical Gauss-Lobatto and Gauss points, respectively. Exponential Freud type weights are introduced for both of nonclassical orthogonal polynomials and weighted interpolation. It is shown that the absolute error in weighted interpolation is dependent on the selected weight, and the weight function can be tuned to improve the quality of the approximation. In the finite-horizon scheme, the functional is approximated based on Gauss-Lobatto quadrature rule, thereby reducing the problem to a nonlinear programming one. For infinite-horizon problems, an strictly monotonic transformation is used to map the infinite domain onto a finite interval. We transcribe the transformed problem to a nonlinear programming using Gauss quadrature rule. Numerical examples demonstrate the accuracy of the proposed methods.     

A new homotopy perturbation method for system of nonlinear integro-differential equations

In this paper, a new homotopy perturbation method (NHPM) is introduced to obtain exact solutions of system of nonlinear integro-differential equations. Theoretical considerations are discussed. Two examples are given to demonstrate the efficiency of NHPM to the classical HPM and variational iteration methods.     

A numerical method for annuity-purchasing decision making to minimize the probability of financial ruin for regime-switching wealth models

This work develops an approximation procedure to find optimal annuity-purchasing strategies for minimizing the probability of lifetime ruin. The wealth is modelled as a regime-switching diffusion modulated by a continuous-time Markov chain. Based on Markov chain approximation techniques, a discrete-time controlled Markov chain with two components is constructed. Under simple conditions, the convergence of the approximation sequence to the wealth process is obtained. The convergence of the approximation to the value function is also established. Several examples are provided to demonstrate the performance of the algorithms.     

山羊绒纤维粘连肤皮的研究

探讨不同羊种山羊绒纤维粘连肤皮量与肤皮点面积分布区间．借助电子扫描仪、电子标尺对粘连肤皮的试样绒纤维进行测试分析,得知母羊绒纤维粘连肤皮量比公羊大,粘连肤皮点面积分布区间也相对公羊大．建议加工不同羊种山羊绒纤维,应采取不同的加工工艺．