Consistency property of extended least-squares parameter estimation for stochastic diffusion equation

The extended least-squares parameter estimate for stochastic heat diffusion equations is considered. The unknown parameter is a heat diffusion coefficient which is a function of a spatial variable. Almost sure convergence for the estimated parameter is proved. A numerical example is demonstrated for supporting the theoretical results developed here.     

Least possible time paths in stochastic, time-varying networks

In this paper, two computationally efficient algorithms are presented for determining the least possible time paths for all origins to a single destination in networks where the arc weights are discrete random variables whose probability distribution functions vary with time. The first algorithm determines the least possible time path from each node for each departure time interval, the least possible travel time and a lower bound on the associated probability of the occurrence of this travel time. The second algorithm determines up to k least possible time paths, the associated travel times and the corresponding probabilities of occurrence of the travel times (or a lower bound on this probability). No such efficient algorithms for determining least time paths in stochastic, time-varying networks exist in the literature.     

The H2-control for jump linear systems: cluster observations of the Markov state

The H₂-norm control problem of discrete-time Markov jump linear systems is addressed in this paper when part of, or the total of the Markov states is not accessible to the controller. The non-observed part of the Markov states is grouped in a number of clusters of observations; the case with a single cluster retrieves the situation when no Markov state is observed. The control action is provided in linear feedback form, which is invariant on each cluster, and this restricted complexity setting is adopted, aiming at computable solutions. We explore a recent result by de Oliveira, Bernussou, and Geromel (Systems Control Lett. 37 (1999) 261) involving an LMI characterization to establish a H₂ solution that is stabilizing in the mean square sense. The novelty of the method is that it can handle in LMI form the situation ranging from no Markov state observation to complete state observation. In addition, when the state observation is complete, the optimal H₂-norm solution is retrieved.     

泥沙随机起动的简化模式

泥沙的起动既有随机性，又有模糊性，据此作者将模糊数学方法引入泥沙起动研究。建立了直接反映泥沙随机起动特性的起动流速计算模式，该模式得到了实测资料的检验。这一模式可以体现泥沙起动的随机性，较好地反映了泥沙起动的本来面目     

随机场理论在随机结构分析中的应用

本文首先介绍了随机场理论的基本概念，并简单讨论了随机场向随机变量转化时的转化精度问题，以及相关结构谱分解理论中谱截断的影响。将随机场理论引入到随机结构分析中，从而在保证精度条件下可以降低结构分析的计算工作量     

Stochastic system transformation using generalized orthonormal basis functions with applications to continuous-time system identification

This paper studies the system transformation using generalized orthonormal basis functions that include the Laguerre basis as a special case. The transformation of the deterministic systems is studied in the literature, which is called the Hambo transform. The aim of the paper is to develop a transformation theory for stochastic systems. The paper establishes the equivalence of continuous and transformed-discrete-time stochastic systems in terms of solutions. The method is applied to the continuous-time system identification problem. It is shown that using the transformed signals the PO-MOESP subspace identification algorithm yields consistent estimates for system matrices. An example is included to illustrate the efficacy of the proposed identification method, and to make a comparison with the method using the Laguerre filter.     

A method for stochastic multiple criteria decision making based on dominance degrees

This paper proposes a method for solving the stochastic multiple criteria decision making (SMCDM) problem, where consequences of alternatives with respect to criteria are represented by random variables with probability distributions. Firstly, definitions and related analysis of dominance degree of one probability distribution over another are given. Then, by calculating the dominance degrees, the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built. Further, using PROMETHEE II method, an overall dominance degree matrix of alternative pairwise comparisons is constructed, and a net flow of each alternative is calculated. Based on the obtained net flows, a ranking of alternatives is determined. Finally, numerical examples for the three cases are given to illustrate the use of the proposed method.     

Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports

The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.     

Solving single-product economic lot-sizing problem with non-increasing setup cost,constant capacity and convex inventory cost in O(N log N) time

This paper considers an economic lot sizing model with constant capacity, non-increasing setup cost, and convex inventory cost function. Algorithms with computational time of O(N×TD_N)have been developed for solving the model, where N is the number of planning periods and TD_N is the total demand. This study partially characterizes the optimal planning structure of the model. A new efficient algorithm with computational time of O(N log N) has also been developed based on the partial optimal structure. Moreover, computational study demonstrates that the new algorithm is efficient.