关于数学建模教学及竞赛改革的思考

从笔者学校实际情况出发,阐述数学建模课程的特点,探讨数学建模教学及竞赛存在的问题,从开设《数学建模与实验》公共选修课、编写教材或讲义、教学方法改革、成立数学建模竞赛教学团队及考核形式多样化等五个方面提出数学建模课程改革的思路,并给出数学建模教学及竞赛改革的具体建议。     

浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。     

Reflections on Bayesian Network models for road tunnel safety design: A case study from Norway

Directive 2004/54/EC from the European Parliament states that all EU member states should have well defined methodologies for risk analysis. This means that decisions regarding the design of road tunnels must be supported by risk information. TRANSIT, a Bayesian Network (BN) model for conducting quantitative road tunnel risk assessments has been developed to comply with the requirements. The developers of TRANSIT claim that their model represents best practice for risk assessments of road tunnels. This article explores the foundation for this claim. Furthermore, we assess TRANSIT as a tool for decision support regarding the design of new and novel road tunnel designs. The interactions between TRANSIT and the engineering environment and between risk analysts and responsible decision makers are studied by analyzing the engineering process of the 25 km Rogfast subsea road tunnel project in Norway.Our analysis shows that TRANSIT could be a useful tool in combination with other risk assessment activities. We also find that the model has severe limitations, especially when used for novel tunnel design projects such as Rogfast. First, the model applies a definition of risk that in most cases fails to provide an adequate risk picture, and hence fails to communicate risk to important stakeholders. Second, both data and models are rigid and presented to the users as a “black box”. This poses challenges with regard to the ownership of the analysis results and the responsibility for decisions made on the basis of the model, i.e., the relationship between the developer/owner and the analysts. Third, a standardized model will lead to standardized problems and solutions, which means that the results obtained from TRANSIT will be predictable when some experience with the model is gathered. In this way the model will preserve existing design and not promote innovation with regards to traffic safety designs. Fourth, the model emphasizes key performance indicators such as average annual daily traffic (AADT), tunnel length and curvature, while causes found in accident reports such as driving behavior, latent conditions and organizational and managerial factors may be neglected in the design process.     

A Bayesian Approach to Capability Testing Based on Cpk with Multiple Samples

Process capability indices provide numerical measures to compare the output of a process to client's expectations. However, most of the existing researches have used traditional distribution frequency method by using a single sample due to assess process capability. An alternative to this approach is to use the Bayesian method. In this paper, we utilize a Bayesian approach based on subsamples to check process capability via capability index C_pk. As a new suggestion, we used the informative normal prior distribution and the characteristics of sufficient statistic of the parameter to drive the posterior distribution. The capability test is done, and the posterior probability p, for which the process under investigation is capable, is derived both based on the most popular index C_pk. Finally, a numerical example is given to clarify the method. Copyright © 2013 John Wiley & Sons, Ltd.     

A distributed approach for track occupancy detection

This paper investigates the problem of track occupancy detection in distributed settings. Track occupancy detection determines which tracks are occupied in a railway system. For each track, the Neyman–Pearson structure is applied to reach the local decision. Globally, it is a multiple hypotheses testing problem. The Bayesian approach is employed to minimize the probability of the global decision error. Based on the prior probabilities of multiple hypotheses and the approximation of the receiving operation characteristic curve of the local detector, a person-by-person optimization method is implemented to obtain the fusion rule and the local strategies off line. The results are illustrated through an example constructed from in situ devices.     

A Dynamic-Bayesian Network framework for modeling and evaluating learning from observation

Learning from observation (LfO), also known as learning from demonstration, studies how computers can learn to perform complex tasks by observing and thereafter imitating the performance of a human actor. Although there has been a significant amount of research in this area, there is no agreement on a unified terminology or evaluation procedure. In this paper, we present a theoretical framework based on Dynamic-Bayesian Networks (DBNs) for the quantitative modeling and evaluation of LfO tasks. Additionally, we provide evidence showing that: (1) the information captured through the observation of agent behaviors occurs as the realization of a stochastic process (and often not just as a sample of a state-to-action map); (2) learning can be simplified by introducing dynamic Bayesian models with hidden states for which the learning and model evaluation tasks can be reduced to minimization and estimation of some stochastic similarity measures such as crossed entropy.     

Multiple intelligences in a MultiAgent System applied to telecontrol

This paper presents a control system, based on artificial intelligence technologies, that implements multiple intelligences. This system aims to support and improve automatic telecontrol of solar power plants, by either automatically triggering actuators or dynamically giving recommendations to human operators. For this purpose, the development of a MultiAgent System is combined with a variety of inference systems, such as Expert Systems, Neural Networks, and Bayesian Networks. This diversity of intelligent technologies is shown to result in an efficient way to mimic the reasoning process in human operators.     

Application of a Fuzzy Feasibility Bayesian Probabilistic Estimation of supply chain backorder aging,unfilled backorders,and customer wait time using stochastic simulation with Markov blankets

Because supply chains are complex systems prone to uncertainty, statistical analysis is a useful tool for capturing their dynamics. Using data on acquisition history and data from case study reports, we used regression analysis to predict backorder aging using National Item Identification Numbers (NIINs) as unique identifiers. More than 56,000 NIINs were identified and used in the analysis. Bayesian analysis was then used to further investigate the NIIN component variables. The results indicated that it is statistically feasible to predict whether an individual NIIN has the propensity to become a backordered item. This paper describes the structure of a Bayesian network from a real-world supply chain data set and then determines a posterior probability distribution for backorders using a stochastic simulation based on Markov blankets. Fuzzy clustering was used to produce a funnel diagram that demonstrates that the Acquisition Advice Code, Acquisition Method Suffix Code, Acquisition Method Code, and Controlled Inventory Item Code backorder performance metric of a trigger group dimension may change dramatically with variations in administrative lead time, production lead time, unit price, quantity ordered, and stock. Triggers must be updated regularly and smoothly to keep up with the changing state of the supply chain backorder trigger clusters of market sensitiveness, collaborative process integration, information drivers, and flexibility.     

Optimization of bridge maintenance strategies based on structural health monitoring information

Highway bridges are subjected to strength degradation processes. Under budget constraints, it is important to determine the best maintenance strategies. Optimized strategies, based on prediction models, are already considered for the maintenance and operation of highway bridges. Prediction models are updated both in space and time by using non-destructive testing methods. Nevertheless, there is an urgent need for the efficient inclusion of structural health monitoring (SHM) data in structural assessment and prediction models. Indeed, SHM allows keeping strength degradation processes under control and should be included in life-cycle cost models. The lifetime reliability of structures is characterized by survivor functions. The SHM data enable to update the probability density function of time to failure through a Bayesian process. The aim of this paper is threefold: (a) to include SHM data in a bridge life-cycle cost analysis, (b) to determine optimal maintenance strategies based on monitoring information, and (c) to show the benefits of SHM. Optimal strategies are determined considering the cases without and with including monitoring results; the benefit of monitoring is then highlighted. The proposed concepts are applied to the I-39 Northbound Bridge over the Wisconsin River in Wisconsin, USA. A monitoring program of that bridge was performed by the ATLSS Engineering Research Center at Lehigh University.     

Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes

Many highly reliable products usually have complex structure, with their reliability being evaluated by two or more performance characteristics. In certain physical situations, the degradation of these performance characteristics would be always positive and strictly increasing. In such a case, the gamma process is usually considered as a degradation process due to its independent and non-negative increments properties. In this paper, we suppose that a product has two dependent performance characteristics and that their degradation can be modeled by gamma processes. For such a bivariate degradation involving two performance characteristics, we propose to use a bivariate Birnbaum-Saunders distribution and its marginal distributions to approximate the reliability function. Inferential method for the corresponding model parameters is then developed. Finally, for an illustration of the proposed model and method, a numerical example about fatigue cracks is discussed and some computational results are presented.