Abstract

     Considering environmental factors such as temperature in structural health monitoring progress has been a consensus. However, the uncertainty of monitoring data usually makes it difficult. In this paper, the uncertainty factor has been introduced into the anomaly diagnosis process, a Markov chain-Monta Carlo (MCMC) anomaly diagnosis method based on temperature-induced response has been proposed. First, a novel diagnosis index has been developed based on the temperature data and static strain response data collected by the SHM system, the MCMC process is used to analyze the diagnosis index, and the posterior frequency distribution histogram of the actual diagnosis index is obtained. Finally, by analyzing the histogram of an unknown state and the initial state (baseline state) of the structure, the anomaly probability of the unknown condition is obtained, which can be used for anomaly probability diagnosis of components. The availability of the method is evaluated by a laboratory truss structure test under a series of working conditions and is verified by field monitoring data of a hanger roof structure. The results show that the method can make better use of the temperature effect of the structure for anomaly diagnosis, and the uncertainty is well considered.

Introduction

     Large building structures, including truss structures, are often used in airports, stations, factories, stadiums, and other important civil infrastructures [1], such structures often encounter sudden load changes (snow loads, high wind loads), changes in restraint conditions, member damage due to material degradation, and other structural anomalies during construction or service. Monitoring and diagnosing these structural anomalies using sensors placed on the surface of the structure is an efective means to ensure the safety of the structure throughout its life, and in recent years, with the development of sensor technology and intelligent algorithms, structural anomaly diagnosis (SAD) technique is becoming an increasingly important area.

     The vibration-based method is one of the most widely used SAD methods, which refects the abnormal state of the structure by monitoring the changes of vibration features [2–4]. However, the structural vibration features (e.g., natural frequencies) are not only related to the state of the structure itself, but also to environmental factors such as temperature, which will have an impact on the accuracy of SAD [5–7]. Although diferent solutions have been proposed for vibration-based SAD under environmental changes, these methods are still greatly limited by other defects in long-term practical monitoring, such as low sensitivity of vibration features to small local damage of the structure, the complicated method of sensor arrangement, and the large data transmission and storage caused by the high sampling frequency of the monitoring process, etc. [8].

Summary and conclusions

     In this paper, a temperature-based anomaly diagnosis of truss structure system using Markov chain-Monte Carlo method is proposed, which not only introduces the uncertainty method into a SAD method based on static response monitoring, but also actively uses the temperature efect of the structure for SAD. In this method, a novel diagnosis index based on T-stress-induced strain that takes uncertainties into account is proposed, which is obtained from the stress-induced strain and temperature measured by sensors arranged in the focus area of the structure. Then, the diagnosis index measurement data set is processed by MCMC to obtain the posterior relative frequency distribution histogram of the actual diagnosis index, and the histogram of the baseline state and an unknown state are analyzed to obtain the structural anomaly probability of the members under this unknown state. As two aspects of anomaly diagnosis, the structural damage diagnosis and state change diagnosis were verifed by a truss test and feld monitoring data of the BDIA hanger roof structure respectively, and the following conclusions were obtained:

This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable from the choice probabilities for the all-products assortment, together with choice probabilities for assortments of all-but-one products. Obtaining and estimating choice probabilities for such large assortments is not desirable in many settings. The main result of this work is that the parameters may be identified from assortments of sizes two and three, regardless of the total number of products. The result is obtained via a simple and efficient parameter recovery algorithm.

Introduction

In assortment planning, the seller’s goal is to select a subset of products (called an assortment) to offer to a customer so as to maximize the expected revenue. This task can be formulated as an optimization problem given the revenue generated from selling each product, along with a probabilistic model of the customer’s preferences for the products. Such a discrete choice model must capture the customer’s substitution behavior when, for instance, the offered assortment does not contain the customer’s most preferred product. Our focus in this paper is the Markov chain choice model (MCCM) proposed by Blanchet et al. [2]. This MCCM chooses to model the product selected by the customer as a Markov chain over products where the products in the offered assortment are absorbing states. The current state represents the desired product; if that product is not offered, the customer transitions to another product according to the Markov chain probabilities, and the process continues until the desired product is offered or the customer leaves. MCCM generalizes widely-used discrete choice models such as the multinomial logit model [6,8], as well as other generalized attraction models [5]; it also well-approximates other random utility models found in the literature such as mixed multinomial logit models [7]. At the same time, the MCCM permits computationally efficient unconstrained assortment optimization as well as efficient approximation algorithms in the constrained case [2,4]; this stands in contrast to some richer models such as mixed multinomial logit models [9] and the nested logit model [3] for which assortment optimization is generally intractable. This combination of expressiveness and computational tractability makes MCCM very attractive for use in assortment planning. A crucial step in this overall enterprise—e.g., before assortment optimization may take place—is the estimation of the choice model’s parameters from observational data. Parameter estimation for MCCM is only briefly considered in the original work of Blanchet et al. [2].

1. Introduction

2. System model and outage probability analysis

3. Establishment and Analysis of System Model

4. System performance analysis

5. System performance simulation and evaluation

6. Conclusions

Acknowledgement

References

Hybrid Automatic Retransmission reQuest (HARQ) protocol can effectively compensate the signal transmission error caused by complex time-varying channels and multi-path effects of wireless communication networks. This paper analyzes and compares the principle and system performance of three HARQ protocols from the perspective of system outage probability, and the expressions of system throughput and energy efficiency are derived by establishing a one-dimensional Discrete Time Markov Chain (DTMC) and calculating the steady-state distribution. MATLAB numerical simulations are applied to evaluate and compare the performance superiority among three HARQ Protocols.

Introduction

Various factors such as noise interference, multi-path effects, shadow effects and complex time-varying channels cause the instability of wireless communication, inducing the phenomenon of communication interrupt when the channel is in a deep fading state, which seriously affects the system performance and Quality of Service of the network. Therefore, effective and reliable error control technology is one of the important means to improve system performance. In the wireless communication network, two of the most popular error control technologies are Automatic Retransmission reQuest (ARQ) protocol and Forward Error Correction (FEC), the former aims at recovering error data frames through performing the feedback responses and data retransmissions between the sender and receiver, and the latter is mainly focused on comparing the redundancy code between the two ends to detect the accuracy of received data. Much works demonstrated their superiority in error control 1.

The condition of the insulation paper is one of the key determinants of the lifetime of a power transformer. The winding insulation paper may deteriorate aggressively and result in the unexpected failure of power transformers, especially under the presence of high moisture, oxygen, and metal contaminants. Such types of scenarios can be prevented if the deterioration is detected on time. Various types of condition monitoring techniques have been developed to detect transformer condition such as dissolved gas analysis (DGA) and frequency response analysis (FRA). They are non-intrusive and provide early warning of accelerated deterioration both chemically and mechanically. However, the accuracy of those techniques is imperfect, which means periodic inspection is still indispensable. In this paper, we discuss the value of continuous condition monitoring for power transformers and present a way to estimate this value. Towards this, a continuous-time Markov decision model is presented to optimize periodic inspections, so that the cost is minimized and the availability is maximized. We then analyze the performance based on the information from both discrete inspection and continuous condition monitoring using DGA and FRA. The result shows the dissolved gas analysis can improve the availability and operation cost, while frequency response analysis can only improve the availability of power transformers.

Introduction

Power transformers are critical assets in a power transmission network. A failure of a power transformer also may cause cascading failure and catastrophic blackout in the power grid. The necessity of increasing reliability and availability of power transformers can be analyzed directly from a financial point of view. Between 1997 and 2001, the total losses caused by power transformer failure in the US were over 286 million [1]. Moreover, the aging population of power transformers has increased since 1975 [2]. These imply that it is expected to have an increase in power transformer failure, and the resulting load curtailment if the maintenance strategy remains the same. In literature, various types of maintenance models have been developed to address the problem of power transformer maintenance. Aldhubaib and Salama have developed a reliability centered maintenance and replacement approach to optimize maintenance and replacement to increase the lifetime of power transformers and reduce annual cost [3]. Dhople et al. proposed a set-theoretic method for capturing the uncertainty in Markov reliability and reward model to maximize the availability of power transformers [4]. Abu-Elanien et al. developed a decision support system to determine the life expectancy of transformers from techno-economic perspective [5]. Lima et al. designed a two-level framework of fault diagnosis and decision making for power transformers with considering the loss for life caused by overload condition [6]. Abiri-Jahromi et al. have developed a two-stages maintenance management model that contains both mid-term and shortterm maintenance to maximize the serviceability of power transformers [7]. Koksal and Ozdemir have improved the power transformer maintenance using a Markovian model [8]. As to the condition state of a power transformer is considered to be discrete, most of the developed models are based on the Markovian deterioration model. However, the deterioration of power transformers is oversimplified and modeled by Markov chain with a single deteriorating path. Such an approach is inaccurate because it overlooks the complexity of the deterioration of power transformers, such as the acceleration deterioration of insulation paper caused by high moisture. Because of this, the effective of condition-based maintenance that solely relies on the periodic inspection is over-estimated. Therefore, to re-estimate the value of continuous monitoring, it is essential to improve the deterioration model of power transformers. In practice, the accuracy of the condition monitoring is imperfect and may be interfered by operation signals and external signals. Therefore, even for the power transformers that have already installed the condition monitoring devices, periodic inspection can still provide additional value to triangulate the estimated condition information by condition monitoring. The objective of the paper is twofold: optimize the condition-based maintenance for power transformers; explore the value of online monitoring from the perspective of the lifecycle of power transformers.

Markov networks and Bayesian networks, also known as undirected and directed acyclic graphical models respectively, are widely used in many fields, such as machine learning and bioinformatics [8,12,22,24,25]. We know that a statistical model is a family of probability distributions, it is a (part of) real algebraic variety from the viewpoint of algebraic geometry [26]. In particular, consider discrete data, a statistical model is the set of all solutions of some polynomials in the probability simplex [15,27]. There are two ways to describe Markov networks and Bayesian networks, either by conditional independence statements or by a factorization of probability distributions. This corresponds to the computational algebraic geometry principle that some varieties can be described using either defining equations or parametric equations [see §3.3 of 9]. We know that these two representations are inequivalent for Markov networks without positivity assumptions on probability distributions [see Proposition 3.8 and Example 3.10 in 22], while these two ways are equivalent for Bayesian networks [see Theorem 3.27 in 22]. Classification is one of the main problems in machine learning. To improve classification, there has been a growing body of work ∗ Corresponding author. E-mail addresses: libc580@nenu.edu.cn (B. Li), ylyang@mail.xidian.edu.cn (Y. Yang). on Markov networks in the computer vision community [21], in social and affiliation networks [39] and in classifier learning [30]. Ghofrani et al. proposed a new probabilistic classifier based on decomposable models and applied it to two real-world internet traffic data sets [16]. Bayesian networks are another powerful tool for classification due to their simplicity and accuracy [4,6,11,13]. Naive Bayes classifiers, a special case of Bayesian network classifiers, are a popular classification tool for processing discrete data [4,34,35]. For more about discrete Bayesian network classifiers, please see a comprehensive survey published recently [3]. Several research groups combined kernel method and probabilistic models, for instance, Ben-David et al. [2], Altun et al. [1], Taskar et al. [31], Chechik et al. [5]. A major advantage of this technique is that one can construct a wide variety of more flexible classifiers. The generalization performance of a learning method is extremely important in practice, because it provides a measure of the quality of the ultimately chosen model. One can use the Vapnik– Chervonenkis (VC) dimension to construct an estimate of generalization error [32], where the VC dimension is an approach of measuring the complexity of a class of functions by assessing how wiggly its members can be [19]. Another measure of complexity of a class of functions, called Euclidean dimension, is the minimum dimension of the Euclidean space equipped with the standard dot product, into which these functions can be embedded. Given a Markov network (Bayesian network) N , one can get a concept class CN induced by it. Since VC dimension and Euclidean dimension are two important indexes to assess the classification ability of a Markov network (Bayesian network). Three natural questions arise: (1) Whether the two dimensional values can be obtained from the dimension of a model as a (smooth) sub-manifold of Euclidean space? (2) Are the two positive integer numbers always equal? (3) How to calculate these dimensional values? In this paper, we study the classification capability induced by a Markov network (Bayesian network) without considering the training data, the algorithm and the construction of the network graph. We aim to solve the three questions above.

In the aftermath of the oil crisis of the early 1970s, the relationship between oil prices and economic growth became a focal point of the scientific discourse and public debate. In 1983, James Hamilton published an influential article showing that an oil price increase had preceded all but one recession in the United States since the end of World II [1]. Since then, a large number of empirical studies have looked into the connection between oil prices and real economic growth and frequently found a significant negative correlation [2,3]. The importance of this link between oil price and economic growth was less clear after the second oil shock [4–7]. Recent studies, with more refined statistical tools and price specifications, have restored the link between the oil price and economic growth [8–12]. There is now a general consensus that this connection did not cease but has become more complex in terms of direction (anticyclical and procyclical), typology of shocks (demand or supply) and lag patterns [4,9,11,13,14]. This line of research tried to explain this tight relationship, given that the cost of energy is only a small part of GDP [13] but satisfactory explanations have remained elusive [2,4,13,15]. Interestingly, this research exploring the link between the oil price and economic indicators seems to have entirely ignored the transport sector, which is heavily reliant on refined crude oil products, and its role in shaping the global division of labor. In the post-war period, world trade grew at a faster pace than world GDP [16]. According to recent studies on globalization, the remarkably high rate was propelled by a dramatic decline in international transport costs [16–19].

Food insecurity is defined as the situation where people are not able to access enough food at all times for an active, healthy life (USDAERS, 2006). The occurrence of food insecurity in the United States (U.S.) is significant, affecting approximately 48.1 million Americans, 15.3 million children and 32.8 million adults. Furthermore, a 2014 study on household food insecurity reported that 14% of U.S. households were unable to access enough food at all times (Coleman-Jensen, Rabbitt, Gregory, & Singh, 2015). The U.S. Government has established several public assistance programs to address this problem. These programs provide financial assistance, supplemental food, and nutrition support to individuals and states to increase access to healthy food for low-income households. Some of the most well-known programs are the Supplemental Nutrition Assistance Program (SNAP), the Women, Infants, and Children (WIC) program, and The Emergency Food Assistance Program (TEFAP) (see fns.usda.gov/ programs-and-services for a comprehensive list). In addition to government funded programs, non-profit organizations, such as Feeding America, also help to address the food insecurity problem. Feeding America (FA), the nation’s leading domestic hungerrelief organization, seeks to eliminate hunger by providing food ∗ Corresponding author. E-mail address: lbdavis@ncat.edu (L.B. Davis). to those in need through a nationwide network of about 200 member food banks and distribution centers across the country (FeedingAmerica, 2014). FA, as the parent food bank, provides administrative support, training of personnel, standards for food safety and food distribution to its member food banks. The local food banks, although partnering with FA, remain largely independent with their own management systems and budget. They solicit funds, food and supplies from individuals, groups, farmers, local manufacturers and retailers. These donations represent sources of supply that enable them to meet the demand of the people at risk of hunger. Hence, supplies to the food bank are based on the goodwill of donors who are not obligated to give at any particular time or in any particular quantity. Consequently, donations may be infrequent, almost expired which makes them inappropriate for consumption after a few days, or may not be what is actually needed. Nevertheless, food banks need to be able to adequately manage their inventory to ensure equitable distribution of supplies since meeting the demands by aid recipients is not possible with limited supply. This paper presents a decision model that assists food banks in equitable allocation of uncertain, donated supplies. We define equity as a function of the pounds distributed per person in poverty (PPIP). FA proposed this indicator as a way to measure the performance of its members. The benchmark is to distribute at least 75 pounds of food products for each person in poverty over a 12-month period. We use PPIP to measure equitable distribution practices within the food bank’s service area and also identify deviations from the performance goal set by FA. The decision making problem is formulated as a discrete-time, discrete state (DTDS) Markov decision process (MDP).