Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input-output probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms

A methodology for determining amino-acid substitution matrices from set covers

We introduce a new methodology for the determination of amino-acid substitution matrices for use in the alignment of proteins. The new methodology is based on a pre-existing set cover on the set of residues and on the undirected graph that describes residue exchangeability given the set cover. For fixed functional forms indicating how to obtain edge weights from the set cover and, after that, substitution-matrix elements from weighted distances on the graph, the resulting substitution matrix can be checked for performance against some known set of reference alignments and for given gap costs. Finding the appropriate functional forms and gap costs can then be formulated as an optimization problem that seeks to maximize the performance of the substitution matrix on the reference alignment set. We give computational results on the BAliBASE suite using a genetic algorithm for optimization. Our results indicate that it is possible to obtain substitution matrices whose performance is either comparable to or surpasses that of several others, depending on the particular scenario under consideration

Modelling electricity prices: from the state of the art to a draft of a new proposal

In the last decades a liberalization of the electric market has started; prices are now determined on the basis of contracts on regular markets and their behaviour is mainly driven by usual supply and demand forces. A large body of literature has been developed in order to analyze and forecast their evolution: it includes works with different aims and methodologies depending on the temporal horizon being studied. In this survey we depict the actual state of the art focusing only on the recent papers oriented to the determination of trends in electricity spot prices and to the forecast of these prices in the short run. Structural methods of analysis, which result appropriate for the determination of forward and future values are left behind. Studies have been divided into three broad classes: Autoregressive models, Regime switching models, Volatility models. Six fundamental points arise: the peculiarities of electricity market, the complex statistical properties of prices, the lack of economic foundations of statistical models used for price analysis, the primacy of uniequational approaches, the crucial role played by demand and supply in prices determination, the lack of clearcut evidence in favour of a specific framework of analysis. To take into account the previous stylized issues, we propose the adoption of a methodological framework not yet used to model and forecast electricity prices: a time varying parameters Dynamic Factor Model (DFM). Such an eclectic approach, introduced in the late ‘70s for macroeconomic analysis, enables the identification of the unobservable dynamics of demand and supply driving electricity prices, the coexistence of short term and long term determinants, the creation of forecasts on future trends. Moreover, we have the possibility of simulating the impact that mismatches between demand and supply have over the price variable. This way it is possible to evaluate whether congestions in the network (eventually leading black out phenomena) trigger price reactions that can be considered as warning mechanisms.

Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values depending on the mode of traffic operation – free flowing, congested or faulty – making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain. This study proposes an expectation-maximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inference algorithms and an online particle filter. The authors also develop an EM parameter estimation that, in combination with a time-window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator

Planning the petrochemical industry in Kuwait using economic and safety objectives

Kuwait, one of the major oil producing countries in the Middle East, is in the process of globalizing its operation in petroleum and petrochemical production. Kuwaiti officials have expressedin terest in acceleratingd evelopmento f the country's relatively small petrochemical industry. The development is to produce new valuable chemicals from the available basic feedstock chemicals. Two of the important planning objectives for a petrochemical industry are the economic gain and the industrial safety involved in the development. For the economic evaluation of the industry, and for the proposed final product chemicals in the development, a long-range plan is needed to identify trends in chemical prices. The chemical prices are related to the oil price, which is considered an important motivator for the whole petrochemical industry. Price trend modelling is performed to be able to forecast these prices for the planning horizon. Safety, as the second objective, is considered in this study as the risk of chemical plant accidents. Risk, when used as an objective fimction, has to have a simple quantitative form to be easily evaluated for a large number of possible plants in the petrochemical network. The simple quantitative form adopted is a risk index that enables the number of people affected by accidents resulting in chemical releases to be estimated. The two objectives, when combined with constraints describing the desired or the possible structure of the industry, will form an optimization model. For this study, the petrochemical planning model consists of a Mixed Integer Linear Programming (MILP) model to select the best routes from the basic feedstocks available in Kuwait to the desired final products with multiple objective functions. The economic and risk objectives usually have conflicting needs. The presence of several conflicting objectives is typical when planning. In many cases, where optimization techniques are utilized, the multiple objectives are simply aggregated into one single objective function. Optimization is then conducted to get one optimal result. However, many results are obtained for different aggregations of the objectives and eventually a set of solutions is obtained. Other tools, such as strategic tools, are used to select the best solution from the set. This study, which is concerned with economic and risk objectives, leads to the identification of important factors that affect the petrochemical industry. Moreover, the procedure, of modelling and model solution, can be used to simplify the decisionmaking for complex or large systems such as the petrochemical industry. It presents the use of simple multiple objective optimization tools within a petrochemical planning tool formulated as a mixed integer linear programming model. Such a tool is particularly useful when the decision-making task must be discussed and approved by officials who often have little experience with optimization theories

The Comparison Study of Short-Term Prediction Methods to Enhance the Model Predictive Controller Applied to Microgrid Energy Management

Electricity load forecasting, optimal power system operation and energy management play key roles that can bring significant operational advantages to microgrids. This paper studies how methods based on time series and neural networks can be used to predict energy demand and production, allowing them to be combined with model predictive control. Comparisons of different prediction methods and different optimum energy distribution scenarios are provided, permitting us to determine when short-term energy prediction models should be used. The proposed prediction models in addition to the model predictive control strategy appear as a promising solution to energy management in microgrids. The controller has the task of performing the management of electricity purchase and sale to the power grid, maximizing the use of renewable energy sources and managing the use of the energy storage system. Simulations were performed with different weather conditions of solar irradiation. The obtained results are encouraging for future practical implementation

FAULT DIAGNOSIS USING SYSTEM IDENTIFICATION FOR CHEMICAL PROCESS PLANT

Fault detection and diagnosis have gained an importance in the automation process industries over the past decade. This is due to several reasons; one of them being that sufficient amount of data is available from the process plants. The goal of this project is to develop such fault diagnosis systems, which use the input-output data of the realm process plant to detect, isolate, and reconstruct faults. The first part of this project focused on developing a different prediction models to the real system. Moreover, a linearized model using Taylor Series Expansion approach and ARX (Autoregressive with external input) model of the real system have been designed. In addition, the most accurate identification model which describes the dynamic behavior of the monitored system has been selected. Furthermore, a technique Statistical Process Control (SPC) used in fault diagnosis. This method depends on central limit theorem and used to detect faults by the analysis of the mismatch between the ARX model estimation and the process plant output. Finally the proposed methodology for fault diagnosis has been applied in numerical simulations to a non-isothermal CSTR (continuous stirred tank reactor) and the results and conclusion have been reported and showed excellent estimation of ARX model and good fault diagnosis performance of SPC