Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

Paving New Ground

This paper explores the inter-connectedness and co-evolution of transportation networks and land use through the application of a Markov Chain model to the Twin Cities from 1958 through 1990. This model investigates how individual cells, with both land use and transportation network attributes, change over time. Cells with more transportation network available are more likely to develop, and cells that are developed are more likely to attract additional highway investment.Transportation Network Growth, Transportation-Land Use Interaction, Markov Chain

A Comparison of Three Different Methods for the Identification of Hysterically Degrading Structures Using BWBN Model

Structural control and health monitoring scheme play key roles not only in enhancing the safety and reliability of infrastructure systems when they are subjected to natural disasters, such as earthquakes, high winds, and sea waves, but it also optimally minimize the life cycle cost and maximize the whole performance through the full life cycle design. In this scheme, system identification is regarded as a major technique to identify system states and related parameter variables, thus preventing degradation of structural or mechanical systems when unexpected disturbances occur. In this paper, three different strategies are proposed to identify general hysteretic behavior of a typical shear structure subjected to external excitations. Different case studies are presented to analyze the dynamic responses of a time varying shear structural system with the early version of Bouc-Wen-Baber-Noori (BWBN) hysteresis model. By incorporating a “Gray Box” strategy utilizing an Intelligent Parameter Varying (IPV) and Artificial Neural Network (ANN) approach, a Genetic algorithm (GA), and a Transitional Markov Chain Monte Carlo (TMCMC) based Bayesian Updating framework system identification schemes are developed to identify the hysteretic behavior of the structural system. Hysteresis characteristics, computational accuracy, and algorithm efficiency are further discussed by evaluating the system identification results. Results show that IPV performs superior computational efficiency and system identification accuracy over GA and TMCMC approaches

Contributions on evolutionary computation for statistical inference

Evolutionary Computation (EC) techniques have been introduced in the 1960s for dealing with complex situations. One possible example is an optimization problems not having an analytical solution or being computationally intractable; in many cases such methods, named Evolutionary Algorithms (EAs), have been successfully implemented. In statistics there are many situations where complex problems arise, in particular concerning optimization. A general example is when the statistician needs to select, inside a prohibitively large discrete set, just one element, which could be a model, a partition, an experiment, or such: this would be the case of model selection, cluster analysis or design of experiment. In other situations there could be an intractable function of data, such as a likelihood, which needs to be maximized, as it happens in model parameter estimation. These kind of problems are naturally well suited for EAs, and in the last 20 years a large number of papers has been concerned with applications of EAs in tackling statistical issues. The present dissertation is set in this part of literature, as it reports several implementations of EAs in statistics, although being mainly focused on statistical inference problems. Original results are proposed, as well as overviews and surveys on several topics. EAs are employed and analyzed considering various statistical points of view, showing and confirming their efficiency and flexibility. The first proposal is devoted to parametric estimation problems. When EAs are employed in such analysis a novel form of variability related to their stochastic elements is introduced. We shall analyze both variability due to sampling, associated with selected estimator, and variability due to the EA. This analysis is set in a framework of statistical and computational tradeoff question, crucial in nowadays problems, by introducing cost functions related to both data acquisition and EA iterations. The proposed method will be illustrated by means of model building problem examples. Subsequent chapter is concerned with EAs employed in Markov Chain Monte Carlo (MCMC) sampling. When sampling from multimodal or highly correlated distribution is concerned, in fact, a possible strategy suggests to run several chains in parallel, in order to improve their mixing. If these chains are allowed to interact with each other then many analogies with EC techniques can be observed, and this has led to research in many fields. The chapter aims at reviewing various methods found in literature which conjugates EC techniques and MCMC sampling, in order to identify specific and common procedures, and unifying them in a framework of EC. In the last proposal we present a complex time series model and an identification procedure based on Genetic Algorithms (GAs). The model is capable of dealing with seasonality, by Periodic AutoRegressive (PAR) modelling, and structural changes in time, leading to a nonstationary structure. As far as a very large number of parameters and possibilites of change points are concerned, GAs are appropriate for identifying such model. Effectiveness of procedure is shown on both simulated data and real examples, these latter referred to river flow data in hydrology. The thesis concludes with some final remarks, concerning also future work

Contributions on evolutionary computation for statistical inference

Evolutionary Computation (EC) techniques have been introduced in the 1960s for dealing with complex situations. One possible example is an optimization problems not having an analytical solution or being computationally intractable; in many cases such methods, named Evolutionary Algorithms (EAs), have been successfully implemented. In statistics there are many situations where complex problems arise, in particular concerning optimization. A general example is when the statistician needs to select, inside a prohibitively large discrete set, just one element, which could be a model, a partition, an experiment, or such: this would be the case of model selection, cluster analysis or design of experiment. In other situations there could be an intractable function of data, such as a likelihood, which needs to be maximized, as it happens in model parameter estimation. These kind of problems are naturally well suited for EAs, and in the last 20 years a large number of papers has been concerned with applications of EAs in tackling statistical issues. The present dissertation is set in this part of literature, as it reports several implementations of EAs in statistics, although being mainly focused on statistical inference problems. Original results are proposed, as well as overviews and surveys on several topics. EAs are employed and analyzed considering various statistical points of view, showing and confirming their efficiency and flexibility. The first proposal is devoted to parametric estimation problems. When EAs are employed in such analysis a novel form of variability related to their stochastic elements is introduced. We shall analyze both variability due to sampling, associated with selected estimator, and variability due to the EA. This analysis is set in a framework of statistical and computational tradeoff question, crucial in nowadays problems, by introducing cost functions related to both data acquisition and EA iterations. The proposed method will be illustrated by means of model building problem examples. Subsequent chapter is concerned with EAs employed in Markov Chain Monte Carlo (MCMC) sampling. When sampling from multimodal or highly correlated distribution is concerned, in fact, a possible strategy suggests to run several chains in parallel, in order to improve their mixing. If these chains are allowed to interact with each other then many analogies with EC techniques can be observed, and this has led to research in many fields. The chapter aims at reviewing various methods found in literature which conjugates EC techniques and MCMC sampling, in order to identify specific and common procedures, and unifying them in a framework of EC. In the last proposal we present a complex time series model and an identification procedure based on Genetic Algorithms (GAs). The model is capable of dealing with seasonality, by Periodic AutoRegressive (PAR) modelling, and structural changes in time, leading to a nonstationary structure. As far as a very large number of parameters and possibilites of change points are concerned, GAs are appropriate for identifying such model. Effectiveness of procedure is shown on both simulated data and real examples, these latter referred to river flow data in hydrology. The thesis concludes with some final remarks, concerning also future work

System identification using evolutionary Markov chain Monte Carlo

System identification involves determination of the functional structure of a target system that underlies the observed data. In this paper, we present a probabilistic evolutionary method that optimizes system architectures for the identification of unknown target systems. The method is distinguished from existing evolutionary algorithms (EAs) in that the individuals are generated from a probability distribution as in Markov chain Monte Carlo (MCMC). It is also distinguished from conventional MCMC methods in that the search is population-based as in standard evolutionary algorithms. The effectiveness of this hybrid of evolutionary computation and MCMC is tested on a practical problem, i.e., evolving neural net architectures for the identification of nonlinear dynamic systems. Experimental evidence supports that evolutionary MCMC (or eMCMC) exploits the e ciency of simple evolutionary algorithms while maintaining the robustness of MCMC methods and outperforms either approach used alone