Data Clustering based on Gaussian Mixture Model and Expectation- Maximization Algorithm for Data-driven Structural Health Monitoring System

Data groups generated by a system often inherit dynamics characteristics unique in data distribution parameters. A degradation in structural health can affect the dynamic behavior hence the probability distribution parameters.  Based on the probabilistic and Expectation-Maximization (EM) algorithm, Gaussian Mixture Model (GMM), one can cluster data groups that may overlap with different data groups based on different orientations and shapes. This article explores GMM probabilistic model applied on vibration data set generated by aircraft wing box structure for Structural Health Monitoring (SHM) application. In the data processing stage, the high dimensional data is transformed into lower dimensions using Kernel Principal Component Analysis (KPCA). KPCA transforms the continuous signal into discrete data, allowing the ellipsoids' fitting (clusters) on the data spread. Based on the baseline data set (undamaged structural condition) and several components (loading class and damage class), the fitting is performed using GMM driven by EM. This paper shows that GMM-EM based data clustering model is an effective clustering probability model in fitting the data density in the presence of operational variations. It highlights clustering of reduced vibration data using KPCA in the interest of SHM based on the baseline’s initial parameters

CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation that does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. Utilizing the criterion from Regression Quantiles, and postulating a variety of dynamic updating processes we propose methods based on a Genetic Algorithm to estimate the unknown parameters of CAViaR models. We propose a Dynamic Quantile Test of model adequacy that tests the hypothesis that in each period the probability of exceeding the VaR must be independent of all the past information. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

Dynamic modeling and parameter estimation for an ethlyene-propylene-diene polymerization process

New Page 1 A general dynamic model for continuous EPDM polymerization in which crosslinking and gel formation are attributable to reactions between pendant double bonds has been developed. A pseudo-kinetic rate constant method is introduced to construct a moment model for a pseudo-homopolymer that approximates the behavior of the actual terpolymer under long chain and quasi-steady state assumptions. The pseudo-homopolymer model is then used as the basis for application of the numerical fractionation method. The proposed dynamic model is capable of predicting polydispersities and molecular weight distributions near the gel point with as few as eleven generations, and in the post-gel region with as few as five. The overall molecular weight distribution (MWD) of the sol was constructed by assuming a Schulz two parameter distribution for each generation. A parameter selection procedure is proposed to determine the kinetic parameters that can be estimated from the limited plant data. The procedure is based on the steady-state parameter output sensitivity matrix. The overall effect of each parameter on the measured outputs is determined using Principal Component Analysis (PCA). The angles between the sensitivity vectors are used as a measure of collinearity between parameters. A simple algorithm which provides a tradeoff between overall parameter effect on key outputs and collinearity yields a ranking of parameters by ease of estimation, independent of the available data. Its nonlinear and dynamic extensions are also developed and tested to address the nonlinearity and dynamics of the parameters\u27 effects on the outputs. The key kinetic parameters determined by the parameter selection procedure were estimated from steady-state data extracted from dynamic plant data, using a newly developed steady state detection tool. A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters of the EPDM kinetic model. The estimator design is based on decomposing the dynamic model into two subsystems, by exploiting the triangular model structure and the different sampling frequencies of the on-line and laboratory measurements directly related to the state variables of each subsystem. Simulation tests show that the hierarchical EKF generates satisfactory predictions even in the presence of measurement noise and plant/model mismatch

A Data-Driven Predictive Model of Reliability Estimation Using State-Space Stochastic Degradation Model

The concept of the Industrial Internet of Things (IIoT) provides the foundation to apply data-driven methodologies. The data-driven predictive models of reliability estimation can become a major tool in increasing the life of assets, lowering capital cost, and reducing operating and maintenance costs. Classical models of reliability assessment mainly rely on lifetime data. Failure data may not be easily obtainable for highly reliable assets. Furthermore, the collected historical lifetime data may not be able to accurately describe the behavior of the asset in a unique application or environment. Therefore, it is not an optimal approach anymore to conduct a reliability estimation based on classical models. Fortunately, most of the industrial assets have performance characteristics whose degradation or decay over the operating time can be related to their reliability estimates. The application of the degradation methods has been recently increasing due to their ability to keep track of the dynamic conditions of the system over time. The main purpose of this study is to develop a data-driven predictive model of reliability assessment based on real-time data using a state-space stochastic degradation model to predict the critical time for initiating maintenance actions in order to enhance the value and prolonging the life of assets. The new degradation model developed in this thesis is introducing a new mapping function for the General Path Model based on series of Gamma Processes degradation models in the state-space environment by considering Poisson distributed weights for each of the Gamma processes. The application of the developed algorithm is illustrated for the distributed electrical systems as a generic use case. A data-driven algorithm is developed in order to estimate the parameters of the new degradation model. Once the estimates of the parameters are available, distribution of the failure time, time-dependent distribution of the degradation, and reliability based on the current estimate of the degradation can be obtained

Inferring Dynamic User Interests in Streams of Short Texts for User Clustering

User clustering has been studied from different angles. In order to identify shared interests, behavior-based methods consider similar browsing or search patterns of users, whereas content-based methods use information from the contents of the documents visited by the users. So far, content-based user clustering has mostly focused on static sets of relatively long documents. Given the dynamic nature of social media, there is a need to dynamically cluster users in the context of streams of short texts. User clustering in this setting is more challenging than in the case of long documents, as it is difficult to capture the users’ dynamic topic distributions in sparse data settings. To address this problem, we propose a dynamic user clustering topic model (UCT). UCT adaptively tracks changes of each user’s time-varying topic distributions based both on the short texts the user posts during a given time period and on previously estimated distributions. To infer changes, we propose a Gibbs sampling algorithm where a set of word pairs from each user is constructed for sampling. UCT can be used in two ways: (1) as a short-term dependency model that infers a user’s current topic distribution based on the user’s topic distributions during the previous time period only, and (2) as a long-term dependency model that infers a user’s current topic distributions based on the user’s topic distributions during multiple time periods in the past. The clustering results are explainable and human-understandable, in contrast to many other clustering algorithms. For evaluation purposes, we work with a dataset consisting of users and tweets from each user. Experimental results demonstrate the effectiveness of our proposed short-term and long-term dependency user clustering models compared to state-of-the-art baselines

Calibration of the numerical model of a freight railway vehicle based on experimental modal parameters

The simulation of the dynamic behavior of the train-track system is strongly dependent on the accuracy of the numerical models of the train and track subsystems. The use of calibrated numerical models of the railway vehicles, based on experimental data, enhances their ability to correctly reproduce the dynamic responses of the train under operational conditions. In this scope, studies involving the experimental calibration of freight wagon models are still scarce. This article aims to fill this gap by presenting an efficient methodology for the calibration of a numerical model of a freight railway wagon based on experimental modal parameters. A dynamic test was performed during the unloading operation of the train, adopting a dedicated approach which does not interfere with its tight operational schedule. From data collected during the dynamic test, five natural frequencies and mode shapes associated with rigid-body and flexural movements of the wagon platform were identified through the Enhanced Frequency-Domain Decomposition (EFDD) method. A detailed 3D finite-element (FE) model of the loaded freight wagon was developed, requiring precise knowledge of the vehicle design details which, in most situations, are difficult to obtain due to confidentiality reasons of the manufacturers. The model calibration was performed through an iterative method based on a genetic algorithm and allowed to obtain optimal values for seven numerical parameters related to the suspension’s stiffnesses and mass distribution. The stability of the parameters considering different initial populations demonstrated the robustness of the optimization algorithm. The average error of the natural frequencies decreased from 8.5% before calibration to 3.2% after calibration, and the average MAC values improved from 0.911 to 0.950, revealing a significant improvement of the initial numerical model.The authors would like to acknowledge the support of the Base Funding UIDB/04708/2020 and Programmatic Funding UIDP/04708/2020 of the CONSTRUCT (Instituto de I&D em Estruturas e Construções) funded by national funds through the FCT/MCTES (PIDDAC). The authors also express their gratitude to Dr. Nuno Pinto and Mr. Valdemar Luís, both technicians of LESE laboratory, for their indispensable assistance during the preparation and execution of the experimental testinfo:eu-repo/semantics/publishedVersio

Real-Time Predictive Modeling and Robust Avoidance of Pedestrians with Uncertain, Changing Intentions

To plan safe trajectories in urban environments, autonomous vehicles must be able to quickly assess the future intentions of dynamic agents. Pedestrians are particularly challenging to model, as their motion patterns are often uncertain and/or unknown a priori. This paper presents a novel changepoint detection and clustering algorithm that, when coupled with offline unsupervised learning of a Gaussian process mixture model (DPGP), enables quick detection of changes in intent and online learning of motion patterns not seen in prior training data. The resulting long-term movement predictions demonstrate improved accuracy relative to offline learning alone, in terms of both intent and trajectory prediction. By embedding these predictions within a chance-constrained motion planner, trajectories which are probabilistically safe to pedestrian motions can be identified in real-time. Hardware experiments demonstrate that this approach can accurately predict pedestrian motion patterns from onboard sensor/perception data and facilitate robust navigation within a dynamic environment.Comment: Submitted to 2014 International Workshop on the Algorithmic Foundations of Robotic