Characterization of the Growth of Corrosion Defects on Energy Pipelines Using Bayesian Dynamic Linear Model

2014 ◽  
Author(s):  
S. Zhang ◽  
W. Zhou ◽  
S. Kariyawasam ◽  
M. Al-Amin
Keyword(s):  
Linear Model ◽  
Growth Model ◽  
Growth Models ◽  
Model Parameters ◽  
Dynamic Linear Model ◽  
Average Growth ◽  
Imperfect Data ◽  
Natural Gas Pipeline ◽  
Proposed Model ◽  
Corrosion Defects

This paper describes the use of the second-order polynomial dynamic linear model (DLM) to characterize the growth of the depth of corrosion defects on energy pipelines using imperfect data obtained from multiple high-resolution in-line inspections (ILI). The growth model is formulated by incorporating the general form of the measurement error (including the biases and random scattering error) of the ILI tools as well as the correlations between the random scattering errors of different tools. The temporal variability of the corrosion growth is captured by allowing the average growth rate between two successive inspections to vary with time. The Markov Chain Monte Carlo simulation is employed to carry out the Bayesian updating of the growth model and evaluate the posterior distributions of the model parameters. An example involving real ILI data collected from an in-service natural gas pipeline is employed to illustrate and validate the growth model. The analysis results show that the defect depths predicted by the proposed model agree well with the actual depths and are more accurate than those predicted by the Gamma process-based growth models reported in the literature.

scholarly journals A Size-Perimeter Discrete Growth Model for Percolation Clusters

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Bendegúz Dezső Bak ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Growth Model ◽  
Branching Process ◽  
Growth Models ◽  
Square Lattice ◽  
Cluster Growth ◽  
Invasion Percolation ◽  
Percolation Clusters ◽  
Proposed Model ◽  
Wide Range ◽  
The Mean

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

A software reliability growth model with Gompertz-logarithmic failure time distribution

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tahere Yaghoobi
Keyword(s):  
Growth Model ◽  
Software Reliability ◽  
Failure Time ◽  
Model Parameters ◽  
Reliability Growth ◽  
Software Reliability Growth Model ◽  
Content Type ◽  
Software Failure ◽  
Proposed Model ◽  
Software Reliability Growth

PurposeThe Gompertz curve has been used in industry to estimate the number of remaining software faults. This paper aims to introduce a family of distributions for fitting software failure times which subsumes the Gompertz distribution.Design/methodology/approachThe mean value function of the corresponding non-homogenous Poisson process software reliability growth model is presented. Model parameters are estimated by the method of maximum likelihood. A comparison of the new model with eight models that use well-known failure time distributions of exponential, gamma, Rayleigh, Weibull, Gompertz, half normal, log-logistic and lognormal is performed according to the several statistical and informational criteria. Moreover, a Shannon entropy approach is used for ranking and model selection.FindingsNumerical experiments are implemented on five real software failure datasets varying from small to large datasets. The results exhibit that the proposed model is promising and particularly outperforms the Gompertz model in all considered datasets.Originality/valueThe proposed model provides optimized reliability estimation.

Anomaly detection of structural health monitoring data using the maximum likelihood estimation-based Bayesian dynamic linear model

2020 ◽  
pp. 147592172097702
Author(s):  
Yi-Ming Zhang ◽  
Hao Wang ◽  
Hua-Ping Wan ◽  
Jian-Xiao Mao ◽  
Yi-Chao Xu
Keyword(s):  
Structural Health Monitoring ◽  
Linear Model ◽  
Health Monitoring ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Monitoring Data ◽  
Model Parameters ◽  
Dynamic Linear Model ◽  
Structural Health ◽  
Log Likelihood

Enormous data are continuously collected by the structural health monitoring system of civil infrastructures. The structural health monitoring data inevitably involve anomalies caused by sensors, transmission errors, or abnormal structural behaviors. It is important to identify the anomalies and find their origin (e.g. sensor fault or structural damage) to make correct interventions. Moreover, online anomaly identification of the structural health monitoring data is critical for timely structural condition assessment and decision-making. This study proposes an online approach for detecting anomalies of the structural health monitoring data based on the Bayesian dynamic linear model. In particular, Bayesian dynamic linear model, consisting of various components, is implemented to characterize the feature of real-time measurements. Expectation maximization algorithm and Kalman smoother are combined to estimate the Bayesian dynamic linear model parameters and generate log-likelihood functions. The subspace identification method is introduced to overcome the initialization issue of the expectation maximization algorithm. The log-likelihood difference of consecutive time steps is then used to determine thresholds without introducing extra anomaly detectors. The proposed Bayesian dynamic linear model-based approach is first illustrated by the simulation data and then applied to the structural health monitoring data collected from two long-span bridges. The results indicate that the proposed method exhibits good accuracy and high computational efficiency and also allows for reconstructing the strain measurements to replace anomalies.

scholarly journals Fractional Growth Model Applied to COVID-19 Data

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1915
Author(s):  
Fernando Alcántara-López ◽  
Carlos Fuentes ◽  
Carlos Chávez ◽  
Fernando Brambila-Paz ◽  
Antonio Quevedo
Keyword(s):  
Fractional Derivative ◽  
Growth Model ◽  
Inflection Point ◽  
Growth Models ◽  
Coefficient Of Determination ◽  
Proposed Model ◽  
Inflection Points

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0<β≤1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R2>0.999.

scholarly journals Predictive Monitoring of Shake Flask Cultures with Online Estimated Growth Models

2021 ◽  
Vol 8 (11) ◽  
pp. 177
Author(s):  
Barbara Pretzner ◽  
Rüdiger W. Maschke ◽  
Claudia Haiderer ◽  
Gernot T. John ◽  
Christoph Herwig ◽  
...  
Keyword(s):  
Growth Model ◽  
Shake Flask ◽  
Growth Models ◽  
Early Stage ◽  
Growth Dynamics ◽  
Growth Conditions ◽  
Logistic Growth ◽  
Model Parameters ◽  
Time Varying ◽  
Strain Characterization

Simplicity renders shake flasks ideal for strain selection and substrate optimization in biotechnology. Uncertainty during initial experiments may, however, cause adverse growth conditions and mislead conclusions. Using growth models for online predictions of future biomass (BM) and the arrival of critical events like low dissolved oxygen (DO) levels or when to harvest is hence important to optimize protocols. Established knowledge that unfavorable metabolites of growing microorganisms interfere with the substrate suggests that growth dynamics and, as a consequence, the growth model parameters may vary in the course of an experiment. Predictive monitoring of shake flask cultures will therefore benefit from estimating growth model parameters in an online and adaptive manner. This paper evaluates a newly developed particle filter (PF) which is specifically tailored to the requirements of biotechnological shake flask experiments. By combining stationary accuracy with fast adaptation to change the proposed PF estimates time-varying growth model parameters from iteratively measured BM and DO sensor signals in an optimal manner. Such proposition of inferring time varying parameters of Gompertz and Logistic growth models is to our best knowledge novel and here for the first time assessed for predictive monitoring of Escherichia. coli (E. coli) shake flask experiments. Assessments that mimic real-time predictions of BM and DO levels under previously untested growth conditions demonstrate the efficacy of the approach. After allowing for an initialization phase where the PF learns appropriate model parameters, we obtain accurate predictions of future BM and DO levels and important temporal characteristics like when to harvest. Statically parameterized growth models that represent the dynamics of a specific setting will in general provide poor characterizations of the dynamics when we change strain or substrate. The proposed approach is thus an important innovation for scientists working on strain characterization and substrate optimization as providing accurate forecasts will improve reproducibility and efficiency in early-stage bioprocess development.

scholarly journals Which Microbial Growth Model Best Fits to Fusarium graminearum?

2018 ◽  
Author(s):  
Edgar Cambaza
Keyword(s):  
Linear Model ◽  
Fusarium Graminearum ◽  
Growth Model ◽  
Yeast Extract ◽  
Microbial Growth ◽  
Growth Models ◽  
Head Blight ◽  
Actual Growth ◽  
Imagej Software ◽  
Yeast Extract Agar

Fusarium graminearum causes head blight in wheat and corn, and produces chemicals harmful for humans and other animals. It is important to understand how it grows in order to prevent outbreaks. There are 3 well-known growth models for microorganisms and they seem applicable to molds: linear, Gompertz and Baranyi. This study aimed to see which could better represent F. graminearum growth. Three replicates were grown in yeast extract agar (YEA) for 20 days. The Feret&rsquo;s radius was measured in ImageJ software, and then related to the models. Linear model was the most closely correlated to the actual growth. Thus, considering that it was the most representative of the reality and it is easier to use, it seems to be the best logical choice for F. graminearum growth studies.

scholarly journals On the Emergence of Islands in Complex Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
J. Esquivel-Gómez ◽  
R. E. Balderas-Navarro ◽  
P. D. Arjona-Villicaña ◽  
P. Castillo-Castillo ◽  
O. Rico-Trejo ◽  
...  
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution ◽  
Growth Models ◽  
Island Size ◽  
First Case ◽  
Proposed Model ◽  
Power Law Function

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution (Is) obeying a power-law function Is~s-α. This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law Is~s-α with a fixed exponent α=1 and in-degree distribution that decays as a power-law Qi~i-γ with γ=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<α<∞ and 2<γ<∞, respectively.

scholarly journals Bayesian Dynamic Linear Model with Adaptive Parameter Estimation for Short-Term Travel Speed Prediction

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Tai-Yu Ma ◽  
Yoann Pigné
Keyword(s):  
Linear Model ◽  
Time Series Data ◽  
Travel Speed ◽  
Series Data ◽  
Model Parameters ◽  
Prediction Errors ◽  
System Behavior ◽  
Dynamic Linear Model ◽  
Short Term ◽  
Speed Prediction

Bayesian dynamic linear model is a promising method for time series data analysis and short-term forecasting. One research issue concerns how the predictive model adapts to changes in the system, especially when shocks impact system behavior. In this study, we propose an adaptive dynamic linear model to adaptively update model parameters for online system state prediction. The proposed method is an automatic approach based on the feedback of prediction errors at each time slot without the needs of external intervention. The experimental study on short-term travel speed prediction shows that the proposed method can significantly reduce the prediction errors of the traditional dynamic linear model and outperform two state-of-the-art methods in the case of major system behavior changes.

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