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Condition monitoring of natural gas distribution networks is a fundamental prerequisite for evaluating safety of the operation during the lifetime of the system. Due to the high level of uncertainty in the observed data, predicting the operational reliability of the networks is complicated. Moreover, there is a fluctuation in most of the monitoring...
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... order to discriminate noisy IMFs from actual signals, statistical significance test (SST) was taken based on energy density and mean period. Table 1 gives the energy density and the mean period of each IMF. Based on the appli- cation of the SST, the first two IMFs, c 1 and c 2 were recognized as noise signals (see Fig. 5). ...
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... Also, EMD does not need the indication of a basic function such as most WTs [28]. Due to its advantages, EMD and its derivative approaches have become popular tools to perform CM and failure diagnoses [29][30][31][32][33][34]. A recent study by Yan et al. [35] proposed a methodology to predict the temperature of a train axle. ...
... Finally, r(t) is the residual term. An IMF could either belong to the noise component or the true signal component, therefore the IMFs which determine the true signal are distinguished from the IMFs related to the random noise, as illustrated by Eq. (2) [29]: ...
... An SST is conducted to distinguish noisy IMFs from the true signal IMFs (Step 6). First, the mean period of each extracted IMF is estimated according to Eq. (3) [29]. ...
Due to higher reliability and safety requirements, the importance of condition monitoring and failure diagnosis has progressively cleared up. In this context, being able to properly deal with noise and data reduction is fundamental for improving failure diagnosis and assuring safe operations. These tasks are particularly difficult in presence of many non-stationary and non-linear signals. Accordingly, this paper proposes a failure diagnosis methodology that integrates Empirical Mode Decomposition (EMD) and Neighborhood Component Analysis (NCA) for noise removal and data reduction. While noise detection and reduction techniques are established to reduce the uncertainties integrated with data acquisition, traditional approaches that cannot capture the non-stationary and non-linear nature of data might result in higher uncertainty. As a validated denoising method, EMD is applied to cope with the previous limitations. The NCA overcomes typical limitations such as imposing class distributions. After data pre-processing, the diagnosis is performed through a Random Forest. The methodology is tested on real data of a compressor subjected to surge, showing an accuracy higher than 97%. Moreover, the surge accuracy is close to 95%, while the regime accuracy is higher than 97%. The developed framework could assist practitioners in evaluating the condition of assets and, accordingly, planning maintenance.
... The Bayes theorem utilizes multistage prior distribution to present the population variability through different hierarchy levels. Correspondingly, the first-stage prior denoted as π 1 (θ|φ) is accounted to denote the variability between the source of data for the parameter of interest indicated by π 0 (θ), as follow (BahooToroody, Abaei et al., 2019b): ...
Analyzing the reliability of autonomous ships has recently attracted attention mainly due to epistemic uncertainty (lack of knowledge) integrated with automatic operations in the maritime sector. The advent of new random failures with unrecognized failure patterns in autonomous ship operations requires a comprehensive reliability assessment specifically aiming at estimating the time in which the ship can be trusted to be left unattended. While the reliability concept is touched upon well through the literature, the operational trustworthiness needs more elaboration to be established for system safety, especially within the maritime sector. Accordingly, in this paper, a probabilistic approach has been established to estimate the trusted operational time of the ship machinery system through different autonomy degrees. The uncertainty associated with ship operation has been quantified using Markov Chain Monte-Carlo simulation from likelihood function in Bayesian inference. To verify the developed framework, a practical example of a machinery plant used in typical short sea merchant ships is taken into account. This study can be exploited by asset managers to estimate the time in which the ship can be left unattended. Keywords: reliability estimation, Bayesian inference, autonomous ship, uncertainty.
... To analyze the failure effects of interrelating components in complex network systems, a novel methodology integrating simulation, Markov chain and belief network is developed in [27]. BahooToroody et al. [28] develop a probabilistic methodology for reliability assessment of natural gas distribution networks by using a Hierarchical Bayesian Model (HBM). A risk-based optimization is proposed in [29] ...
This study proposes a method based on Bayesian networks (BNs) to optimize the reliability of gas supply in natural gas pipeline networks. The method integrates probabilistic safety analysis with preventive maintenance to achieve the targets of minimizing gas shortage risk and reducing maintenance costs. For this, the tasks of unit failure probability calculation, system maximum supply capacity analysis, gas supply reliability assessment and system maintenance planning are performed. A stochastic capacity network model is coupled with a Markov model and graph theory to generate the state space of the pipeline network system. BN, is then, proposed as the modeling framework to describe the stochastic behavior of unit failures and customer gas shortage. The system maintenance problem is converted into a Markov decision process (MDP), and solved by using deep reinforcement learning (DRL). The effectiveness of the proposed method is validated on a case study of a European gas pipeline network. The results show that the proposed method outperforms others in identifying optimal maintenance strategies. The DRL-optimized maintenance strategy is capable of responding to a dynamic environment through continuous online learning, considering the randomness of the unit failures and the uncertainty in gas demand profiles.
... Moreover, Bayesian Inference can provide better results than other parametric regression methods, such as Maximum Likelihood Estimation (MLE) (BahooToroody et al., 2020a). Finally, the adoption of a hierarchy structure allows addressing the correlations among nonlinear data and the variation of non-stationary data, leading to a more coherent regression model compared to other classic approaches (BahooToroody et al., 2019b). A relevant example of a BN-based condition monitoring approach is presented by BahooToroody et al. (2019b). ...
... Finally, the adoption of a hierarchy structure allows addressing the correlations among nonlinear data and the variation of non-stationary data, leading to a more coherent regression model compared to other classic approaches (BahooToroody et al., 2019b). A relevant example of a BN-based condition monitoring approach is presented by BahooToroody et al. (2019b). In their paper, they integrate an Empirical Mode Decomposition with a Statistical Significant Test for noise removal, while they employ a Bayesian Network with a hierarchical structure to predict the time of the following pressure exceedance. ...
Thanks to the advances in the Internet of Things (IoT), Condition-based Maintenance (CBM) has progressively become one of the most renowned strategies to mitigate the risk arising from failures. Within any CBM framework, non-linear correlation among data and variability of condition monitoring data sources are among the main reasons that lead to a complex estimation of Reliability Indicators (RIs). Indeed, most classic approaches fail to fully consider these aspects. This work presents a novel methodology that employs Accelerated Life Testing (ALT) as multiple sources of data to define the impact of relevant PVs on RIs, and subsequently, plan maintenance actions through an online reliability estimation. For this purpose, a Generalized Linear Model (GLM) is exploited to model the relationship between PVs and an RI, while a Hierarchical Bayesian Regression (HBR) is implemented to estimate the parameters of the GLM. The HBR can deal with the aforementioned uncertainties, allowing to get a better explanation of the correlation of PVs. We considered a numerical example that exploits five distinct operating conditions for ALT as a case study. The developed methodology provides asset managers a solid tool to estimate online reliability and plan maintenance actions as soon as a given condition is reached.
... According to the structural reliability analysis basis, the level of the proposed criteria through different standards would experience a change. Reliability analysis has been carried out widely in different engineering fields to improve the systems' serviceability [9][10][11][12][13]. In contrast with the remarkable improvement and significant development of structural reliability theory in the last few decades, it has not been applied frequently for assessing offshore structures' performance. ...
Offshore jacket platforms (OJPs) may be exposed to harsh environmental conditions during their operation in different return periods. It is necessary to evaluate the dynamic performance of the OJPs subjected to extreme wave loadings to secure a safe operation. In the earlier studies, various approaches were introduced to analyze the response of an OJP in different sea states. However, the serious shortcoming of the proposed methods is computationally time consuming and requires a considerable amount of simulations to evaluate the performance of the OJP. Accordingly, these approaches would not analyze the dynamic performance of the OJP realistically. In this study, the dynamic performance of an OJP subject to a harsh environment is evaluated considering a time-domain simulation. e developed model will result in a more realistic response by simulating the whole structure subjected to 1800 seconds of extreme wave loading in the light of the sea environment randomness. e application of the methodology is demonstrated by assessing the performance of a fabricated OJP subjected to extreme wave loadings in the North Sea. e dynamic analysis shows that among all assigned probability distribution functions (PDFs), the most suitable distribution for predicting the maximum deck displacement in all return periods was generalized extreme value (GEV). Moreover, the results show that the response of the structure is likely to remain in the safe limit condition in the 1-year return period. In contrast, in other return periods, the OJP will exceed the safe limit condition. e proposed method is beneficial for future risk and reliability analyses that require a great deal of data derived from numerical simulations.
... The application of hierarchical Bayesian inference (HBI) has been vastly extended in different research areas, from econometrics (Kastner 2019) to phycology (Wagenmakers, Marsman, et al. 2018) and medicine (Elkin, Schlegel et al. 2018). This extension is principally thanks to two main reasons; first, the development of random-effect models (REM) and specially Markov Chain Monte Carlo (MCMC) simulation (BahooToroody, De Carlo et al. 2020a, Leoni, BahooToroody, et al. 2021a, and second, the capability of HBI in modeling the variability of non-stationary data and the correlation between nonlinear data (BahooToroody, Abaei et al. 2019a, BahooToroody, Abaei et al. 2019b, Basnet, et al. 2022. Related literature also set sound examples of MCMC sampling-based HBI for failure modeling of maritime autonomous systems (Brito and Griffiths 2016, Abaei and Hekkenberg 2020b. ...
... A two-parameter Weibull distribution, ( ) , with shape parameter, , and scale parameter, , is generated through modeling the inter-arrival times between successive observations by power-law (BahooToroody, Abaei et al. 2019b) given by Equation 5; ...
... where and are the last and th observation of the exceedances event from health threshold in the simulation, respectively (Abaei, Arzaghi et al. 2018b, BahooToroody, Abaei et al. 2019b). This will allow Openbugs to perform the simulation through Bayesian updating via likelihood function and specify the marginal posterior distribution as outlined by Equation 15. ...
Maritime characteristics make the progress of automatic operations in ships slow, especially compared to other means of transportation. This caused a great progressive deal of attention for Autonomy Degree (AD) of ships by research centers where the aims are to create a well-structured roadmap through the phased functional maturation approach to autonomous operation. Application of Maritime Autonomous Surface Ship (MASS) requires industries and authorities to think about the trustworthiness of autonomous operation regardless of crew availability on board the ship. Accordingly, this paper aims to prognose the health state of the conventional ships, assuming that it gets through higher ADs. To this end, a comprehensive and structured Hierarchal Bayesian Inference (HBI)-based reliability framework using a machine learning application is proposed. A machinery plant operated in a merchant ship is selected as a case study to indicate the advantages of the developed methodology. Correspondingly, the given main engine in this study can operate for 3, 17, and 47 weeks without human intervention if the ship approaches the autonomy degree of four, three, and two, respectively. Given the deterioration ratio defined in this study, the acceptable transitions from different ADs are specified. The aggregated framework of this study can aid the researchers in gaining online knowledge on safe operational time and Remaining Useful Lifetime (RUL) of the conventional ship while the system is being left unattended with different degrees of autonomy.
... Observed data, manipulated information, and gathered knowledge are three milestones of making an inference in a theoretical model (BahooToroody et al., 2019). The posterior distribution is achieved by updating the prior distribution with observed data. ...
The increasing system complexity due to technological advances in recent decades requires the implementation of Model-Based System Engineering (MBSE) languages. While MBSE languages can support in creating detailed and precise system descriptions, requirements, functions, and component interactions, the development of several modelling languages has formed a challenge for system engineers to select a suitable modelling language for complex operations. Since the implementation of MBSE modelling languages is extensive and requires high resources, system engineers need to select the most suitable one for their project. Furthermore, the prepared system models are utilized by different end-users such as system engineers, operators, and marketing professionals. As a result, it is necessary to integrate the perception of end-users in the modelling language selection process. Hence, a decision-making support framework needs to be developed, which will incorporate the opinions of end-users in the selection process. Correspondingly, this study proposes a Multi-Criteria Decision-Making framework aimed to select the most appropriate and practical modelling language. The framework integrates the end-user’s perception in the selection process using the Technology Acceptance Model and reckons the MBSE language features as comparison criteria. To analyze the data collected from the end-users, integration of Multinomial Process Tree modelling and Bayesian inference is developed. The applicability of the proposed model was tested in a ship pilotage operation case study. The results show that the framework can support system engineers during the initial selection process of the MBSE modelling language.
... Due to the complexity of systems in autonomous ships, the prediction model needs to react as a function of a desired goal state and feedback regarding the experimental conditions of a system. Recent research on evaluating the reliability of marine operations and predicting the availability of systems highlights key attributes of the Bayesian method, namely the ability to incorporate qualitative information (i.e., evidence obtained from events) into the parameters [36][37][38]. Hierarchical Bayesian inference is a probabilistic approach that provides the organization of inference based on real observations [12,28,[36][37][38]. The advent of Markov chain Monte Carlo (MCMC) sampling has proliferated Bayesian inference by setting up a Bayesian network to quantify the uncertainty. ...
... Recent research on evaluating the reliability of marine operations and predicting the availability of systems highlights key attributes of the Bayesian method, namely the ability to incorporate qualitative information (i.e., evidence obtained from events) into the parameters [36][37][38]. Hierarchical Bayesian inference is a probabilistic approach that provides the organization of inference based on real observations [12,28,[36][37][38]. The advent of Markov chain Monte Carlo (MCMC) sampling has proliferated Bayesian inference by setting up a Bayesian network to quantify the uncertainty. ...
... In addition, the topology of the RPT for the current problem always have paths with an equal length similar to Fig. 2 in which the noninformative prior can be a good choice for populating the tree. This forces the posterior function to completely depend on observation data [12,28,[35][36][37]. Therefore, the predicted posterior distribution will consider the uncertainty in available observation data and accurately reflect their true nature [37]. ...
Over the next few years, digitalization and automation are expected to be key drivers for maritime transport innovation to be key drivers for maritime transportation innovation. This revolutionary shift in the shipping industry will heavily impact the reliability of the machinery which is intended to be operated remotely with minimum support from humans. Despite a large amount of research into autonomous navigation and control systems in maritime transportation, the evaluation of unattended engine rooms has received very little attention. For autonomous vessels to be effective during their unmanned mission, it is essential for the engine room understand its health condition and self-manage performance. The unattended machinery plant (UMP) should be resilient enough to have the ability to survive and recover from unexpected perturbations, disruptions, and operational degradations. Otherwise, the system may require unplanned maintenance or the operation will stop. Therefore, the UMP must continue its operation without human intervention and safely return the ship to port. This paper aims to develop a machine learning-based model to predict an UMP's performance and estimate how long the engine room can operate without human assistance. A Random Process Tree is used to model failures in the unattended components, while a Hierarchical Bayesian Inference is adopted to facilitate the prediction of unknown parameters in the process. A probabilistic Bayesian Network developed and evaluated the dependent relationship between active and standby components to assess the effect of redundant units in the performance of unattended machinery. The present framework will provide helpful additional information to evaluate the associate uncertainties and predict the untoward events that put the engine room at risk. The results highlight the model's ability to predict the UMP's trusted operation period and evaluate an unattended engine room's resilience. A real case study of a merchant vessel used for short sea shipping in European waters is considered to demonstrate the model's application.
... In recent years, many researchers have enriched the scope of process monitoring from the standpoint of safety and risk management. For example, BahooToroody et al. proposed a process monitoring based signal filtering method for the safety assessment of the natural gas distribution process (BahooToroody et al., 2019). Yin et al. deployed a supervised data mining method for the risk assessment and smart alert of gas kick during the industrial drilling process (Yin et al., 2021). ...
Industrial processes are becoming increasingly large and complex, thus introducing potential safety risks and requiring an effective approach to maintain safe production. Intelligent process monitoring is critical to prevent losses and avoid casualties in modern industry. As the digitalization of process industry deepens, data-driven methods offer an exciting avenue to address the demands for monitoring complex systems. Nevertheless, many of these methods still suffer from low accuracy and slow response. Besides, most black-box models based on deep learning can only predict the existence of faults, but cannot provide further interpretable analysis, which greatly confines their usage in decision-critical scenarios. In this paper, we propose a novel orthogonal self-attentive variational autoencoder (OSAVA) method for process monitoring, consisting of two components, orthogonal attention (OA) and variational self-attentive autoencoder (VSAE). Specifically, OA is utilized to extract the correlations between different variables and the temporal dependency among different timesteps; VSAE is trained to detect faults through a reconstruction-based method, which employs self-attention mechanisms to comprehensively consider information from all timesteps and enhance detection performance. By jointly leveraging these two models, our OSAVA method can effectively perform fault detection and identification tasks simultaneously and deliver interpretable results. Finally, through extensive evaluation on the Tennessee Eastman process (TEP), we demonstrate that our proposed OSAVA shows promising fault detection rate as well as low detection delay and can correctly identify the abnormal variables, compared with representative statistical methods and state-of-the-art deep learning models.
... Meanwhile, the improvements in opensource MCMC software, such as OpenBugs, have resulted in wider adoption of the HBM [42], which, compared to the standard BN, provides more robust estimators [43], and it can also cope with source-to-source variability [44]. HBM has been exploited by many researchers for prioritizing maintenance tasks [45][46][47], condition monitoring [48,49], and reliability analysis [50,51]. In a work presented by Andrade and Teixeira [52], the HBM was adopted to evaluate the degradation of the railway between Lisbon and Oporto in Portugal. ...
Over the last few decades, reliability analysis has attracted significant interest due to its importance in risk and asset integrity management. Meanwhile, Bayesian inference has proven its advantages over other statistical tools, such as maximum likelihood estimation (MLE) and least square estima-tion (LSE), in estimating the parameters characterizing failure modelling. Indeed, Bayesian infer-ence can incorporate prior beliefs and information into the analysis, which could partially overcome the lack of data. Accordingly, this paper aims to provide a closed-mathematical representation of Bayesian analysis for reliability assessment of industrial components while investigating the effect of the prior choice on future failures predictions. To this end, hierarchical Bayesian modelling (HBM) was tested on three samples with distinct sizes, while five different prior distributions were con-sidered. Moreover, a beta-binomial distribution was adopted to represent the failure behavior of the considered device. The results show that choosing strong informative priors leads to distinct pre-dictions, even if a larger sample size is considered. The outcome of this research could help maintenance engineers and asset managers in integrating their prior beliefs into the reliability es-timation process.
