Bayesian networks for model updating inspection support of marine structures subject to fatigue
There is significant uncertainty in the structural health and resulting capabilities of a marine structure during service life. Design stage marine structural engineering models offer limited information on the as built structure's health during its service life. Despite copious amounts of data provided by structural monitoring techniques, synthesizing these different data types to offer support in decision making for inspection remains challenging and underexplored. A Bayesian network data to decision framework fusing through life inspection data with design stage fatigue calculations is demonstrated to afford data fusion and inspection extent decision support. Using parametric encoding for a Weibull pressure distribution governing cyclic loading, and a lognormal probabilistic fatigue initiation model, the network represents a large stiffened metallic grillage with fatigue critical details typical of a marine structure. Updating is performed with inspection observation and maximum strain values. Extension of the Bayesian network to an Influence Diagram with utility and decision nodes offers inspection extent decision support. The ability of the network approach to provide reasonable inspection guidance and forecast of future structural performance is tracked for different evidence sets. Recommendations for adapting the network approach for fatigue life support are drawn based on the systematic study conducted. An increased awareness of a vessel's structural condition through its service life could significantly increase the safety and operational capability of the vessel. Such awareness would also grant the ability to make cost reducing inspection and maintenance decisions. Over the past several decades our ability to sense and record structural performance data has increased dramatically through new sensor and data acquisition systems (Wang, Lynch, and Sohn 2014) Monitoring techniques include a variety of sensors recording related but different data types at high sampling rates, often on the order of hundreds of hertz. As a result, as Collette and Lynch describe, "we swim in an ocean of data but remain thirsty for information" (Collette and Lynch 2013) In addition to data recorded by sensing methods, there are many phenomena physically recorded in the structure that can be used for model updating. The abovementioned benefits of structural awareness can only be achieved with a data to decision (D2D) framework. D2D requires both the interpretation of abundant data to yield relevant information, and a decision support system capable of evaluating the information produced. Data acquired from these systems can be used to update structural forecasting models to make better life cycle structural updating decisions. The current work examines techniques to interpret and synthesize the physical record, which has seen limited investigation, and update design stage engineering models to more closely match the current condition of the vessel. These updated models can then be used for inspection decision support. A Bayesian network extended 12 th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12 15, 2015 2 to an Influence Diagram framework is used to fuse different in service observations with a common underlying structural model. This approach is explored for a stiffened grillage subject to fatigue failures and permanent set of the grillage plate. Application of Bayesian networks in the realm of Risk Based Inspection for fatigue damages has been studied by Goyet et al. (2011) who introduced a Probabilistic System Approach including economical optimization of the FPSO service life based on a hierarchical model of the hull. This approach uses Bayesian networks to propagate probabilities from component level to the system level. Heredia Zavoni, SilvaGonzalez, and Montes Iturrizaga (2008) presented a general framework for integrity management of offshore steel structures allowing for the risk based planning of inspection and maintenance activities accounting for both deterioration and damage processes using a Bayesian network for decision making. The proposed risk based inspection (RBI) framework combines damage processes and uses a threshold acceptable total system failure probability to dictate optimal inspection points. Sorensen (2011) explored the use of Bayesian preposterior decision theory to evaluate deterioration from various sources being monitored and inspected. Further supporting the use of Bayesian networks in application to RBIs of vessel structural health, Tammer and Kaminski (2013) reviewed the use of this methodology for determining the inspection scope, and inspection intervals of FPSOs in application to fatigue related degradation, determining it to have an inevitable role in future decision making. These publications show there has been application of Bayesian statistics for evaluation of structural health and inspection periodicity. However, the use of Bayesian networks and Influence Diagrams for synthesis of multiple data types for structural health model updating and decision making has not been explored. Leveraging fusion of multiple stochastic data types and sources is presently being overlooked. The present work focuses on the problem of updating probabilistic structural fatigue crack initiation models for inspection extent decision support of marine structures. Marine structures are inherently susceptible to fatigue failures as the primary stress field alternates between tension and compression under wave loading. Without repair, these cracks grow and can cause fracture potentially resulting in catastrophic failure. Synthesizing data from permanent set (deformation of shell plates from local sea pressure exceeding elastic limit) crack initiation, and a maximum strain recording, the presented method demonstrates the ability to provide both model updating of the in service vessel and decision support for inspection extents. Updating capabilities are demonstrated via Monte Carlo simulation. Results are shown for evidence fused from three distinct types of observations providing inspection extent strategies for the present and a future point in time. 1. METHODOLOGY Ships are typically built in small run production settings. Economically, this makes prototype structural testing cost prohibitive. Thus, a common challenge is how to interpret in service inspections in light of a non validated structural design model. Here, a series of design stage structural prediction models related to observable outcomes are integrated into a Bayesian network. The underlying parameters of these models are assumed to be stochastic. Through service life updating, the posterior belief in these parameters is adjusted to better reflect the as built vessel. The overall methodology used includes a parametrically encoded Bayesian network extended to an Influence Diagram for decision support. The network is encoded with reliability models from design priors and is updated with evidence from fatigue failures, permanent set, and the maximum recorded strain of a grillage structure undergoing lateral (normal) pressure loading. Posterior distributions more accurately 12 th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12 15, 2015 3 represent the in service structural reliability model and are then used to find the maximum expected utility for decision of inspection extent for the considered juncture and a future point. The future inspection strategy is determined assuming execution of the present inspection strategy with the highest utility. 1.1. Fatigue Model Sections 1.1 1.3 are taken from Groden and Collette (2013) it did not appear in printed proceedings so it is reproduced here. The fatigue capacity model used was presented previously by (Collette 2011) It uses a lognormal modeling approach to solve the S N crack initiation reliability problem analytically, inspired by Wirsching (1984) In this approach, the number of cycles to fatigue crack initiation at a given structural location is determined to by the S N equation below, where A and m are experimentally determined constants, s is the equivalent stress range acting on the fatigue location, kf is a stress modeling uncertainty factor, and Dcr is the cumulative damage index from the Palmgren Miner cumulative damage rule. N DcrA kf s (1) In this model, it is assumed that A, Dcr, and kf all follow a lognormal distribution with s and m constant. The lognormal distribution has the following probability density function, and has previously been shown to be a reasonable fit for ship like structure fatigue data (Collette and Incecik 2006)