Matthew Collette

A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem.

A multi-objective variable-fidelity optimization method for genetic algorithms

A novel variable-fidelity optimization (VFO) scheme is presented for multi-objective genetic algorithms. The technique uses a low- and high-fidelity version of the objective function with a Kriging scaling model to interpolate between them. The Kriging model is constructed online through a fixed updating schedule. Results for three standard genetic algorithm test cases and a two-objective stiffened panel optimization problem are presented. For the stiffened panel problem, statistical analysis of four performance metrics are used to compare the Pareto fronts between the VFO method, full high-fidelity optimizer runs, and Pareto fronts developed by enumeration. The fixed updating approach is shown to reduce the number of high-fidelity calls significantly while approximating the Pareto front in an efficient manner.

Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm

This archive provides source code for the example cases in the above-titled paper. The paper abstract reads: Surrogate-assisted evolutionary optimization has proved to be effective in reducing optimization time, as surrogates, or meta-models can approximate expensive fitness functions in the optimization run. While this is a successful strategy to improve optimization efficiency, challenges arise when constructing surrogate models in higher dimensional function space, where the trade space between multiple conflicting objectives is increasingly complex. This complexity makes it difficult to ensure the accuracy of the surrogates. In this article, a new surrogate management strategy is presented to address this problem. A k-means clustering algorithm is employed to partition model data into local surrogate models. The variable fidelity optimization scheme proposed in the authors previous work is revised to incorporate this clustering algorithm for surrogate model construction. The applicability of the proposed algorithm is illustrated on six standard test problems. The presented algorithm is also examined in a three-objective stiffened panel optimization design problem to show its superiority in surrogate-assisted multi-objective optimization in higher dimensional objective function space. Performance metrics show that the proposed surrogate handling strategy clearly outperforms the single surrogate strategy as the surrogate size increases.

Multiobjective Particle Swarm Optimization of a Planing Craft with Uncertainty

Uncertainty exists in many of the design variables and system parameters for planing craft. This is especially true in the early stages of design. For this reason, and others, optimization of a craft’s performance characteristics is often delayed until later in the design process, after uncertainties have been at least partially resolved. However, delaying optimization can also limit its potential, because freedom to make changes to a design is also highly limited in the later stages. This paper demonstrates how uncertainty can be directly incorporated into optimization using particle swarm. A simple synthesis model for a planing craft is built, and a deterministic Pareto front of optimal solutions is found, minimizing two objectives; drag and vertical acceleration at the center of gravity. The craft’s weight is then modelled as a normally distributed random variable and sampling methods are used to quantify the uncertainty in the estimated drag for points along the Pareto front. Preliminary results reveal that drag uncertainty is not constant along the Pareto front, presenting useful trade-off information for designers and decisions makers.

Understanding lifecycle cost trade-offs for naval vessels: minimising production, maintenance, and resistance

ABSTRACT Current optimisers struggle to explore the multi-disciplinary trade-space that defines vessel lifecycle cost. This paper tests an enhanced multi-objective collaborative optimiser on a three-objective hull and structural lifecycle costing problem. The optimiser extends multi-disciplinary collaborative optimisers by including goal-programming and a novel genetic algorithm at the discipline level. The optimiser finds the trade-space between vessel resistance, production cost, and structural maintenance cost. Simultaneous changes to the hullform geometry and structural scantlings are used to explore this design space. The approach is demonstrated on a naval optimisation problem. With fixed maintenance schedules, the trade-space is shown to be steeply walled. This topology indicates that single-discipline optimisation for lifecycle cost may lead to large increases in lifecycle cost for the disciplines not considered. In conclusion, multi-disciplinary optimisation is shown to be a useful tool for addressing lifecycle costing during design.

A Bayesian approach for shipboard lifetime wave load spectrum updating

Updating design stage loading predictions with in-service measurements is an essential step for predicting the fatigue life of complex structures. This is especially true when the loading process is not statistically stationary. Ships and marine structures are an example of such structures. They are fatigue prone from being subject to alternating wave forces, and can also change their loading environment owing to their mobility. This manuscript proposes a two-level offline lifetime load updating scheme to address updating of non-stationary load processes. First, corrections to hydrodynamic predictions are established in short-term statistically stationary operating cells based upon spectral parameters. A hierarchical Bayesian model interpolates corrections between cells and infers correction factors for cells that are not yet observed. Finally, projected operational profiles of the vessel are used to combine cell predictions into an updated lifetime fatigue load profile. The effectiveness of this process is demonstrated on an example vessel in two case studies.

Understanding the Trade-offs Between Producibility and Resistance for Differing Vessels and Missions

Design optimization to increase the efficiency of vessels is common place in engineering. However, most optimization focuses on a single aspect of design such as hydrodynamics, structures, or production. In reality, the lifetime cost of a ship is a combination of these different categories and, for an engineer in the design phase, it is important to understand the trade-offs between them. By understanding these trade-offs, design decisions can be made that ensure reduced costs to the shipowner. However, the development of these trade spaces is difficult and necessitates exploration over a large region of design space. As an example, this work develops these trade spaces between two major competing facets of the lifetime costs: fuel consumption and build cost. Hull forms are transformed using two independent transformation functions to rapidly alter the table of offsets defining the ships geometry. Using this transformation method with a multiobjective genetic algorithm, Pareto fronts between a lifetime resistance metric and a producibility metric based on curvature are developed. Pareto-optimal fronts are then found for both a nominal DTMB-5145 combatant and a KCS SIMMAN container ship. With these fronts, the trade-offs in early stage hull form design is explored, and vessels that minimize these two costs are examined. The work also explores the differences between the trade spaces for the differing types of vessels and mission profiles. Using this method, these trade spaces can be used to explore the design space of vessels earlier in the design phase and gain an understanding of how decisions will affect the total lifetime costs of the ship.

Response and fatigue assessment of high speed aluminium hulls using short-term wireless hull monitoring

Abstract This paper proposes a wireless hull monitoring system that is quick to install as a short-term monitoring solution. Hull measurements have the potential to increase the accuracy of ship response predictions at a lower cost than computer simulation or towing tank models. The performance of the wireless monitoring system is validated on the all-aluminium United States Coast Guard Response Boat-Medium. The system is designed to measure ship motions and hull strain responses during high-speed operations and in harsh weather conditions. An analytical framework is developed to extract sea states from inertial measurements recorded at the ship centre-of-gravity and in a bow compartment. To assess the fatigue life of the hull during harsh weather operations, response amplitude operators (RAOs) are empirically derived to map sea states to root mean square accelerations and strain cycles measured from a high-stress hull element. A RAO that maps sea state to consumed fatigue in the hull, so termed a consumed fatigue operator (CFO), is presented which can assist in the management of an asset over its life cycle. The study reveals reliable hull monitoring during a one-week sea trial. RAO and CFO fit to hull response data are proven to provide accurate estimates.

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, SilvaGonzález, 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. Sørensen (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, ∆σ 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 ∆σ (1) In this model, it is assumed that A, Dcr, and kf all follow a lognormal distribution with ∆σ 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):

The Significance of Storm Avoidance on Macroscopic Fatigue Crack Growth

Ship weather routing is routinely employed to assist ship-masters in avoiding storms. During these storms, however, both material and hydrodynamic nonlinearities grow with the significant wave height (Hs). Hence, to fully understand the importance of weather routing, it may be necessary to go beyond a conventional spectral-based fatigue analysis which incorporates a linear damage hypothesis (i.e., the Palmgren-Miner rule).To this end, the present paper examines macroscopic fatigue crack growth in which the nonlinear phenomena omitted in current design practices are included. We start by considering time-dependent ship structural loading sequences which include non-linear wave-induced bending and whipping responses taken from time-domain seakeeping simulations. These stresses are then analyzed using a fatigue crack growth model previously developed by the authors [1] in which material hysteresis is included using a mechanistic rather than phenomenological approach based on numerical simulations requiring only experimentally measured fatigue crack growth rates under constant amplitude cyclic loading (e.g., ASTM E647-13) and a full material constitutive model defined through experimental push-pull tests for the same material. Using this approach, we quantify the importance of weather routing by systematically substituting storms above a certain threshold with more moderate sea conditions.© 2014 ASME