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Inspection and maintenance planning for offshore wind structural components: integrating fatigue failure criteria with Bayesian networks and Markov decision processes
Abstract
Exposed to the cyclic action of wind and waves, offshore wind structures are subject to fatigue deterioration processes throughout their operational life, therefore constituting a structural failure risk. In order to control the risk of adverse events, physics-based deterioration models, which often contain significant uncertainties, can be updated with information collected from inspections, thus enabling decision-makers to dictate more optimal and informed maintenance interventions. The identified decision rules are, however, influenced by the deterioration model and failure criterion specified in the formulation of the pre-posterior decision-making problem. In this paper, fatigue failure criteria are integrated with Bayesian networks and Markov decision processes. The proposed methodology is implemented in the numerical experiments, specified with various crack growth models and failure criteria, for the optimal management of an offshore wind structural detail under fatigue deterioration. Within the experiments, the crack propagation, structural reliability estimates, and the optimal policies derived through heuristics and partially observable Markov decision processes (POMDPs) are thoroughly analysed, demonstrating the capability of failure assessment diagram to model the structural redundancy in offshore wind substructures, as well as the adaptability of POMDP policies.
... In addition, crack growth data reported in offshore standards is based on the characteristics that are representative of typical offshore structures in the oil and gas industry. Instead of directly relying on material parameters listed in standards, it is also possible to estimate them by performing a calibration analysis that minimizes the difference in structural reliability with respect to estimates computed via Palmgren-Miner's rule (DNVGL, 2019;Hlaing et al., 2020Hlaing et al., , 2022. ...
... Failure probability over time should be considered because, while fracture mechanics models compute crack growth evolution, S-N data only provides information about the failure or survival of the considered hotspot due to fatigue damage (DNVGL, 2019). The reader is advised to refer to Hlaing et al. (2022) for more information on the procedure to carry out the fracture mechanics parameter calibration based on a probabilistic approach. Alternatively, unknown fracture mechanics parameters can also be calibrated following a deterministic approach, by adjusting crack growth parameters so that through-thickness failure is reached at the same time as fatigue damage failure computed via Palmgren-Miner's rule and representative S-N data. ...
This study investigates the behavior of interacting surface cracks at the circumferential weld toe of monopile-supported offshore wind turbines. Relying on a numerical model that explicitly considers weld profiles, we explore the impact of crack interaction and loading scenarios on crack propagation. Our findings reveal that, initially, surface cracks grow independently, resembling single crack behavior. However, a pronounced interaction effect accelerates their growth as cracks propagate further, potentially leading to crack coalescence, high stress intensity factors, and reduced fatigue life. Consequently, this work highlights the need for integrating specific weld geometry representation in numerical models, as neglecting this can lead to significantly inaccurate fatigue life estimates in typical practical applications. Moreover, this study points out the challenge in accessing representative crack growth material parameters, vital for accurately evaluating the fatigue life of structural connections in offshore wind turbines.
... Some methods focus on the optimization of predefined static decision rules, planning inspections at equidistant intervals or when a prescribed failure probability threshold is surpassed, and prescribing maintenance interventions if a certain damage indicator is observed, e.g., crack detection [3,7,8]. While these approaches can provide reasonable and effective policies in some specific scenarios, the optimality of the policies depends greatly on the designer's experience when defining the heuristic combinations for the policy search, since they cannot consider all policies within the vast available policy space, which could in turn produce better results than the originally considered predefined heuristics [9,10]. In other existing methods, while inspection planning decision rules are defined a priori, the maintenance policy is adaptive, properly updating the involved thresholds based on new information [11]. ...
... In a stochastic environment, the initial crack depth, 0 , along with fracture mechanics model parameters are either represented by random variables or deterministic parameters as listed in Table 1. The failure probability , defined as = [ ≤ 0], can be computed following, for instance, a through-thickness failure criterion [10] by formulating the failure limit state at time step as: The fatigue deterioration is encoded in a deterioration rate DBN model, ultimately shaping a factored POMDP, as shown on the left side of Fig. 2, and presented in Section 2. The continuous crack depth, , is adequately discretized into | | = 30 states conditional on | | = 31 fully observable deterioration rates states. The intervals and state space utilized for this deterioration rate model are listed in Table 2. ...
In the context of modern engineering, environmental, and societal concerns, there is an increasing demand for methods able to identify rational management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level, often assuming statistical, structural, or cost independence among components, due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level.
In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks, decoupling the originally joint system state space to component networks conditional on shared random variables. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies.
... Clere Smithe, 2023), formalising co-design problems (Zardini et al., 2021), data management Johnson et al., 2012), and creation of digital twins (Qi et al., 2022). For sequential decisionmaking, the value of information theory and partially observable Markov decision process (POMDP) model has been used to express relationship between an agent and its dynamic system environment along with related uncertainties (Papakonstantinou and Shinozuka, 2014;Andriotis et al., 2021), with applications in a wind energy context Liang et al., 2022;Hlaing et al., 2022). It should be noted that many of the above-mentioned formalisms have not yet received widespread adoption and therefore often lack practical technological implementations (see Sect. 4), as opposed to DL and FOL. ...
With the rapid evolution of the wind energy sector, there is an ever-increasing need to create value from the vast amounts of data made available both from within the domain and from other sectors. This article addresses the challenges faced by wind energy domain experts in converting data into domain knowledge, connecting and integrating them with other sources of knowledge, and making them available for use in next-generation artificial intelligence systems. To this end, this article highlights the role that knowledge engineering can play in the digital transformation of the wind energy sector. It presents the main concepts underpinning knowledge-based systems and summarises previous work in the areas of knowledge engineering and knowledge representation in a manner that is relevant and accessible to wind energy domain experts. A systematic analysis of the current state of the art on knowledge engineering in the wind energy domain is performed with available tools put into perspective by establishing the main domain actors and their needs, as well as identifying key problematic areas. Finally, recommendations for further development and improvement are provided.
... Clere Smithe, 2023), formalising co-design problems (Zardini et al., 2021), data management (Spivak, 2012;Johnson et al., 2012), and cre-205 ation of digital twins (Qi et al., 2022). For sequential decision making, value of information theory and Partially Observable Markov Decision Process (POMDP) model has been used to express relationship between an agent and its dynamic system environment along with related uncertainties (Papakonstantinou and Shinozuka, 2014;Andriotis et al., 2021), with applications in wind energy context Liang et al., 2022;Hlaing et al., 2022). It should be noted that many of the above-mentioned formalisms have not yet received wide-spread adoption and therefore often lack practical technological 210 implementations (see Section 4), as opposed to DL and FOL. ...
With the rapid evolution of the wind energy sector, there is an ever-increasing need to create value from the vast amounts of data made available both from within the domain, as well as from other sectors. This article addresses the challenges faced by wind energy domain experts in converting data into domain knowledge, connecting and integrating it with other sources of knowledge, and making it available for use in next-generation artificial intelligence systems. To this end, this article highlights the role that knowledge engineering can play in the digital transformation of the wind energy sector. It presents the main concepts underpinning Knowledge-Based Systems and summarises previous work in the areas of knowledge engineering and knowledge representation in a manner that is relevant and accessible to wind energy domain experts. A systematic analysis of the current state-of-the-art on knowledge engineering in the wind energy domain is performed, with available tools put into perspective by establishing the main domain actors and their needs, as well as identifying key problematic areas. Finally, recommendations for further development and improvement are provided.
... The I&M decision problem is here formulated as a POMDP, which is then solved through the SAR-SOP point-based solver (Kurniawati et al., 2008). The reader is directed to (Hlaing et al., 2022) for a more detailed description of this case study. ...
The application of Deep Reinforcement Learning (DRL) for the management of engineering systems has shown very promising results in terms of optimality and scalability. The interpretability of these policies by decision-makers who are so far mostly familiar with traditional approaches is also needed for implementation. In this work, we address this topic by providing a comprehensive overview of POMDP-and DRL-based management policies, along with simulation-based implementation details, for facilitating their interpretation. By mapping a sufficient statistic, namely a belief state, to the current optimal action, POMDP-DRL strategies are able to automatically adapt in time considering long-term sought objectives and the prior history. Through simulated policy realizations, POMDP-DRL-based strategies identified for representative inspection and maintenance planning settings are thoroughly analyzed. The results reveal that if the decision-maker opts for an alternative, even suboptimal, action other than the one suggested by the DRL-based policy, the belief state will be accordingly updated and can still be used as input for the remainder of the planning horizon, without any requirements for model retraining.
... Combined with engineering models, manual and/or robotic inspections can be conducted in order to reduce the uncertainties associated with deterioration estimations, hence supporting more rational and informed maintenance decisions. 1,2 With the advent of modern sensor technologies, monitoring systems are increasingly being deployed with the objective of continuously monitoring the deterioration experienced by offshore wind structures, thus also enabling decision-makers to make timely and informed decisions. 3,4 For example, fatigue load monitoring through strain gauges provides valuable information that can be used to estimate the remaining useful fatigue lifetime [5][6][7] and/or to update probabilistically modeled time-varying deterioration mechanisms. ...
Offshore wind structures are exposed to a harsh marine environment and are subject to deterioration mechanisms throughout their operational lifetime. Even if the deterioration evolution of structural elements can be estimated through physics-based deterioration models, the uncertainties involved in the process hurdle the selection of lifecycle management decisions, e.g., lifetime extension. In this scenario, the collection of relevant information through an efficient monitoring system enables the reduction of uncertainties, ultimately driving more optimal lifecycle decisions. However, a full monitoring instrumentation implemented on all wind turbines in a farm may become unfeasible due to practical and economical constraints. Besides, certain load monitoring systems often become defective after a few years of marine environment exposure. Addressing the aforementioned concerns, a farm-wide virtual load monitoring scheme directed by a fleet-leader wind turbine offers an attractive solution. Fetched with data retrieved from a fully instrumented wind turbine, a model can be first trained and then deployed, yielding load predictions for non-fully monitored wind turbines, from which only standard data are available, e.g., supervisory control and data acquisition. During the deployment stage, the pretrained virtual monitoring model may, however, receive previously unseen monitoring data, leading to inaccurate load predictions. In this article, we propose a virtual load monitoring framework formulated via Bayesian neural networks (BNNs) and provide relevant implementation details needed for the construction, training, and deployment of BNN data-based virtual monitoring models. As opposed to their deterministic counterparts, BNNs intrinsically announce the uncertainties associated with generated load predictions and allow to detect inaccurate load estimations generated for non-fully monitored wind turbines. The proposed virtual load monitoring is thoroughly tested through an experimental campaign in an operational offshore wind farm and the results demonstrate the effectiveness of BNN models for “fleet-leader”-based farm-wide virtual monitoring.
... where the evolution over time, t, of the crack depth, d, is formulated through a fracture mechanics law with material parameters ln C FM ð Þ � N μ ¼ À 35:2; σ ¼ 0:5 ð Þ and m = 3.5, stress range S R � N μ ¼ 70; σ ¼ 10 ð Þ N=mm 2 , n = 10 6 annual stress cycles, and initial crack depth d 0 � Exp μ ¼ 1 ð Þ mm. At the hotspot level, fatigue failure p Ft occurs once the crack depth, d, exceeds a critical size, d c = 20 mm, formally defined as p F t ¼ Pr g t � 0 ½ � and computed via a through-thickness failure criterion (Hlaing et al. 2022), i.e. g t ¼ d c À d t . Adopting the probabilistic methodology proposed in Section 2, the fatigue deterioration is encoded in a deterioration rate DBN model. ...
In conventional industrial practices, the structural performance is evaluated against deterioration mechanisms as well as extreme and/or accidental events. However, most existing approaches treat the aforementioned structural assessments separately. In this work, we identify system inspection and maintenance strategies by jointly modeling deterioration processes and accidental/extreme events within the overall life-cycle management optimization. In particular, the decision-making objective is formulated considering a system failure risk metric that depends on the damage caused by deterioration processes and accidental/extreme hazards. In order to enable efficient inference and uncertainty propagation, we propose an underlying probabilistic approach relying on dynamic Bayesian networks. The efficacy of the proposed approach is tested in a life-cycle management setting where the risk of an offshore wind frame substructure is controlled by timely allocating inspection and maintenance actions. Within the investigation, we also observe the influence of ship collision events frequency on the resulting asset management strategies.
... Embeded Tacit [195], [196], [170], [58], [197], [188], [13], [53], [55], [198], [174], [144] ✓ Simulator [199], [59], [171], ✓ Gauge [199], [59], [171], [200], [183], [167], [201], [169], [169] ✓ Extractor [182], [36], [62], [172,213,63], [113], [149] ✓ Operator [118], [43], [165], [51] ✓ Operator [81], [130], [209] ✓ Operator [37], [210], [113], [217] ✓ Structure blueprint [114], [129], [121], [115], [186], [179], [50], [120], [91], [114] [156], [178] [95], [166], [211], [212], [20], [107] ✓ Structure blueprint [57], [142], [76], [149], [187] ✓ Initializer [154], [168] ✓ Initializer [96] , [133], [123] [132], [150] ✓ Consistency [177], [214] ✓ Consistency [146], [131] ✓ Consistency [176], [84] ✓ Conflict [143], [126] , [173] ✓ Conflict 1. Due to explicit analytical equations or models that define clear input-output mathematical relationships, explicit knowledge is the most common way for building PIML. It is widely used in the construction of "simulators", "extractors", "operators", and "consistency checks". ...
... The I&M decision problem is here formulated as a POMDP, which is then solved through the SAR-SOP point-based solver (Kurniawati et al., 2008). The reader is directed to (Hlaing et al., 2022) for a more detailed description of this case study. ...
The application of Deep Reinforcement Learning (DRL) for the management of engineering systems has shown very promising results in terms of optimality and scalability. The interpretability
of these policies by decision-makers who are so far mostly familiar with traditional approaches is also needed for implementation.
In this work, we address this topic by providing a comprehensive overview of POMDP- and DRL-based management policies, along with simulation-based implementation details, for facilitating their interpretation. By mapping a sufficient statistic, namely a belief state, to the current optimal action, POMDP-DRL strategies are able to automatically adapt in time considering long-term sought
objectives and the prior history. Through simulated policy realizations, POMDP-DRL-based strategies identified for representative inspection and maintenance planning settings are thoroughly analyzed.
The results reveal that if the decision-maker opts for an alternative, even suboptimal, action other than the one suggested by the DRL-based policy, the belief state will be accordingly updated and can still be used as input for the remainder of the planning horizon, without any requirements for model retraining.
... More recently, there has been an increased interest in fatigue crack growth methods for marine structures, needed for the development of rational prognosis approaches [11,12,26,27,28,29,30] as well as inspection and maintenance planning schemes [31,32,33,34,35,36]. Counting few exceptions, research studies considering crack interaction effects cannot, however, be easily found [26,27,29]. ...
The structural integrity of marine structures is significantly influenced in many practical applications by their fatigue behavior, especially when dealing with dynamically sensitive structural systems, e.g., offshore wind substructures. The propagation of cracks found in structural components can be estimated through fracture mechanics-based methods, in which the crack growth under cyclic loading is mainly driven by the stress intensity factor (SIF). To simplify the computation of the SIF, closed-form solutions are often suggested in industrial standards, yet their applicability is limited to specific geometries and loading conditions. Overcoming the aforementioned constraints, we propose here a general methodology for numerically simulating the SIF and growth of multiple cracks by computing the SIF of adjacent cracks in a unified finite element analysis, in which interaction effects are implicitly considered. In our proposed method, the coalescence of bordering cracks is also adequately modeled and fatigue failure is defined based on fracture mechanics principles. With the objective of enabling an efficient SIF computation , we also provide the necessary modeling details for the appropriate implementation of the corresponding finite element analysis. The proposed methodology is then tested and validated in a finite thickness plate under cyclic loading setting, whereas in a more practical case study, we investigate the fatigue analysis of interacting surface cracks in an offshore wind welded connection. The results emphasize the importance of considering interaction effects and crack coalescence when simulating the fatigue evolution of structural details in practical applications, and within the study, specific insights are additionally provided for the fatigue analysis of offshore wind structural components. With respect to the investigated fatigue failure criteria, the results show that a through-thickness limit state might yield overly conservative fatigue life estimates compared to the fatigue limit that results when failure is defined based on the material fracture toughness.
... Combined with engineering models, manual and/or robotic inspections can be conducted in order to reduce the uncertainties associated with deterioration estimations, hence supporting more rational and informed maintenance decisions. 1,2 With the advent of modern sensor technologies, monitoring systems are increasingly being deployed with the objective of continuously monitoring the deterioration experienced by offshore wind structures, thus also enabling decision-makers to make timely and informed decisions. 3,4 For example, fatigue load monitoring through strain gauges provides valuable information that can be used to estimate the remaining useful fatigue lifetime [5][6][7] and/or to update probabilistically modeled time-varying deterioration mechanisms. ...
Offshore wind structures are subject to deterioration mechanisms throughout their operational lifetime. Even if the deterioration evolution of structural elements can be estimated through physics-based deterioration models, the uncertainties involved in the process hurdle the selection of lifecycle management decisions. In this scenario, the collection of relevant information through an efficient monitoring system enables the reduction of uncertainties, ultimately driving more optimal lifecycle decisions. However, a full monitoring instrumentation implemented on all wind turbines in a farm might become unfeasible due to practical and economical constraints. Besides, certain load monitoring systems often become defective after a few years of marine environment exposure. Addressing the aforementioned concerns, a farm-wide virtual load monitoring scheme directed by a fleet-leader wind turbine offers an attractive solution. Fetched with data retrieved from a fully-instrumented wind turbine, a model can be trained and then deployed, thus yielding load predictions of non-fully monitored wind turbines, from which only standard data remains available. In this paper, we propose a virtual load monitoring framework formulated via Bayesian neural networks (BNNs) and we provide relevant implementation details needed for the construction, training, and deployment of BNN data-based virtual monitoring models. As opposed to their deterministic counterparts, BNNs intrinsically announce the uncertainties associated with generated load predictions and allow to detect inaccurate load estimations generated for non-fully monitored wind turbines. The proposed virtual load monitoring is thoroughly tested through an experimental campaign in an operational offshore wind farm and the results demonstrate the effectiveness of BNN models for fleet-leader-based farm-wide virtual monitoring.
... Some methods focus on the optimization of predefined static decision rules, planning inspections at equidistant intervals or when a prescribed failure probability threshold is surpassed, and prescribing maintenance interventions if a certain damage indicator is observed, e.g., crack detection [6,11,12,13]. While these approaches can provide reasonable and effective policies in some specific scenarios, the optimality of the policies depends greatly on the designer's experience when defining the heuristic combinations for the policy search, since they cannot consider all policies within the vast available policy space, which could in turn result more optimal than the originally considered predefined heuristics [14,15]. In other existing methods, while inspection planning decision rules are defined a priori, the maintenance policy is adaptive, properly updating the involved thresholds based on new information [16,17]. ...
In the context of modern environmental and societal concerns, there is an increasing demand for methods able to identify management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies.
... Bayesian inference can then be conducted every one or two years, thus continuously reducing the statistical uncertainty. It is worth-noting that, the Weibull scale parameter can be considered as a time-invariant random variable in certain decision-making tasks in order to attenuate the computational demand associated to modelling the stochastic deterioration process (Hlaing N. , et al., 2022;Morato, Papakonstantinou, Andriotis, Nielsen, & Rigo, 2022). In that case, the uncertainty of the Weibull scale parameter, once updated through strain sensor data, will not increase, and the applicability of the virtual monitoring will be limited. ...
In this work, a virtual load monitoring framework is proposed for deriving a mapping from either high or low frequency (1-Hz /10-minute time averaged) SCADA data to load signals, while preserving the high frequency dynamic components of the latter. Specifically, the proposed virtual load monitoring scheme relies on a data-driven model that receives features retrieved from SCADA data and yields the probability distribution of the structural response. The constituent neural networks are trained via supervised learning based on the labelled data retrieved while strain sensors are still functional, since at that operational stage, both SCADA and structural response can be collected concurrently. Once the strain sensors are not functional, the trained deep neural network is deployed, providing structural response predictions from on-site SCADA data. The proposed virtual monitoring approach is tested on a monopile-supported offshore wind turbine and cross-validated in terms of the predicted stress range distribution of a structural connection located at the mudline. The results show good agreement between structural response predictions and measurements, thus demonstrating the efficacy and utility of the tested scheme.
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Offshore wind turbine (OWT) support structures need to be designed against fatigue failure under cyclic aerodynamic and wave loading. The fatigue failure can be accelerated in a corrosive sea environment. Traditionally, a stress–life approach called the S–N (stress–number of cycles) curve method has been used for the design of structures against fatigue failure. There are a number of limitations in the S–N approach related to welded structures which can be addressed by the fracture mechanics approach. In this paper the limitations of the S–N approach related to OWT support structure are addressed and a fatigue design framework based on fracture mechanics is developed. The application of the framework to a monopile OWT support structure is demonstrated and optimisation of in-service inspection of the structure is studied. It was found that both the design of the weld joint and non-destructive testing (NDT) techniques can be optimised to reduce in-service inspection frequency. Furthermore, probabilistic fracture mechanics as a form of risk-based design is outlined and its application to the monopile support structure is studied. The probabilistic model showed a better capability to account for NDT reliability over a range of possible crack sizes as well as to provide a risk associated with the chosen inspection time which can be used in inspection cost–benefit analysis. There are a number of areas for future research, including a better estimate of fatigue stress with a time-history analysis, the application of the framework to other types of support structures such as jackets and tripods, and integration of risk-based optimisation with a cost–benefit analysis.
In most structural systems, it is neither possible nor optimal to inspect all system components regularly. An optimal inspection-repair strategy controls deterioration in structural systems efficiently with limited cost and acceptable reliability. At present, an integral risk-based optimization procedure for entire structural systems is not available; existing risk-based inspection methods are limited to optimizing inspections component by component. The challenges to an integral approach lie in the large number of optimization parameters in the inspection-repair process of a structural system, and the need to perform probabilistic inference for the entire system at once to address interdependencies among all components. In this paper, we outline a methodology for an integral risk-based optimization of inspections in structural systems, which utilizes a heuristic approach to formulating the optimization problem. It takes basis in a recently developed dynamic Bayesian network (DBN) framework for rapid computation of the system reliability conditional on inspection results. The optimization problem is solved by nesting the DBN inside a Monte-Carlo simulation for computing the expected cost associated with a system-wide inspection strategy. The proposed methodology is applied to a structural system subject to fatigue deterioration and it is demonstrated that it enables an integral risk-based inspection planning for structural systems.
The continued growth of the offshore wind industry will depend essentially on reductions in wind energy production cost. Large cost reductions can be achieved through efficient, economic and optimised wind turbine support structures. To achieve maximum offshore wind adoption beyond 2020, significant industrial and research efforts are being made in optimised material selection and application. Fatigue and corrosion damage are the greatest challenges today in design and life estimation of wind turbine support structures. S355 steel is currently used in fabrication of most wind turbine monopile support structures. Clear understanding of their corrosion-fatigue properties and accurate steel selection will support the optimisation and economic design of extra-large wind turbines. This paper presents the fatigue crack growth test results of advanced S355 TMCP steel in air and seawater, and compares the results with studies on commonly available S355 steel. The results show that S355 TMCP steels generally offer higher fatigue damage tolerance than normalised S355 steels in air and the factor decreases and tends towards a common value with increase in stress intensity factor range. However, in seawater there is no significant difference in fatigue crack growth rates for all the S355 ferritic steels considered in this study.
This paper presents a computational framework for risk-based planning of inspections and repairs for deteriorating components. Two distinct types of decision rules are used to model decisions: simple decision rules that depend on constants or observed variables (e.g. inspection outcome), and advanced decision rules that depend on variables found using Bayesian updating (e.g. probability of failure). Two decision models are developed, both relying on dynamic Bayesian networks (dBNs) for deterioration modelling. For simple decision rules, dBNs are used directly for exact assessment of total expected life-cycle costs. For advanced decision rules, simulations are performed to estimate the expected costs, and dBNs are used within the simulations for decision-making. Information from inspections and condition monitoring are included if available. An example in the paper demonstrates the framework and the implemented strategies and decision rules, including various types of condition-based maintenance. The strategies using advanced decision rules lead to reduced costs compared to the simple decision rules when condition monitoring is applied, and the value of condition monitoring is estimated by comparing the lowest costs obtained with and without condition monitoring.
Development of reliability-based management of inspection, monitoring, maintenance and repair (IMMR) of various types of offshore structures is described, with a focus on management of hull damage due to crack growth and corrosion. Operational experiences with respect to degradation of various types of offshore structures are summarized. The interrelation between design criteria and IMMR is emphasized. Explicit design for robustness in terms of an accidental collapse limit state and monitoring by the use of the leak before break principle to identify damage are highlighted. It is shown how design for robustness, choice of inspection method and scheduling as well as repair strategy, need to be implemented to obtain an acceptable risk for various types of offshore structures. Finally, the particular features of reliability based structural reassessment for extension of the service life, are briefly outlined and exemplified.
The failure of a structure is bounded by two extremes of behaviour: linear elastic and fully plastic. The procedures developed within the C.E.G.B. for assessing the effect of defects on the integrity of structures require the user to define the state of the structure in terms of each of these two extremes in turn. This is done by calculating the ratio of the applied loading condition to that required to cause failure. These two ratios then form the coordinates of a point on a failure assessment diagram. If the point falls inside the assessment line on that diagram, failure is avoided. The approach is extremely versatile in operation. The methods used to define the two ratios are chosen and justified by the user. This allows full advantage to be taken of a wide range of such methods, and the successive refinement of those methods for selected aspects as the assessment proceeds and the critical areas are identified. In addition, methods for dealing with specific problems such as thermal and residual stresses and ductile crack growth are shown to be readily incorporated.
A generic framework for stochastic modeling of deterioration processes is proposed, based on dynamic Bayesian networks (DBN). The framework facilitates computationally efficient and robust reliability analysis and, in particular, Bayesian updating of the model with measurements, monitoring and inspection results. These properties make it ideally suited for near-real time applications in asset integrity management and deterioration control. The framework is demonstrated and investigated through two applications of probabilistic fatigue crack growth modeling.
A probabilistic approach is proposed to help select the most suitable nondestructive inspection NDI technique and associated optimal schedule for fracture-critical member/detail fatigue inspections on a specific steel bridge. The probability of detection POD function for the NDI technique, which is a measure of the detection accuracy, is employed. By combining probability calculations based on use of the POD function together with numerical Monte Carlo simulations of the crack propagation of the fracture-critical detail, a cost function is formulated that includes the expected cost of inspections and failure resulting from the chosen NDI technique and alternative inspection schedules. In summary, the selection of an NDI technique with an associated inspection schedule for fracture-critical inspec-tions is formulated as an optimization problem that can guarantee minimum total cost. The inspection frequency is determined as part of the optimization that utilizes appropriate constraints on inspection intervals and a minimum acceptable target structural safety level. A case study for a box girder bridge is presented to demonstrate the application of the proposed probabilistic method.
Bridge maintenance and replacement optimization methods use deterioration models to predict the future condition of bridge components. The purpose of this paper is to develop a framework for bridge maintenance optimization using a deterioration model that takes into account aspects of the history of the bridge condition and maintenance, while allowing the use of efficient optimization techniques. Markovian models are widely used to represent bridge component deterioration. In existing Markovian models, the state is the bridge component condition, and the history of the condition is not taken into account, which is seen as a limitation. This paper describes a method to formulate a realistic history-dependent model of bridge deck deterioration as a Markov chain, while retaining aspects of the history of deterioration and maintenance as part of the model. This model is then used to formulate and solve a reliability-based bridge maintenance optimization problem as a Markov decision process. A parametric study is conducted to compare the policies obtained in this research with policies derived using a simpler Markovian model.
Motion planning in uncertain and dynamic environments is an essential capability for autonomous robots. Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for solving such problems, but they are often avoided in robotics due to high computational complexity. Our goal is to create practical POMDP algorithms and software for common robotic tasks. To this end, we have developed a new point-based POMDP algorithm that exploits the notion of optimally reachable belief spaces to improve computational efficiency. In simulation, we successfully applied the algorithm to a set of common robotic tasks, including instances of coastal navigation, grasping, mobile robot exploration, and target tracking, all modeled as POMDPs with a large number of states. In most of the instances studied, our algorithm substantially outperformed one of the fastest existing point-based algorithms. A software package implementing our algorithm will soon be released at
for the 2 nd ASRANET Colloquium KEYNOTES Risk based inspection planning, fatigue deterioration, Bayesian decision theory, structural reliability ABSTRACT Engineering systems are ideally designed to ensure an economical operation throughout the anticipated service life in compliance with given requirements and acceptance criteria. Such acceptance criteria are typically related to the safety of personnel and risk to environment. Deterioration processes such as fatigue crack growth and corrosion will always be present to some degree and depending on the adapted design philosophy in terms of degradation allowance and protective measures the deterioration processes may reduce the performance of the system beyond what is acceptable. In order to ensure that the given acceptance criteria are fulfilled throughout the service life of the engineering systems it may thus be necessary to control the development of deterioration and if required to install corrective maintenance measures. In usual practical applications inspection is the most relevant and effective means of deterioration control.
Civil and maritime engineering systems, among others, from bridges to offshore platforms and wind turbines, must be efficiently managed, as they are exposed to deterioration mechanisms throughout their operational life, such as fatigue and/or corrosion. Identifying optimal inspection and maintenance policies demands the solution of a complex sequential decision-making problem under uncertainty, with the main objective of efficiently controlling the risk associated with structural failures. Addressing this complexity, risk-based inspection planning methodologies, supported often by dynamic Bayesian networks, evaluate a set of pre-defined heuristic decision rules to reasonably simplify the decision problem. However, the resulting policies may be compromised by the limited space considered in the definition of the decision rules. Avoiding this limitation, Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical methodology for stochastic optimal control under uncertain action outcomes and observations, in which the optimal actions are prescribed as a function of the entire, dynamically updated, state probability distribution. In this paper, we combine dynamic Bayesian networks with POMDPs in a joint framework for optimal inspection and maintenance planning, and we provide the relevant formulation for developing both infinite and finite horizon POMDPs in a structural reliability context. The proposed methodology is implemented and tested for the case of a structural component subject to fatigue deterioration, demonstrating the capability of state-of-the-art point-based POMDP solvers of solving the underlying planning stochastic optimization problem. Within the numerical experiments, POMDP and heuristic-based policies are thoroughly compared, and results showcase that POMDPs achieve substantially lower costs as compared to their counterparts, even for traditional problem settings.
Structural deterioration due to environmental and mechanical stressors is a major concern for civil and marine structures. Inspection actions can reduce uncertainties, facilitate decision-making on maintenance, and in general assist life-cycle management. Risk-based inspection (RBI) planning is a useful tool to minimize life-cycle cost while preserving safety margin of structures. This paper compares (a) static RBI (SRBI) planning where inspection schedule and maintenance criteria are time- and evidence-invariant and (b) adaptive RBI (ARBI) planning where decisions on inspection and maintenance (I&M) are made sequentially and reactively to I&M actions. Specifically, three RBI planning methods, i.e., SRBI with Monte Carlo simulation, ARBI based on Bayesian networks, and ARBI based on partially observable Markov decision processes (POMDP), are compared based on a generic Markovian deterioration model (MDM). In addition, it is demonstrated that ARBI planning can be extended from MDMs to many physics-based deterioration models such as corrosion and fatigue models. The advantages and disadvantages of different RBI planning methods are summarized. Potentials of ARBI planning are also discussed.
Determination of inspection and maintenance policies for minimizing long-term risks and costs in deteriorating engineering environments constitutes a complex optimization problem. Major computational challenges include the (i) curse of dimensionality, due to exponential scaling of state/action set cardinalities with the number of components; (ii) curse of history, related to exponentially growing decision-trees with the number of decision-steps; (iii) presence of state uncertainties, induced by inherent environment stochasticity and variability of inspection/monitoring measurements; (iv) presence of constraints, pertaining to stochastic long-term limitations, due to resource scarcity and other infeasible/undesirable system responses. In this work, these challenges are addressed within a joint framework of constrained Partially Observable Markov Decision Processes (POMDP) and multi-agent Deep Reinforcement Learning (DRL). POMDPs optimally tackle (ii)-(iii), combining stochastic dynamic programming with Bayesian inference principles. Multi-agent DRL addresses (i), through deep function parametrizations and decentralized control assumptions. Challenge (iv) is herein handled through proper state augmentation and Lagrangian relaxation, with emphasis on life-cycle risk-based constraints and budget limitations. The underlying algorithmic steps are provided, and the proposed framework is found to outperform well-established policy baselines and facilitate adept prescription of inspection and intervention actions, in cases where decisions must be made in the most resource- and risk-aware manner.
Offshore Wind Turbine (OWT) support structures are subjected to harsh deterioration mechanisms due to the combined action of wind loading, sea induced load actions and corrosive environment. Fatigue failure becomes a key failure mode for offshore wind structures, as they experience considerable number of stress cycles (more than 10 million cycles per year). Fatigue failure can be assessed through fatigue assessment approaches. However, such assessments possess various uncertainties which may be quantified and updated through findings from in-service inspections. Since, offshore maintenance actions incur significant costs, an optimal maintenance strategy which balances the maintenance efforts against the risk of failure is desired. Based on pre-posterior decision theory, a risk-informed maintenance optimization can be performed to define the optimal maintenance strategy and support the decision maker(s). Within the risk maintenance optimization scheme, the probabilistic deterioration model is updated based on the inspection outcomes. Several fracture mechanics models have been used in the literature to estimate the deterioration of the structure containing flaws. Although, a through-thickness failure criterion is commonly used in the literature as the failure criteria, a Failure Assessment Diagram (FAD) approach has been receiving increasingly attention, as well. This investigation examines the effect of the selected fracture mechanics models and failure criteria on the optimal maintenance strategy. Moreover, the obtained maintenance strategies corresponding to different fracture mechanics models are compared for a tubular joint case study structure.
In this paper, the procedure for flaw acceptability assessment is examined through a case study of a semi-elliptical surface crack in an offshore monopile as it grows till it forms a through thickness crack. Using the procedure prescribed in an industrial standard (BS 7910), the fracture ratio, Kr is shown to increase monotonically with increasing crack depth. The load ratio, Lr, is initially insensitive to the crack depth. However, there is a rapid increase in Lr when the crack depth to thickness ratio exceeds 80%. Lr values obtained from detailed 3D FE limit analysis using elastic-perfectly-plastic material behaviour do not exhibit the asymptotic behaviour predicted by BS 7910 as the flaw transitions from deep crack to through-thickness crack. Furthermore, Kr predicted by BS 7910 is shown to be an over-estimation for the typical dimensions of offshore monopiles. The findings suggest that a structure with a deep flaw may be identified as unacceptable based on BS 7910 when it may still possess a non-trivial amount of structural residual life. This is a concern for monopiles where crack growth as a large flaw forms a significant part of the total life.
Optimum inspection and maintenance planning is essential for the successful management of deteriorating structures. The reliability and accuracy of inspection and maintenance planning can be significantly improved by integrating new information obtained from inspections. For this reason, the inspection and maintenance planning should include an updating process after each inspection. This paper presents such a probabilistic approach for optimum inspection and maintenance planning. The proposed approach includes two multi-objective optimization (MOOP) processes before and after damage detection for effective updating. The first MOOP before damage detection is performed to determine the optimum inspection times by minimizing both the expected damage detection delay and expected total inspection cost. The fatigue crack detected at the inspection time scheduled from the first MOOP is used to update the probabilistic fatigue crack propagation. The updated crack propagation is applied to formulate the second MOOP, which determines the optimum times for maintenance with the objectives of minimizing both the expected maintenance delay and expected total inspection cost. The decision making process is applied to select the best Pareto solution from the Pareto optimal solutions of the first and second MOOPs. The proposed approach is applied to a fatigue critical detail of an existing steel bridge.
Bridges, ships, and other civil and marine structures are subjected to fatigue damage due to repeated load fluctuations. Fatigue damage is likely to jeopardize the functionality and even structural safety of these structures. Therefore, inspections and timely repair actions are needed to ensure adequate structural performance throughout their lifetime. Nevertheless, inspection/repair actions involve additional life-cycle costs. Therefore, efficient planning of inspection and repair actions of fatigue-critical details are not only essential to ensure structural functionality and safety, but also important to control the total life-cycle cost. In this paper, a novel framework for optimizing inspection/repair planning is developed by using efficient Bayesian updating with dynamic Bayesian network. Specifically, inspection plans, including inspection schedules and inspection techniques, are optimized using pre-posterior analysis. Decisions of repair actions are made based on inspection results following an evidence-informed and cost-driven repair strategy. This strategy allows for time-dependent and adaptive repair actions considering fatigue damage development, available inspection results, and previous repair actions. Optimal inspection/repair plans with the lowest expected life-cycle cost are then obtained using both single- and multi-objective optimizations.
Optimized maintenance of operating aging infrastructures is of paramount importance to ensure safe and cost effective operation during their original design lifetime and even beyond that. Modern answers to the problem should focus on automated planning and decision making techniques taking advantage of informative but uncertain data that become available during the structural life-cycle. In this paper such a solution framework is presented, based on partially observable Markov decision processes (POMDPs). In a
POMDP framework, the evolution of the system is described by stochastic processes, real-time observation data update the system state estimations, and all possible future actions, about where, when and what type of inspection and repair should be performed, are taken into account in order to optimize the long-term life-cycle objectives. As a consequence of their advanced mathematical attributes, POMDP models are unfortunately hard to solve. In recent years, however, significant breakthroughs have been achieved, mainly due to the introduction of point-based value iteration algorithms. In this work, several POMDP point-based methods are examined, with various characteristics in the selection of the belief space points/subset and the value function update procedures. To investigate the strengths and limitations of the various solution methods for structural maintenance problems of deteriorating infrastructure and to draw conclusions regarding their efficiency and applicability to problems of this kind, a realistic nonstationary example is selected, concerning corrosion of reinforcing bars of concrete structures in a spatial stochastic context.
The operation and maintenance cost of offshore wind tur- bine substructures contributes significantly in the cost of a kWh. That cost may be lowered by application of reliability- and risk- based maintenance strategies and reliability updating based on inspections performed during the design lifetime. Updating the reliability of a welded joint can theoretically be done using Bayesian updating. However, for tubular joints in offshore wind turbine substructures when considering a two dimensional crack growth and a failure criterion combining brittle fracture and ma- terial strength, the updating is quite complex due to the wind turbine loading obtained during operation. This paper solves that updating problem by using the Failure Assessment Diagram as a limit state function. It is discussed how application of the updating procedure can be used for inspection planning for off- shore wind turbine substructures, and thus also for reducing the required safety factors at the design stage.
To estimate and update the reliability of deteriorating structural systems with inspection and monitoring results, we develop a modeling and computational framework based on dynamic Bayesian networks (DBNs). The framework accounts for dependence among deterioration at different system components and for the complex structural system behavior. It includes the effect of inspection and monitoring results, by computing the updated reliability of the system and its components based on information from the entire system. To efficiently model dependence among component deterioration states, a hierarchical structure is defined. This structure facilitates Bayesian model updating of the components in parallel. The performance of the updating algorithm is independent of the amount of included information, which is convenient for large structural systems with detailed inspection campaigns or extensive monitoring. The proposed model and algorithms are applicable to a wide variety of structures subject to deterioration processes such as corrosion and fatigue, including offshore platforms, bridges, ships, and aircraft structures. For illustration, a Daniels system and an offshore steel frame structure subjected to fatigue are investigated. For these applications, the computational efficiency of the proposed algorithm is compared with that of a standard Markov Chain Monte Carlo algorithm and found to be orders of magnitude higher.
Fatigue is one of the main deteriorating mechanisms that affect the safety and reliability of ship structures. Fatigue cracks can appear at various locations along the ship structure and may occur at early stages in the service life of a ship. Inspection, monitoring and/or repair actions are applied to prevent sudden failures of damaged structural components and their associated consequences. However, these actions increase the operational cost of the ship and should be optimally planned during its service life. Due to the presence of significant uncertainties associated with crack initiation and propagation, the planning of such actions should be performed probabilistically. In this paper, a probabilistic approach for inspection, monitoring, and maintenance optimization for ship details under fatigue effects is proposed. Based on the stress profile and the crack geometry at the damaged location, intervention times and types are determined by solving an optimization problem which simultaneously minimizes the life-cycle cost, maximizes the expected service life, and minimizes the expected maintenance delay over the life-cycle. The life-cycle cost includes the cost of inspection, monitoring, and maintenance actions, as well as the cost of failure of the detail. The proposed approach is applied to a side shell detail of a steel ship.
Due to the nature of the fatigue phenomena it is well known that small changes in basic assumptions for fatigue analysis can have significant influence on the predicted crack growth lives. Calculated fatigue lives based on the S–N approach are sensitive to input parameters. Fracture mechanics analysis is required for prediction of crack sizes during service life in order to account for probability of detection after an inspection event. Analysis based on fracture mechanics needs to be calibrated to that of fatigue test data or S–N data. Calculated probabilities of fatigue failure using probabilistic methods are even more sensitive to the analysis methodology and to input parameters used in the analyses. Thus, use of these methods for planning inspection requires considerable knowledge and engineering skill. Therefore the industry has asked for guidelines that can be used to establish reliable inspection results using these methods. During the last years DNV GL has performed a joint industry project on establishing probabilistic methods for planning in-service inspection for fatigue cracks in offshore structures. The recommendations from this project are now included in a Recommended Practice. The essential features of the probabilistic methods developed for this kind of inspection planning are described in this paper.
Operation and maintenance of an infrastructure system rely on information collected on its components, which can provide the decision maker with an accurate assessment of their condition states. However, resources to be invested in data gathering are usually limited and observations should be collected based on their Value of Information (VoI). Assessing the VoI is computationally intractable for most applications involving sequential decisions, such as long-term infrastructure maintenance. In this article, we propose an approach for integrating adaptive maintenance planning based on Partially Observable Markov Decision Process (POMDP) and inspection scheduling based on a tractable approximation of VoI. Two alternative myopic approaches, namely pessimistic and optimistic, are introduced, and compared theoretically and by numerical examples.
Partially Observable Markov Decision Processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent’s belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Contrary to other point-based methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems.
The overall objective of this two part study is to highlight the advanced attributes, capabilities and use of stochastic control techniques, and especially Partially Observable Markov Decision Processes (POMDPs), that can address the conundrum of planning optimum inspection/monitoring and maintenance policies based on stochastic models and uncertain structural data in real time. In this second part of the study a distinct, advanced, infinite horizon POMDP formulation with 332 states is cast and solved, related to a corroding reinforced concrete structure and its minimum life-cycle cost. The formation and solution of the problem modernize and extend relevant approaches and motivate use of POMDP methods in challenging practical applications. Apart from uncertain observations the presented framework can also support uncertain action outcomes, non-periodic inspections and choice availability of inspection/monitoring types and intervals, as well as maintenance actions and action times. It is thus no surprise that the estimated optimum policy consists of a complex combination of a variety of actions, which cannot be achieved by any other method. To be able to solve the problem we resort to a point-based value iteration solver and we evaluate its performance and solution quality for this type of applications. Simpler approximate solvers based on MDPs are also used and compared and the important notions of observation gathering actions and the value of information are briefly discussed.
To address effectively the urgent societal need for safe structures and infrastructure systems under limited resources, science-based management of assets is needed. The overall objective of this two part study is to highlight the advanced attributes, capabilities and use of stochastic control techniques, and especially Partially Observable Markov Decision Processes (POMDPs), that can address the conundrum of planning optimum inspection/monitoring and maintenance policies based on stochastic models and uncertain structural data in real time. Markov Decision Processes are in general controlled stochastic processes that move away from conventional optimization approaches in order to achieve minimum life-cycle costs and advice the decision-makers to take optimum sequential decisions based on the actual results of the inspections or the non-destructive testings they perform. In this first part of the study we exclusively describe, out of the vast and multipurpose stochastic control field, methods that are fitting for structural management, starting from simpler to sophisticated techniques and modern solvers. We present Markov Decision Processes (MDPs), semi-MDP and POMDP methods in an overview framework, we have related each of these to the others, and we have described POMDP solutions in many forms, including both the problematic grid-based approximations that are routinely used in structural maintenance problems, and the advanced point-based solvers capable of solving large scale, realistic problems. Our approach in this paper is helpful for understanding shortcomings of the currently used methods, related complications, possible solutions and the significance the different solvers have, not only on the solution but also on the modeling choices of the problem. In the second part of the study we utilize almost all presented topics and notions in a very broad, infinite horizon, minimum life-cycle cost structural management example and we focus on point-based solvers implementation and comparison with simpler techniques, among others.
A formulation of optimal design, inspection and maintenance against damage caused by fatigue crack growth is formulated. A stochastic model for fatigue crack growth based on linear elastic fracture mechanics is applied. Failure is defined by crack growth beyond a critical crack size. The failure probability and associated sensitivity factors are computed by first-order reliability methods. Inspection reliability is included through a pod (probability of detection) curve. Optimization variables are structural design parameters, inspection times and qualities. The total expected cost of design, inspection, repair and failure is minimized with a constraint on the life time reliability.
This paper presents an empirical stress-intensity factor equation for a surface cracks as a function of parametric angle, crack depth, crack length, plate thickness and plate width for tension and bending loads. The stress-intensity factors used to develop the equation were obtained from a previous three-dimensional, finite-element analysis of semielliptical surface cracks in finite elastic plates subjected to tension or bending loads. A wide range of configuration parameters was included in the equation. The ratios of crack length to plate thickness and the ratios of crack depth to crack length ranged from 0 to 1.0. The effects of plate width on stress-intensity variations along the crack front were also included.The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. The equation was also used to correlate surface-crack fracture data for a brittle epoxy material within ± 10 percent for a wide range of crack shapes and crack sizes.
The utilization of Markov decision processes as a sequential decision algorithm in the management actions of infrastructure (inspection, maintenance and repair) is discussed. The realistic issue of partial information from inspection is described, and the classic approach of partially observable Markov decision processes is then introduced. The use of this approach to determine optimal inspection strategies is described, as well as the role of deterioration and maintenance for steel structures. Discrete structural shapes and maintenance actions provide a tractable approach. In-service inspection incorporates Bayesian updating and leads to optimal operation and initial design. Finally, the concept of management policy is described with strategy vectors.
A comprehensive treatment of fracture mechanics suitable as a graduate
text and as a reference for engineers and researchers is presented. The
general topics addressed include: fundamental concepts of linear elastic
and elastic-plastic fracture mechanics; dynamic and time-dependent
fracture mechanics; micromechanisms of fracture in metals and alloys;
fracture mechanisms in polymers, ceramics, and composites; applications
to fracture toughness testing of metals and nonmetals, to structures,
fatigue crack propagation, and computational fracture mechanics.
Reference materials usually found in fracture mechanics handbooks is
provided.
Detection Theory is an introduction to one of the most important tools for analysis of data where choices must be made and performance is not perfect. Originally developed for evaluation of electronic detection, detection theory was adopted by psychologists as a way to understand sensory decision making, then embraced by students of human memory. It has since been utilized in areas as diverse as animal behavior and X-ray diagnosis. This book covers the basic principles of detection theory, with separate initial chapters on measuring detection and evaluating decision criteria. Some other features include: complete tools for application, including flowcharts, tables, pointers, and software;. student-friendly language;. complete coverage of content area, including both one-dimensional and multidimensional models;. separate, systematic coverage of sensitivity and response bias measurement;. integrated treatment of threshold and nonparametric approaches;. an organized, tutorial level introduction to multidimensional detection theory;. popular discrimination paradigms presented as applications of multidimensional detection theory; and. a new chapter on ideal observers and an updated chapter on adaptive threshold measurement. This up-to-date summary of signal detection theory is both a self-contained reference work for users and a readable text for graduate students and other researchers learning the material either in courses or on their own. © 2005 by Lawrence Erlbaum Associates, Inc. All rights reserved.
Nondestructive inspection tools are commonly used to inspect structures or structural components with resistance deterioration due to defect size growth. The quality of the tools is mainly defined by the rate of detecting a defect with defect size s, ϱ(s), and the accuracy in sizing a detected defect. The uncertainty of sizing a detected defect can be incorporated in limit state functions that include defect size, and a reliability evaluation can be carried out with the efficient first-order reliability method (FORM). The rate of detecting a defect can also be incorporated in the reliability evaluation of an inspected structure or structural component. This is done, in this paper, by introducing a standard normally distributed variate, Z, and defining a limit state function as a function of and ϱ(s). Advantages of using this limit state function, rather than using a limit state function based on the actual defect size and the critical defect size distributed according to the rate of detection curve, are discussed. It is shown that one only needs to use the mean rate of defect detection curve to consider the uncertainty in the rate of detection. The incorporation of the uncertainty in rate of detection for reliability updating analysis with inspection results, and for reliability-based selection of optimal inspection and maintenance schedule for resistance deteriorating structures are also presented. The proposed approach is illustrated by two examples in evaluating reliability with inspection information and in selecting an optimal inspection and maintenance schedule by minimizing the probability of time to failure before inspection and before the time at the end of remaining service life.
Risk based inspection (RBI) planning for engineering systems is considered. Due to difficulties in formulating computationally tractable approaches for RBI for systems, most procedures hitherto have focused exclusively on individual components or have considered system effects in a very simplified manner only. Several studies have pointed to the importance of taking systems effect into account in inspection planning. Especially for large engineering systems it is not possible to identify cost optimal solutions if the various types of functional and statistical dependencies in the systems are not explicitly addressed. Based on new developments in RBI for individual components, the present paper presents an integral approach for the consideration of entire systems in inspection planning. The various aspects of dependencies in the systems are presented and discussed, followed by an introduction to the decision problems encountered in inspection and maintenance planning of structural systems. It is then shown how these decision problems can be consistently represented by decision theoretical models. The presentation of a practical procedure for the inspection planning for steel structures subject to fatigue concludes the paper.
The two-criteria approach to the study of defects in structures assumes that failure occurs when the applied load reaches the lower of either a load to cause brittle failure in accordance with the theories of linear elastic fracture mechanics or a collapse load dependent on the ultimate stress of the material and the structural geometry. This simple approach is described and compared with previously published experimental results for various geometries and materials. The simplicity of this method of defect analysis lies in the fact that each criterion is sufficiently well understood to permit scaling and geometry changes to be accommodated readily.It becomes apparent that a sizeable transition region exists between the two criteria but this can be described in an expression relating the criteria. This expression adequately predicts the behaviour of cracked structures of both simple and complex geometry. A design curve for defect assessment is proposed for which it is unnecessary to consider the transition region.
Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agents belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Contrary to other point-based methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems.
The practice of attempting validation of crack-propagation laws (i.e., the laws of Head, Frost and Dugdale, McEvily and Illg, Liu, and Paris) with a small amount of data, such as a few single specimen test results, is questioned. It is shown that all the laws, though they are mutually contradictory, can be in agreement with the same small sample of data. It is suggested that agreement with a wide selection of data from many specimens and over many orders of magnitudes of crack-extension rates may be necessary to validate crack-propagation laws. For such a wide comparison of data a new simple empirical law is given which fits the broad trend of the data.
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BS7910:2019 Guide to methods for assessing the acceptability of flaws in metallic structures
- British Standards
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flaws in metallic structures. (BSI Standards Publication). 389 Chiswick High Rd, Chiswick,
London W4 4AL, United Kingdom.
A fracture mechanics approach to the assessment of the remaining fatigue life of defective welded joints
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Dijkstra, O. (1991). A fracture mechanics approach to the assessment of the remaining fatigue
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