A Markov resilience assessment framework for tension leg platform under mooring failure

https://doi.org/10.1016/j.ress.2022.108939Get rights and content

Highlights

  • Novel resilience assessment framework for TLP under mooring failure is generated.

  • The failure process and recovery process are modeled by Markov process and continuous-time Markov process, respectively.

  • Two resilience metrics are defined to measure different aspects of resilience.

  • The effect of extreme environment, structural degradation, recovery rate and strength on system resilience is considered.

Abstract

During the service life of Tension Leg Platform (TLP), it may be exposed to various risk, with mooring failure being one of the most catastrophic events. Resilience, as an integrated assessment philosophy, can evaluate the overall post-event response performance and further improve system's operation safety. In this paper, a Markov resilience assessment framework for TLP under mooring failure is firstly proposed. The failure process and recovery process are mathematically described by Markov process and continuous-time Markov process, respectively. The internal and external effect has been taken into account, including extreme environment, structural degradation, recovery process schedule and structural strength etc. The resilience assessment framework is developed by 2 aspects, including robustness and recovery resilience. Besides, an illustrative example is developed as a walk-through of proposed methodology. The applications here demonstrate the versatility of the Markov framework towards handling resilience problems with varying levels of complexity, especially the offshore structure systems.

Introduction

The floating production system is one of main offshore structures in deepwater oil and gas development. Mooring system plays a pivotal role in maintaining its stability. However, a number of high-profile mooring failures have highlighted its high risk of high financial, environmental and fatality risk in floating structures [1]. Considering the significance of mooring system, mooring failures have aroused concerns. In recent years, more and more researches on structural performance under mooring failure have been proposed [2], [3], [4], [5]. Tension Leg Platform (TLP) is one of the main structures. And its robustness design is code-prescribed in API-RP-2T [6]. To further improve its safety, it is valuable to adopt resilience-based design philosophy. Resilience is a definition that a system's ability to withstand, respond to, and recover from disruptions [7]. It covers several concepts, like robustness, integrity, maintenance, reliability, rapidity, redundancy [8], availability etc. Resilience takes the system as a whole and overcomes the limitations of individual component evaluation. It is a more scientific overall evaluation method and is conducive to further optimizing the design and safe operation of large-scale marine structural systems.

For now, resilience of mooring system has not been studied. But the reliability of mooring system has attracted attention of researchers. Mousavi et al. [9] proposed Progressive Reliability Method (PRM) of offshore mooring system. One of the main contributions of this method is to determine all the possible system configurations in terms of the failure statuses of components. Based on the conditional probabilities of failure of the system components, the integrity index is proposed to measure the balance between the reliability of the system components [10]. Then, a simplified reliability-based method of mooring system is developed and the return period of environment is used as a measure of system safety [11]. These studies mainly focused on the failure process, ignoring the recovery process. Once the mooring failure occurs, the potential risk is inevitable. It leads to highlight the ability of mooring system to respond to and recovery from failure.

Resilience researches have been embraced in critical infrastructure systems. Quantitative resilience evaluation methods have gained more and more attention. Hosseini et al. [7] classified them into two groups, that is, measures-based approaches and structural-based models. A resilience curve was first proposed in 2003 by Bruneau et al. [12]. It is a main measure-based appoach illustrating the systems’ performance over time. The method also named as “resilience triangle”, which mainly evaluate the systems’ performance loss. Later, Cimellaro et.al [13] expanded it to evaluate recovery rapidity.

One pertinent consideration in resilience curve is how to quantitatively measure the systems’ performance considering internal and external complexity. For now, there are several different kinds of performance measures. Given the reliability perspective, the performance was measured with probability of exceedance [14]. In view of systems’ economic benefit, economic loss was proposed [15]. Considering the recovery process, it was quantified with a dimensionless (percentage) function of time [16]. From the point of system function, it was measured with service quantity [17], flow capacity [18] etc. And for the performance over time, Cimellaro et al. [19] adopted recovery models in the form of linear, exponential, and cosine functions to simulate recovery at the component level. These are generic equations selected by the user based on the system and society's response to the event. Besides, historical data [20], and expert experience [21] were used to generate the resilience curve. The above researches assumed that the system's performance was continuous. However, for the lack of databases and the complexity of offshore structure at system level, it is not applicable for offshore structures. A multi-state model would be of great help to address this problem. There are only a few works regarding quantifying resilience using multi-state models. Based on continuous time Markov Chain, Lin et al. [22] proposed a simulation-based building portfolio recovery model (BPRM) to model the recovery process. Younesi et al. [23] used homogeneous Markov chain to assess the resilience of power systems against natural disasters. Cao et al. [24] used the continuous-time semi-Markov chain to model ageing effects for systems. Dehghani et al. proposed a Markovian approach to model the interplay of hazard effects and recovery [25] and later extended the applications of Markov recovery modeling in multiple hazards [26]. Liu et al. [27] adopted a Markov process analysis on the lifeline resilience. Eldosouky et al. [28] inferred resilience index based on CI's performance state defined by a Markov chain. Zeng et al. proposed a Markov reward process-based framework for resilience analysis [29] and later expanded it using non-homogeneous semi-Markov process model [30]. But considering complexity of offshore systems’ response, it still remains an issue for suitable states description of TLP under mooring failure.

However, the resilience curves disable comparison of system behavior across scenarios and configurations. And it is what the resilience indices enable. In comprehensive resilience framework, suitable resilience indices were proposed further following the resilience curves. Since resilience is essentially a complex and comprehensive concept. Generally, an integrated resilience framework is combined with several different aspects. According to [31], they were categorized into six kinds, namely, magnitude-based metrics, duration-based metrics, integral-based metrics, rate-based metrics, threshold-based metrics and ensemble summary metrics. From our point of view, their taxonomy of summary metrics is based on their calculation forms. Though in different forms, they can be divided into 4 categories according to different aspects of resilience, namely robustness, rapidity, function and economic respectively. The resilience index categories are shown as Table 1, including the examples and their considerations of resilience. For specific stakeholders and decision-makers, they would require for a single value for optimization or succinct communication [31]. Such kind of indices, called summary metrics, can be obtained by weighting the sub metrics or choosing a certain one of the most importance. Their drawback is that the details of system may be easily obscured or misinterpreted [31]. In words, it is of great importance to propose suitable and characteristic resilience index based on the internal and external characteristics of the object system.

However, in contrast with onshore critical infrastructure systems, there appears to be no precedent research for resilience assessment of offshore structures, especially under mooring failure. This paper is intended to fill this gap and improve the offshore system's operation safety through introducing resilience assessment philosophy. Compared to the existing works, the contributions of this paper include: 1) It is firstly proposed based on Markov model to mathematically describe the whole process of TLP under mooring failure. The failure process and recovery process are modeled by Markov process and continuous-time Markov process, respectively. The used Markov process model is straightforward for which a closed form solution is available. However, the purpose of this paper is to propose its use for degradation type of failures. A suitable state description is developed based on the characteristics of TLP under mooring failure. 2) The proposed method takes into account the internal and external effect, including extreme environment and single event fatigue, recovery process schedule, structural strength etc. 3) A resilience assessment index framework of TLP under mooring failure is firstly established for 2 aspects of system's resilience, including robustness and recovery. Besides, an illustrative example is developed as a walk-through of proposed methodology, discussing quantitatively the effect of the internal and external effect on the system resilience.

Remaining sections of this paper are outlined as follows. The detailed resilience assessment framework, including the failure process, recovery process and resilience index, is introduced in Section 2. Case study of a TLP is presented for the illustration and verification of the proposed framework in Section 3. And the sensitivity analysis is conducted as well, including extreme environment, structural degradation, recovery rate and strength etc. Conclusions and perspectives are outlined lastly in Section 4.

Section snippets

State description

After initial mooring failure, the system may experience a sequence of progressive failure process and recovery process. Based on existing studies [49], it is found that, TLPs under mooring failure, are confronted with three major kinds of progressive failure modes, that is, multiple moorings failure, excessive offset, and overturning. In this research, the failure modes are divided into 3 different states categories, that is, intact, recoverable and uncoverable states. Among them, recoverable

Structural information

This study adopts a traditional TLP “ISSC TLP [60]”, which is composed of the platform body (the main platform body, four columns and lower body floating box), tension leg mooring system and submarine foundation, as shown in Fig. 5. The layout of tendons is shown as well. Structural data of TLP is displayed in Table 2. We number the tendons from T1 to T8 anticlockwise. The depth of water is 450m.

There are several assumptions below:

  • a

    To simplify the calculation, it is assumed that 2 tendons are

Conclusion

Based on Markov process models, A resilience evaluation model is developed for TLP under mooring failure considering external and internal effect. In the developed model, the states are categorized as intact state, recovery state that system with different failure moorings and unrecoverable state. The failure process, illustrating the dynamics of system performances is modeled by Markov process with absorbing states. And the recovery process is modeled by a continuous time discrete state Markov

CRediT authorship contribution statement

Jingyi Wu: Conceptualization, Methodology, Formal analysis, Investigation, Writing – original draft. Yang Yu: Conceptualization, Methodology, Writing – review & editing, Validation. Jianxing Yu: Writing – review & editing, Resources, Validation. Xueying Chang: Writing – review & editing, Validation. Lixin Xu: Resources, Data curation. Wenhao Zhang: Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

It is acknowledged that the present research is supported by National Natural Science Foundation of China (Grant No. 52071234).

References (64)

  • P.H. Lin et al.

    Stochastic post-disaster functionality recovery of community building portfolios I: modeling

    Struct Saf

    (2017)
  • Z. Zeng et al.

    A Markov reward process-based framework for resilience analysis of multistate energy systems under the threat of extreme events

    Reliab Eng Syst Saf

    (2021)
  • Z. Zeng et al.

    Resilience analysis of multi-state systems with time-dependent behaviors

    Appl Math Model

    (2021)
  • C. Nan et al.

    A quantitative method for assessing resilience of interdependent infrastructures

    Reliab Eng Syst Saf

    (2017)
  • R. Filippini et al.

    A modeling framework for the resilience analysis of networked systems-of-systems based on functional dependencies

    Reliab Eng Syst Saf

    (2014)
  • S.N. Mugume et al.

    A global analysis approach for investigating structural resilience in urban drainage systems

    Water Res.

    (2015)
  • N. Goldbeck et al.

    Resilience assessment for interdependent urban infrastructure systems using dynamic network flow models

    Reliab Eng Syst Saf

    (2019)
  • R. Yarveisy et al.

    A simple yet robust resilience assessment metrics

    Reliab Eng Syst Saf

    (2020)
  • S. Moslehi et al.

    Sustainability of integrated energy systems: a performance-based resilience assessment methodology

    Appl Energy

    (2018)
  • J. Wu et al.

    Probabilistic multilevel robustness assessment framework for a tlp under mooring failure considering uncertainties

    Reliab Eng Syst Saf

    (2022)
  • M. Ouyang et al.

    A three-stage resilience analysis framework for urban infrastructure systems

    Struct Saf

    (2012)
  • M. Ouyang et al.

    Multi-dimensional hurricane resilience assessment of electric power systems

    Struct Saf

    (2014)
  • M.C. Eti et al.

    Integrating reliability, availability, maintainability and supportability with risk analysis for improved operation of the Afam thermal power-station

    Appl Energy

    (2007)
  • K.-.T. Ma et al.

    Chapter 14 - Integrity management

  • R. Eatock-Taylor et al.

    Variability of hydrodynamic load predictions for a tension leg platform

    Ocean Eng

    (1986)
  • B. Keshtegar et al.

    Reliability analysis of corroded pipes using conjugate HL–RF algorithm based on average shear stress yield criterion

    Eng Fail Anal

    (2014)
  • Floating production system—JIP FPS mooring integrity

    Research Report

    (2006)
  • H. Wu et al.

    Transient response of a TLP-type floating offshore wind turbine under tendon failure conditions

    Ocean Eng

    (2021)
  • Planning, designing, and constructing tension leg platforms

    (2010)
  • S.S.H. Toroghi et al.

    A framework for the resilience analysis of electric infrastructure systems including temporary generation systems

    Reliab Eng Syst Saf

    (2020)
  • M. Bruneau et al.

    A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities

    Earthquake Spectra

    (2003)
  • G.P. Cimellaro

    Improving seismic resilience of structural systems through integrated design of smart structures

    (2008)
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