A new preventive maintenance strategy optimization model considering lifecycle safety
Introduction
It is expected that the product should have high reliability or availability no matter for the designer or the customer. However, in order to achieve this purpose, it generally requires large costs. For balancing these two aspects, several efficient design optimization models have been proposed. The first type of design optimization models aims at obtaining the optimal design parameter by making the product satisfy the reliability requirement simultaneously minimize the cost, which mainly involves reliability-based design optimization (RBDO) [1], [2], [3] and risk optimization (RO) [4], [5], [6]. The major difference between the two models is that the former one does not include the expected cost of failure in the objective function, while the latter one treats the expected cost of failure as a part of objective function. In other words, the RBDO only consider the initial cost, and the RO measures not only the initial cost but also the expected cost of failure. The second type of design optimization models is the maintenance strategy optimization (MSO) [7, 8], which does not focus on optimizing the design parameter in the product design stage but formulating the maintenance strategy in the product operation stage. The MSO can provide the optimal maintenance activity and maintenance time, so to guide the staff to maintain product and improve the reliability or availability. The third type of design optimization models is the lifecycle cost optimization (LCO) [9], [10], [11], which optimizes the design parameter in the design stage at the same time takes the maintenance of operation stage into account. For the purpose of handling different cases and requirements, several other auxiliary techniques such as the inspection and monitoring may be combined with these design optimization models. In this work, we focus on studying the MSO for the sake of improving the reliability of product.
Up to now, the MSO models can be classified into corrective maintenance [12] and preventive maintenance [13]. Corrective maintenance means that the correction action is proceeded to bring the product back to the functional state after it unexpectedly stops working. Therefore, corrective maintenance is only suitable for the product whose failure consequence is minimal [14]. Preventive maintenance is taken on an operational equipment in order to avoid any potential failure or severe degradation that may affect the product reliability or availability in near future. Condition-based maintenance or, more broadly, predictive maintenance, is one type of preventive maintenance [15]. It employs the condition monitoring to diagnose faults and predict future working condition of product so to facilitate maintenance decisions [16]. Deloux et al. [17] proposed a predictive maintenance policy for a continuously deteriorating system subject to stress and with two failure mechanisms, i.e., due to an excessive deterioration level and a shock. Moreover, an efficient method and mathematical model are given to solve this maintenance policy. Curcurù et al. [18] developed a predictive maintenance policy by using a stochastic model to simulate the degradation process, hypothesizing the case with imperfect monitoring system, and updating the procedure by a Bayesian approach. Compare et al. [19] presented a comprehensive outlook of the predictive maintenance involving the corresponding limitations, strengths, challenges and opportunities, etc. Frangopol el al. [20] proposed a preventive maintenance optimization model for identifying the optimal maintenance time of deteriorating structures, in which the expected total life-cycle cost is established as the optimization objection and the reliability is set to be the constraint. For the deteriorating structure with emphasis on bridge, Kong and Frangopol [21] proposed a computational model to identify the optimal preventive maintenance interventions, which can consider the effects of various types of actions on the reliability. Konakli et al. [22] presented a framework to determine the optimal preventive maintenance action not only for prior analysis but also for pre-posterior analysis based on the concept of the value of information, in which the pre-posterior analysis is used to measure the necessity of inspection activity. By formulating the preventive maintenance optimization as a time-variant reliability-based optimization, Angelis et al. [23] proposed an efficient general numerical technique to solve this problem with just once reliability analysis. Rocchetta et al. [24] developed a reinforcement learning framework for life cycle management and maintenance scheduling of power grids equipped with prognostics and health management. In this framework, the artificial neural network is used to replace the tabular representation so to describe the realistic problems with large and continuous state spaces. Liu et al. [7] employed maintenance functions to quantify the effects of maintenance on structure resistance and resistance decay function, and then proposed a reliability-based optimization method to identify the preventive maintenance strategy. In this method, a piecewise performance function is used to represent the influence of maintenance on the structure during the operation time period, and the time-dependent reliability is estimated by regarding this piecewise performance function as the performance of a series system. More details about the maintenance can be found in Refs. [25], [26], [27]. Most of the preventive maintenance models [20], [21], [22], [23], [24] are established based on the inspection of components’ operation state, i.e., normal or failure, and this work focuses on establishing general preventive maintenance framework of structure by deeply exploring the effect of maintenance on structure performance function, with which the reliability is estimated instead of directly assuming a reliability function for structure. Furthermore, most of the preventive maintenance models such as the one in Ref. [20], degenerates into the model with optimization objection being the sum of fixed cost and expected cost of failure, and optimization constraint being the maximum failure probability of different operation intervals divided by different maintenance time less than the target failure probability when no inspection is considered. Moreover, the expected cost of failure is expressed by the product of the maximum failure probability and failure cost. Actually, the maximum failure probability of different operation intervals divided by different maintenance times directly measures the safety of structure in corresponding operation interval. Although the maximum failure probability assesses the weakest state of different operation intervals, it's physical meaning of measuring the lifecycle safety of structure under maintenance may be weak. Therefore, it is necessary to establish a new preventive maintenance strategy optimization (PMSO) model that can consider the lifecycle safety of structure under maintenance.
In order to establish the PMSO model to consider the lifecycle safety of structure under maintenance, the failure state of the structure during lifecycle is decomposed as different failure states or conditional failure states during different operation time intervals divided by different maintenance times. After further derivation, the lifecycle failure probability is expressed as the joint time-dependent failure probability of different operation time intervals. Then, the expected cost of failure can be described by the product of the joint time-dependent failure probability and failure cost, and the new PMSO model is further obtained. Since maintenance can alter the resistance [28] and resistance decay function [29], the maintenance function [7] is employed to quantify the effects of maintenance on structure resistance and resistance decay function. Therefore, the structure will possess different performance functions if maintenance is implemented at different time instants. Directly solving the established PMSO model requires huge computational costs, thus a novel strategy for constructing adaptive ordinary Kriging surrogate model [30] of the performance function is proposed to improve the computational efficiency. Only one surrogate model needs to be constructed and it can accurately estimate the failure probabilities of different performance functions corresponding to different operation time intervals. However, identifying the optimal maintenance time is an optimization process, it needs large computational costs if unsuitable method is used although the surrogate model is constructed to replace the real performance function. Moreover, the joint time-dependent failure probability is estimated by simulation method based on the constructed surrogate model, and it possesses variability, or in other words, called noise. This will introduce some difficulties in identifying the optimal maintenance time if traditional optimization techniques are used. In order to deal with these difficulties, the stochastic Kriging surrogate model [31] that containing extrinsic and intrinsic noise parts is further employed to approximate the relationship between the joint time-dependent failure probability and the maintenance time, in which the extrinsic part is used to measure the model uncertainty, and the intrinsic part is employed to quantify the simulation uncertainty of the joint time-dependent failure probability. Based on the constructed stochastic Kriging surrogate model, the augmented expected improvement (AEI) method [32] is modified in this work to determine the optimal maintenance time.
The outline of this study is shown below. Several basic definitions are given in Section 2. The new expression of lifecycle failure probability of structure under maintenance and new PMSO model are proposed in Section 3. Advanced estimation strategy for solving the PMSO model is established in Section 4. Engineering applications are introduced in Section 5. Conclusions are drawn in Section 6.
Section snippets
Performance function of structure after maintenance
For the time-dependent structure, the performance function can be expressed by , where and . and mean the -dimensional and -dimensional input random variable vectors representing the structure resistance and the structure load respectively. and represent the -dimensional and -dimensional input stochastic process vectors representing the structure resistance and the structure load respectively. The considered lifecycle is
New expression for PMSO model
The new expression for measuring the lifecycle safety of structure under maintenance is the key of the new PMSO model. Before constructing this new expression, let us define , and as the safety sate of the structure during the operation time intervals , and respectively, define , and as the failure state of the structure during the operation time intervals , and respectively, and
Efficient estimation strategy
In different maintenance times or using different maintenance activities, the structure possesses different performance functions shown in Eq. (3). Directly solving the established PMSO model requires calling these different performance functions many times, thus a novel strategy for constructing adaptive ordinary Kriging surrogate model [30] of the performance function is proposed to improve the computational efficiency. Only one surrogate model is constructed and it can accurately estimate
Examples
Since the joint time-dependent failure probability possesses stochastic uncertainty, the estimated optimal maintenance time is not deterministic and may change when the algorithm is operated several times. In this work, the final results are obtained by using the mean value of 10 independent runs of the second part of the established estimation strategy.
Conclusions
A new PMSO model is developed in this work for identifying the maintenance strategy of structures by considering the lifecycle safety. In order to develop the PMSO model, the failure state of the structure during the lifecycle is decomposed into different conditional failure states in different operation time intervals, and the lifecycle failure probability is expressed as the joint time-dependent failure probability in different operation time intervals. Then, the expected cost of failure is
Author statement
Yan Shi: Conceptualization, Methodology, Software, Writing
Zhenzhou Lu: Writing - review & editing
Hongzhong Huang: Modification, Writing - review & editing
Yu Liu: odification, Writing - review & editing
Yanfeng Li: Modification
Enrico Zio: Writing - original draft, Validation
Yicheng Zhou: Software, Investigation
Declaration of Competing Interest
The authors declare that they have no conflict of interest.
Acknowledgement
This work was supported by the National Natural Science Foundation of China under contract numbers 51475370 and 51775090, the National Major Science and Technology Projects of China under contract number 2017-IV-0009–0046. The comments and suggestions from all the editors and reviewers are very much appreciated.
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2022, Reliability Engineering and System SafetyCitation Excerpt :The presence of objective function terms related to different stages of a system’s lifetime naturally arouses the consideration of time-dependent reliability problems. This is the case in Risk and Maintenance Strategy Optimization [11,19–23]. It is well known that solution of time-dependent reliability problems alone may call for specific solution approaches, since it is significantly costlier than its time-independent counterpart [24–30].