Practical systems often include functional modules whose degradation affects the performance of a core module responsible for the primary task. While real-time degradation of functional modules (e.g., control units, hydraulic actuators) can typically be detected and classified into discrete states, intermediate degradation in core modules (e.g., drive shafts, threshing mechanisms) is difficult to monitor due to structural complexity or limited sensor access. This study investigates a representative system comprising one core module and two functional modules that provide degradation mitigation and shock resistance. Each functional module operates in three discrete degradation states, with interactions between their deteriorations. The core module experiences both gradual and shock-induced degradation, mitigated by the functional modules. Exact models for module degradation and reliability are derived and validated via Monte Carlo simulation. A multi-threshold dynamic maintenance policy is developed, integrating preventive, corrective, and opportunistic actions based on core module operating time and functional module conditions. The policy is optimized using a hybrid genetic algorithm-Monte Carlo simulation approach, employing reliability models to predict failures and estimate downtime. Both a numerical example based on a combine harvester and an illustrative example constructed using representative real-world wind turbine data are used to demonstrate the proposed method, whose performance is compared with two alternative optimization approaches and validated against three benchmark maintenance strategies. Sensitivity analyses quantify main and interaction effects of critical reliability and cost parameters, providing practical guidance for industrial applications.

The trans-critical CO2 cycle has garnered significant attention due to its exceptional heating properties. To further improve the heating performance of the CO2 heat pump (HP) system, this paper conducts optimization research on the control strategy of a single-stage compression secondary throttling CO2 HP system. Initially, we analyze the effects of varying ambient temperatures on the system's parameter characteristics when it achieves the optimal coefficient of performance (COP). Subsequently, the relationship between the optimal discharge pressure and the evaporator outlet pressure was explored by changing the operating conditions for the same supply air temperature across different ambient temperatures. A dynamic adjustment control strategy utilizing dual electronic expansion valves (EXVs) is proposed, and the performance before and after optimization is compared with different ambient temperatures. Finally, the impact on the driving range before and after optimization is assessed based on the climatic characteristics of typical cold cities. The results indicate that the system achieves optimal COP when the supply air temperature is set at 45 degrees C, a decrease in ambient temperature from 0 degrees C to -20 degrees C leads to a reduction in refrigerant temperatures at the inner gas cooler and evaporator outlet by 4.36 degrees C and 12.38 degrees C, respectively. Combined with the high-confidence optimal pressure fitting correlation, the proposed dynamic adjustment control strategy for EXVs effectively reduces the compressor's discharge temperature and enhances the driving range under low temperatures. At -5 degrees C, optimization results in a reduction of the discharge temperature by 5.92 degrees C, while the COP increases by 12.6%. Furthermore, the driving range in typical low-temperature cities can be improved by 8.9% to 12.7%.

Load-sharing mechanism is a worldwide redundancy designed to enhance system reliability by distributing the total system load among surviving units. Traditional load-sharing systems typically encounter continuous and constant loads that everlastingly influence the system degradation process. However, practical engineering systems, e.g., power supply systems, may simultaneously withstand both continuous loads and discrete loads, where the latter will also have a certain influence on system reliability. To fill the gap of this innovative load characteristic, this paper examines a novel load-sharing system subject to hybrid continuous and discrete loads. Unit basic degradation process is modelled by a nonlinear Wiener process with a continuous-load-related covariate, while discrete loads, arriving according to a homogeneous Poisson process, cause sudden degradation increments. Lifetime distribution of the presented load-sharing system is analytically derived, serving as the basis for downtime cost analysis related to further condition-based operation and maintenance strategy, which is newly proposed by the introduction of dynamic adjustment of unit loads based on their degradation inspections. The Markov decision process is modelled and formulated for joint optimization of inspection interval, condition-based maintenance and dynamic load reallocation. Compared with traditional condition-based maintenance with equal load allocation, numerical studies are conducted to investigate the effectiveness and robustness of dynamic load allocation.

In modern industrial two-stage production systems, units inevitably degrade due to natural wear and are vulnerable to external random shocks during continuous operation. This paper focuses on the joint optimization of maintenance and production scheduling for a two-stage system with two interactive units and a buffer zone under the combined effects of random shocks and natural degradation. The actual operation time of the system is calculated by Monte Carlo simulation. Based on the Markov Decision Process, the Deep Q- Network is employed to optimize the joint production and maintenance scheduling. Through multiple simulations with replaced case data, the effectiveness and robustness of the proposed model are evaluated.

This study addresses the joint optimization problem of spare parts inventory management and preventive maintenance in complex industrial systems, proposing an integrated decision-making framework based on deep reinforcement learning. The core innovation of this framework is threefold: it integrates dynamic multi-supplier selection, circular management of repairable spare parts, and preventive maintenance strategies into a unified Markov decision process. The study employs a Wiener process-based continuous degradation model to characterize equipment performance evolution, uses truncated normal distribution to model suppliers' stochastic lead times, and achieves effective learning in high-dimensional state-action spaces through the Dueling Double DQN architecture combined with a prioritized experience replay mechanism. Numerical experiments show that after 30000 training episodes, the average total cost rate decreases from an initial 110 to 15.5, a reduction of 86%. The system forms a reasonable cost structure, with system downtime cost accounting for only 11.9%, indicating that the preventive maintenance strategy effectively controls system failure risks. Notably, the repairable spare parts mechanism contributes 46.3% of spare parts supply with 3.5% repair cost, significantly improving resource utilization efficiency. The research results verify that deep reinforcement learning methods can learn effective joint optimization strategies through interaction with the environment, providing a feasible decision support method for maintenance management of complex industrial systems.

Condition-based maintenance (CBM) and spare provisioning are both important to guarantee the operation of redundant systems composed of degrading components. However, most existing studies on joint optimization of CBM and spare inventory assume maintenance actions are instantaneous and the lead time for spares are fixed, which are not consistent with the reality. Therefore, this paper focus on the joint optimization problems to minimize the total cost rate considering stochastic maintenance time for components and stochastic lead time for spares. The problem is modeled as a Markov decision process model and solved by an improved reinforcement learning algorithm, i.e., the improved Q-learning algorithm, which converges more quickly and reaches a smaller value of the total cost rate than the traditional Q-learning algorithm. Moreover, the simulated environment based on discrete event simulation method is introduced in detail and the convergence of the algorithm is proved theoretically. Based on the numerical study, we further demonstrate the convergence and effectiveness of the proposed algorithm and perform sensitivity analysis on several model parameters to provide management insights for decision makers.

The maintenance policies based on random working time guarantee the continuity of system functionality. This paper studies a random-time component reallocation and system replacement (RCS) policy, in which the random-time system replacement is to replace the system at the planned preventive time or the random working time, whichever comes first, the random-time component reallocation is to balance the degradation of components by reallocating components at random working time before system replacement, and minimal repair is implemented for failed components. To improve the efficiency and flexibility of RCS policy, we first establish an optimization model to minimize the expected system maintenance cost per unit time based on a given interval for random-time component reallocation, and analytical results are derived by comparing the proposed policy with the preventive component reallocation and random-time system replacement policy, and the simple random-time system replacement policy. Next, we construct another optimization model to maximize the interval length for the random-time component reallocation constrained by the threshold of the efficiency level of RCS policy. Numerical experiments demonstrate the performance of the RCS policy and provide guidance for the interval for the random-time component reallocation.

Condition‐based maintenance has been studied for managing the degradation of components in a system. However, components in different positions may undergo different workload, leading to imbalanced components degradation. Component reallocation is an effective method to balance the degradation of components in different positions with different degradation rates. Thus, this paper investigates the joint optimization of condition‐based maintenance and condition‐based reallocation for a non‐repairable system with multiple identical and functionally‐exchangeable components that undergo different continuous degradation processes due to different workload. We model this problem through Markov decision process, which is solved by a dynamic programming algorithm, and the objective is to provide the optimal maintenance and reallocation actions exactly for each system state, that is, the joint optimal policy, to minimize the discounted long‐run total cost. Especially, our joint policy is on component‐level and proved to be optimal. Finally, the numerical analysis shows the structural insights and effectiveness of the proposed joint policy, for which the sensitivity analysis on the degradation parameters, setup cost, reallocation cost, and downtime cost is performed. We also propose a new reallocation strategy and show the results and computation time for systems with different scales, which indicates that our model can handle systems with reasonable size.

Maintenance and inventory control of spare parts are of great importance for efficiently managing onshore wind farms. Considering the economic and graphical dependencies among wind turbines and the stochastic degradations of the components in the turbines, this article studies the joint optimization of opportunistic condition-based maintenance and spare parts supply for onshore wind farms to minimize the operation and maintenance cost rate. For each field maintenance, the specific turbines, with failed components, are selected for replacement using a clustering method, and the shortest route for visiting the turbines with failed components is scheduled. The maintenance team departs from a maintenance center with spare parts, maintains the selected turbines with failed or degraded components, and then returns to the center. This complicated and practical problem has never been considered as a whole in the literature. An optimization model is established, and a simulation-based approach is developed to solve it. A special case, for which a solution can be obtained by directly solving a nonlinear programming model, is provided to verify the results obtained by the simulation-based approach. Examples for various scales of wind farms are provided, and an analysis is performed for determining the length of a recommended maintenance interval.

The pumped two-phase cooling system has been proven to be effective in dissipating battery heat. However, the system configuration and performance of the integrated thermal management system(ITMS) based on the pumped two-phase cooling system still lacks in-depth investigation. In this paper, a novel integration system configuration coupling the pumped two-phase cooling system and air-conditioning system for EVs is developed. A simulation platform is established for the proposed integrated system. Two cooling modes named as radiator cooling mode and chiller cooling mode are numerically investigated under different operating parameters. The results showed that the pack average temperature raised with moist air mass flow rate, compressor speed, ambient temperature and discharge rate. The temperature non-uniformity was aggravated when the R1233zd mass flow rate, the moist air mass flow rate and the compressor speed increased. This aggravation would be more significant with the increasing discharge rate. The energy consumption of radiator cooling mode was only around 3 % of that of chiller cooling mode when achieving the same pack average temperature at an ambient tem-perature of 15 & DEG;C. While, the chiller cooling mode was more adaptable to harsh conditions. The pack average temperature can be used as an index to determine the system cooling mode. The up limit of the discharge rate in RCM were 1.8C, 1.6C, 1.4C and 1.2C for the ambient temperature at 16 & DEG;C, 20 & DEG;C, 24 & DEG;C and 26 & DEG;C, respectively. The novel findings of this work are intended to provide a theoretical tool for the optimal design and control strategy of the ITMS based on the pumped two-phase cooling system.

A satellite communications system transmits signals from one point on Earth to another distant location through a series of satellites as relays. The performance of each satellite is controllable, which determines its capability of connecting with the following satellites and affects its degradation rate. Accumulated degradation poses a risk of satellite failure and further system failure. This paper aims to minimize long-term discounted costs associated with maintenance and system failure. We provide optimal maintenance planning and performance control through Markov decision process modeling and a dynamic programming algorithm. The system degradation state, a rocket’s satellite-carrying capacity, maintenance preparation time, high maintenance setup costs, and load-sharing are considered in the model. We also offer structural insights into the optimal maintenance and performance control policy and the model, including a sensitivity analysis of maintenance setup costs.

Industrial systems such as signal relay stations and oil pipeline systems can be modeled as linear multi-state consecutively connected systems, which comprise sequentially ordered elements and fail if the first and the final elements are not connected. The performance level of each element is controllable, which determines how many elements an element can connect and affects its degradation rate. Accumulated degradation can cause element failure, which may lead to costly system failure. This paper aims to minimize long-term maintenance-related costs, including system failure costs. We provide optimal maintenance planning and performance control for every system degradation state through Markov decision process modeling and a dynamic programming algorithm. Load-sharing, restricted maintenance capacity, maintenance setup costs, and the structural characteristics of the system are considered in the model, all of which influence the optimal maintenance and performance control policy. Regarding degradation management, reducing the difference in degradation levels between elements, e.g., replacing more-degraded elements first, can be cost-effective. However, increasing the difference in degradation by maintenance or performance control can also lower maintenance-related costs in specific situations, which is discussed in numerical experiments. We also illustrate structural insights regarding the proposed model, including sensitivity analyses of maintenance capacity, setup costs, and the difference between preventive and corrective replacement costs.

It is critical to understand the cell-to-cell inconsistency among cells to obtain a better performance of the battery module. However, the battery inconsistency is always not considered in the traditional designs of the battery module, especially for liquid-cooled modules. In this study, a liquid-cooled 8S2P cylindrical module with thermal-conductive blocks and a single flat tube was designed. A multiphysics model was established to capture the electrical, thermal and aging behavior of the module numerically. First, the cell-to-cell inconsistency among cells was simulated with the verified multiphysics model for different module layouts. The results showed that the module with S configuration offered superior thermal and aging performance to the module with I configuration. The maximum temperature difference among cells was decreased by 0.4 K for the module with S configuration. The module SOH and SOH consistency improved by 0.8 % and 210 % after 400 cycles for the S configuration, respectively. Then, the effects of the height (h) and height increment (Delta h) of thermal-conductive blocks on the electrical and thermal performance of the module were discussed. The maximum temperature of the module and maximum temperature difference among cells were decreased by 0.6 K and 0.1 K with increasing h, respectively. However, the maximum temperature of the module and maximum temperature difference among cells were decreased by 0.001 K and 0.6 K with increasing Delta h, respectively. The mean value of maximum current variation over time and maximum SOC difference among cells at the end of discharge were slightly increased by 0.01A and 0.02 % with increasing Delta h, respectively but almost insensitive to the variation of h.

Modern high-end computing systems, such as storage servers used in Youtube and Tiktok, serve large numbers of concurrent streams, each of which requires aggressive prefetching. This multi-stream prefetching problem, which strives to serve as many requests as possible from the memory cache and minimize response time, remains as an open challenge in computer science research. To address the efficient resource management for data prefetching, this paper introduces a novel method adopted from inventory management of multiple products in operations research. It proposes a unique constrained multi-stream (Q, r) model which simultaneously determines the prefetching degree (order quantity) Q and trigger distance (reorder point) r for each application stream, taking into account the distinct data request rates of the streams. The model has the objective of minimizing the cache miss level (backorder level), which determines the access latency, as well as constraints on the cache space (inventory space) and the total prefetching frequency (total order frequency). Specifically, the disk access time (lead time) is a function of both the prefetching degree and the total prefetching frequency, the latter of which represents the system load. We present the analytical properties of the model, provide numerical optimization examples, and conduct sensitivity analysis to further demonstrate the insights of this prefetching problem. Significantly, an empirical evaluation proves the effectiveness of the prefetching policy provided by our model. (C) 2021 Elsevier B.V. All rights reserved.

Motived by cost savings, this paper studies a new periodic maintenance policy for multi-component systems, for which multiple component reallocations and system overhauls are jointly implemented aperiodically at fixed times and components are minimally repaired immediately after failures in a life cycle. Different workloads or conditions of different positions can lead to different degradation processes of components, thus component reallocation can be used to balance the degradation between components at different positions, which has been widely studied. System overhaul can improve the conditions of components by imperfect or perfect repair. Component reallocation and system overhaul are mutually dependent and jointly affect the degradation of components and the maintenance cost of a system. In this paper, the failure rate functions of components are modeled using virtual age, and then a binary mixed integer nonlinear programming model is established to determine the optimal time and assignment for component reallocations, and the optimal time and degree for system overhauls by minimizing the long-run average maintenance cost of the system. Further, the number of system overhauls is proved to be finite, and a decomposition method is proposed. Numerical examples are provided to show the effectiveness of the joint of component reallocations and system overhauls.

The pumped two-phase cooling method is a practical way to dissipate heat from the battery module. The operating parameters of the cooling system should be investigated thoroughly to improve the performance of the battery thermal management system (BTMS). However, the previous BTMS designs only explored the thermal performance and ignored the electrical performance in the battery module. This study designed a pumped two-phase cooling BTMS with the refrigerant of R1233zd. An electrothermal coupled model was established for a series-connected battery module to predict thermal and electrical behavior. The results showed that the pumped two-phase cooling system could obtain excellent cooling performance with low system pressure under 2C discharging condition. The average temperature of the module and the temperature difference among cells could be maintained under 40 °C and 5 K under a 2C discharging rate. A lower saturation temperature, higher mass flux, and higher subcooling degree could enhance heat dissipation for the cooling system based on R1233zd. An increase in the saturation temperature and a decrease in the subcooling degree could enhance the temperature uniformity within the module. The battery consistency was mainly dominated by the temperature difference and deteriorated with a lower average temperature in the pack. The research outcome of this paper can guide the design and optimization of the pumped two-phase cooling BTMS.

The components in a system undergo different workload due to being in different positions, resulting in unbalanced component degradation level. In order to balance the degradation and extend the lifetime of the system, component reallocation is a feasible way to achieve degradation balance in some cases that we cannot manage the operator's behavior to control components' workload. In this paper, we incorporate component reallocation into condition-based maintenance for a non-repairable series system consisting of two components. The degradation processes of components are assumed to follow the Wiener process with different degradation parameters. The problem is formulated as a Markov decision process and solved by the value iteration algorithm to obtain the optimal replacement and reallocation policy that minimizes the discounted system long-term total cost. A numerical example gives the optimal inspection interval and the properties of the optimal policy. The sensitivity analysis with respect to reallocation cost is provided to illustrate the optimal replacement and reallocation policy.

Maintaining a system of multiple degrading components requires having a supply of spare components to replace deteriorated ones in a timely manner. Decisions on whether to replace the deteriorated components are made based on the statuses of components and the system and are further restricted by the inventory level of spares. Inventory replenishment decisions themselves depend both on system status and maintenance policy. Both maintenance and replenishment decisions affect the system reliability and system maintenance and spare inventory cost. This paper considers the joint optimization of periodic condition-based replacement of components and inventory control for a k-out-of-n:F system of non-repairable degrading components under various system statuses. For modeling the degradation of components, both the Wiener process and gamma process are considered. We model the maintenance and inventory policy using the number of components in each discretized degradation state rather than the traditional approach, which uses the state of each component. Our approach considerably reduces the solution space. Based on that, we address the joint optimization using Markov decision process along with dynamic programming; we then analyze the complexity of the algorithm. We provide a numerical study on a 2-out-of-3:F system of components in three states to illustrate structural insights regarding the proposed model, including a sensitivity analysis on the length of inspection interval, system downtime cost, and inventory holding cost. We demonstrate the efficiency of the model and solution method by testing k-out-of-n:F systems with different numbers of components and discretized degradation states. (C) 2020 Elsevier B.V. All rights reserved.

Considering the working and failure modes and maintenance process of a data storage system with data redundancy, we propose and study a reliability and maintenance model of a k-out-of-n:F system, in which the system experiences a rebuilding process with downgraded performance that follows preventive maintenance (PM) with replacement of failed components, and the system is subject to failure with different failure criteria during such rebuilding process. In addition, maintenance time is not negligible, and the external shocks would occur and possibly result in the failure of all the components. The maintenance of the k-out-of-n:F system with these characteristics has not been studied, and these characteristics bring in a new reliability and maintenance model and a new optimization problem that synthetically determine system reliability design and PM schedule. Such a problem is motivated by improving availability and efficiency of a data storage system running data redundancy technology. We conduct a numerical study in which the parameters of the models are set according to real data and practice considerations. In addition to demonstrating the established models and presenting optimal results, we also perform sensitivity analysis for the design and maintenance of data storage systems.

In this study we investigate the failure mechanism of the data storage system of a supercomputer and introduce an age-based cost-minimization preventive maintenance (PM) model. The data storage system of a supercomputer consists of hundreds of storage nodes, and each storage node contains several independently and identically distributed nonrepairable hard disks (HDs). Based on the data storage mechanism of the HDs and the failure mechanism of the storage nodes, the k-out-of-n:F system is used to model the data storage nodes. The lifetime of all HDs is assumed to be exponentially distributed. The age-based PM policy is to replace the failed HDs every PM interval or upon system failure. We establish an optimization model to identify the optimal PM interval with the goal of minimizing the long-run average cost while meeting the requirements for system reliability. Our numerical case study shows the application of the present model and method, and analyzes the relationship between the long-run average cost and PM interval.