随着工业生产的发展，现代生产企业对机械设备可靠性的要求越来越高，设备维护工作至关重要。在设备维护时，设备的退化信息预测不确定性问题将导致设备维护不足或过度维护，对多设备维护的经济相关性问题考虑欠缺将导致维护成本的增加。因此，本文针对设备的退化信息预测不确定性问题和多设备维护的经济相关性问题，提出基于剩余使用寿命概率预测的多设备动态成组维护决策方法，主要研究内容如下：

（1）构建基于重采样的剩余使用寿命概率预测模型。针对设备的退化信息预测不确定性问题，首先使用变分自编码器以正态分布作为先验分布，对设备的退化数据进行重采样。然后使用LSTM模型对重采样结果进行预测，得到剩余使用寿命概率预测结果，为后续的维护决策模型提供依据。

（2）构建多设备动态成组维护决策模型。针对多设备的维护经济相关性问题，将剩余使用寿命概率预测结果考虑到维护决策模型中，基于动态成组策略建立了多设备动态成组维护决策模型。以所有设备的维护成本率最小化为目标，降低设备的维护成本。

（3）应用瞪羚优化算法对维护决策模型进行优化求解。针对维护决策模型的复杂性与经典优化算法的局限性，提出应用具有鲁棒性搜索能力的瞪羚优化算法求解维护决策模型。通过两个仿真对比实验，表明该算法在求解精度方面的优越性以及多设备动态成组维护决策模型的有效性。最后，通过灵敏度分析实验表明建立多设备动态成组维护模型的必要性。

（4）开发多设备寿命预测与维护决策管理系统。为了将设备剩余使用寿命预测与维护决策应用于企业实际生产过程中，开发多设备寿命预测与维护决策管理系统。依据Browser/Server体系确定系统架构，依据系统功能设计系统的前端界面和后端程序。通过对系统功能的运行结果进行展示，表明该系统能够满足企业对设备的基本管理需求。

综上所述，本文所提出的基于剩余使用寿命概率预测的多设备动态成组维护决策方法，能够较为准确地量化设备剩余使用寿命的不确定性，能够为企业相关工作人员提供合理的维护决策方案，有效地降低了设备的维护成本，提升了企业效益和管理效率。同时，对于多设备的预测性维护提供了良好的理论指导。

With the development of industrial production, modern production enterprises have higher and higher requirements for the reliability of mechanical equipment, and equipment maintenance is crucial. In equipment maintenance, the problem of uncertainty in the prediction of equipment degradation information will lead to insufficient or excessive maintenance of equipment, and the lack of consideration of the economic relevance of multi-equipment maintenance will lead to an increase in maintenance costs. Therefore, this paper proposes a dynamic multi-equipment group maintenance decision-making method based on the probability prediction of remaining useful life for the problem of uncertainty in the prediction of degradation information of equipment and the problem of economic relevance of multi-equipment maintenance, and the main research contents are as follows:

(1) Construct the probabilistic remaining useful life prediction model based on resampling. Aiming at the problem of uncertainty in the prediction of the degradation information of the equipment, firstly, we use the Variational Auto-Encoder to resample the degradation data of the equipment with the normal distribution as the a priori distribution. Then the LSTM model is used to predict the resampling results to obtain the probabilistic remaining useful life prediction results, which provide the basis for the subsequent maintenance decision-making model.

(2) Construct a multi-equipment dynamic grouping maintenance decision-making model. Aiming at the economic relevance of maintenance of multiple equipment, the probabilistic remaining useful life prediction results are taken into account in the maintenance decision-making model, and a multi-equipment dynamic grouping maintenance decision-making model is established based on the dynamic grouping strategy. With the goal of minimizing the maintenance cost rate of all equipment, the maintenance cost of equipment is reduced.

(3) Apply the gazelle optimization algorithm to optimize the maintenance decision model. Aiming at the complexity of the maintenance decision model and the limitations of the classical optimization algorithm, it is proposed to apply the gazelle optimization algorithm with robust search capability to solve the maintenance decision model. Two simulation and comparison experiments are conducted to show the superiority of the algorithm in terms of solving accuracy and the effectiveness of the maintenance decision model for multi-equipment dynamic grouping. Finally, the sensitivity analysis experiment shows the necessity of establishing a multi-equipment dynamic grouping maintenance model.

(4) Develop a multi-equipment life prediction and maintenance decision management system. In order to apply the remaining useful life prediction and maintenance decision-making to the actual production process of the enterprise, a multi-equipment life prediction and maintenance decision-making management system is developed. The system architecture was determined based on the Browser/Server system, and the front-end interface and back-end program were designed based on the system functions. Through the demonstration of the operation results of the system functions, it is shown that the system can meet the basic management needs of the enterprise for the equipment.

In summary, the multi-equipment dynamic grouping maintenance decision-making method based on the probabilistic remaining useful life prediction proposed in this paper can more accurately quantify the uncertainty of the remaining useful life of the equipment and can provide reasonable maintenance decision-making programs for the relevant staff of the enterprise, which effectively reduces the maintenance cost of the equipment, and improves the enterprise efficiency and management efficiency. At the same time, the predictive maintenance of multiple equipment provides good theoretical guidance.

[1]钱志远.不完美维护活动干预下设备的剩余使用寿命预测与维护决策研究[D].赣州:江西理工大学,2023.

[2]黄扣.基于深度学习的旋转类机械预测性维护方法研究[D].镇江:江苏科技大学,2021.

[3]CHEN C, LU N, JIANG B, et al. A risk-averse remaining useful life estimation for predictive maintenance[J]. IEEE/CAA Journal of Automatica Sinica, 2021, 8(2): 412-422.

[4]冯乐乐.多设备生产线健康状态评估与预防性维护研究[D].成都:电子科技大学,2022.

[5]Wang Y S, Jiang K, Xu L. Sensor-data-driven fusion prognostic framework for complex engineered systems[J]. IEEE Sensors Journal, 2021, 21(18):20421-20430.

[6]易观秀.面向透平机械的性能衰退预测及维护决策研究[D].成都:电子科技大学,2022.

[7]赵申坤,姜潮,龙湘云.一种基于数据驱动和贝叶斯理论的机械系统剩余寿命预测方法[J].机械工程学报,2018,54(12):115-124.

[8]Rai A, Upadhyay S H. The use of MD-CUMSUM and NARX neural network for anticipating the remaining useful life of bearings[J]. Measurement, 2017, 111: 397-410.

[9]Kang Z, Catal C, Tekinerdogan B. Remaining useful life (RUL) prediction of equipment in production lines using artificial neural networks[J]. Sensors, 2021, 21(3): 932.

[10]Xu X, Li X, Ming W, et al. A novel multi-scale CNN and attention mechanism method with multi-sensor signal for remaining useful life prediction[J]. Computers & Industrial Engineering, 2022, 169: 108204.

[11]Jafari S, Byun Y C. Xgboost-based remaining useful life estimation model with extended kalman particle filter for lithium-ion batteries[J]. Sensors, 2022, 22(23): 9522.

[12]Lixin W, Zhenhuan W, Yudong F, et al. Remaining life predictions of fan based on time series analysis and BP neural networks[C]//2016 IEEE Information Technology, Networking, Electronic and Automation Control Conference. IEEE, 2016: 607-611.

[13]Tang S, Xu X, Yu C, et al. Remaining useful life prediction with fusing failure time data and field degradation data with random effects[J]. Ieee Access, 2019, 8: 11964-11978.

[14]Wu C, Sun H, Lin S, et al. Remaining useful life prediction of bearings with different failure types based on multi-feature and deep convolution transfer learning[J]. Eksploatacja i Niezawodność – Maintenance and Reliability, 2021, 23(4): 685-694.

[15]Cui J, Cao L, Zhang T. A two-stage Gaussian process regression model for remaining useful prediction of bearings[J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2024, 238(2): 333-348.

[16]Wang T, Liu Z, Mrad N. A probabilistic framework for remaining useful life prediction of bearings[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 70: 1-12.

[17]Nguyen K T P, Medjaher K, Gogu C. Probabilistic deep learning methodology for uncertainty quantification of remaining useful lifetime of multi-component systems[J]. Reliability Engineering & System Safety, 2022, 222: 108383.

[18]Zhao Z, Wu J, Wong D, et al. Probabilistic remaining useful life prediction based on deep convolutional neural network[C]//In Proc. 9th Int. Conf. Through-Life Eng. Services, 2020: pp. 1–15.

[19]Wang B, Lei Y, Yan T, et al. Recurrent convolutional neural network: A new framework for remaining useful life prediction of machinery[J]. Neurocomputing, 2020, 379: 117-129.

[20]杜海东,曹军海,申莹等.非完美维修策略下退化系统可靠性仿真评估研究[J].系统仿真学报,2018,30(08):2834-2840.

[21]Jing Z, Hua J, Yi Z. Multi-objective integrated optimization problem of preventive maintenance planning and flexible job-shop scheduling[C]// Proceedings of the 23rd International Conference on Industrial Engineering and Engineering Management 2016: Theory and Application of Industrial Engineering. Atlantis Press, 2017: 137-141.

[22]Do P, Voisin A, Levrat E, et al. A proactive condition-based maintenance strategy with both perfect and imperfect maintenance actions[J]. Reliability Engineering & System Safety, 2015, 133: 22-32.

[23]侯鹏飞,韩磊.基于状态的煤矿大型固定设备维护系统[J].煤矿现代化,2019,(05):160-163.

[24]Chen Y, Wang Z, Cai Z. Optimal maintenance decision based on remaining useful lifetime prediction for the equipment subject to imperfect maintenance[J]. Ieee Access, 2020, 8: 6704-6716.

[25]Salem M B, Fouladirad M, Deloux E. Variance Gamma process as degradation model for prognosis and imperfect maintenance of centrifugal pumps[J]. Reliability Engineering & System Safety, 2022, 223: 108417.

[26]陆宁云,陈闯,姜斌等.复杂系统维护策略最新研究进展:从视情维护到预测性维护[J].自动化学报,2021,47(01):1-17.

[27]Yan J, Meng Y, Lu L, et al. Industrial big data in an industry 4.0 environment: Challenges, schemes, and applications for predictive maintenance[J]. Ieee Access, 2017, 5: 23484-23491.

[28]Wu S, Gebraeel N, Lawley M A, et al. A neural network integrated decision support system for condition-based optimal predictive maintenance policy[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2007, 37(2): 226-236.

[29]Cao X, Li P, Ming S. Remaining useful life prediction-based maintenance decision model for stochastic deterioration equipment under data-driven[J]. Sustainability, 2021, 13(15): 8548.

[30]Hameed Z, Wang K. Development of optimal maintenance strategies for offshore wind turbine by using artificial neural network[J]. Wind Engineering, 2012, 36(3): 353-364.

[31]Nguyen K T P, Medjaher K. A new dynamic predictive maintenance framework using deep learning for failure prognostics[J]. Reliability Engineering & System Safety, 2019, 188: 251-262.

[32]Chen C, Wang C, Lu N, et al. A data-driven predictive maintenance strategy based on accurate failure prognostics[J]. Eksploatacja i Niezawodność – Maintenance and Reliability, 2021, 23(2): 387-394.

[33]Kim S, Choi J H, Kim N H. Inspection schedule for prognostics with uncertainty management[J]. Reliability Engineering & System Safety, 2022, 222: 108391.

[34]Lee J, Mitici M. Deep reinforcement learning for predictive aircraft maintenance using probabilistic remaining-useful-life prognostics[J]. Reliability Engineering & System Safety, 2023, 230: 108908.

[35]Mitici M, de Pater I, Barros A, et al. Dynamic predictive maintenance for multiple components using data-driven probabilistic RUL prognostics: The case of turbofan engines[J]. Reliability Engineering & System Safety, 2023, 234: 109199.

[36]周晓军,沈炜冰,奚立峰等.一种考虑修复非新的多设备串行系统机会维护动态决策模型[J].上海交通大学学报,2007,(05):769-773.

[37]Zhang Z, Wu S, Li B. A condition-based and opportunistic maintenance model for a two-unit deteriorating system[C]//2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. IEEE, 2011: 590-595.

[38]俞梦琦,史凯龙,周晓军.基于双时间窗的多设备串行系统机会维护策略[J].上海交通大学学报,2020,54(01):69-75.

[39]Van Horenbeek A, Pintelon L. A dynamic predictive maintenance policy for complex multi-component systems[J]. Reliability engineering & system safety, 2013, 120: 39-50.

[40]Vu H C, Do P, Barros A. A study on the impacts of maintenance duration on dynamic grouping modeling and optimization of multicomponent systems[J]. IEEE Transactions on Reliability, 2018, 67(3): 1377-1392.

[41]Iung B, Do P, Levrat E, et al. Opportunistic maintenance based on multi-dependent components of manufacturing system[J]. CIRP Annals, 2016, 65(1): 401-404.

[42]Kingma D P, Welling M. Auto-encoding variational bayes[J]. arXiv preprint arXiv, 2013, 1312.6114.

[43]Xu H, Chen W, Zhao N, et al. Unsupervised anomaly detection via variational auto-encoder for seasonal kpis in web applications[C]//Proceedings of the 2018 world wide web conference. International World Wide Web Conferences Steering Committee, 2018: 187-196.

[44]杨涛.基于变分自编码器的文本生成模型研究[D].重庆:西南大学,2023.

[45]Zhang H, Zhang Q, Shao S, et al. Attention-based LSTM network for rotatory machine remaining useful life prediction[J]. Ieee Access, 2020, 8: 132188-132199.

[46]李梦蝶,赵光,罗灵鲲等.基于改进CNN-LSTM的飞控系统RUL预测[J].计算机工程与应用,2022,58(16): 274-283.

[47]王昊.航空发动机剩余使用寿命预测研究[D].大连:大连理工大学,2023.

[48]李杰.基于LSTM的轴承寿命预测方法研究与软件实现[D].成都:电子科技大学,2023.

[49]Acoustics and Vibration Database.

[50]Bechhoefer E, Van Hecke B, He D. Processing for improved spectral analysis[C]//Annual Conference of the PHM Society. 2013: 5(1).

[51]Salih S K, Aljunid S A, Aljunid S M, et al. Adaptive filtering approach for denoising electrocardiogram signal using moving average filter[J]. Journal of Medical Imaging and Health Informatics, 2015, 5(5): 1065-1069.

[52]De Azevedo H D M, Araújo A M, Bouchonneau N. A review of wind turbine bearing condition monitoring: State of the art and challenges[J]. Renewable and Sustainable Energy Reviews, 2016, 56: 368-379.

[53]楚丰毅.基于威布尔分布的风场机会维修策略的研究[D].太原:中北大学,2020.

[54]Murthy D N P, Xie M, Jiang R. Weibull models[M]//John Wiley & Sons. Hoboken, NJ, USA: Wiley, 2004.

[55]张旻昊.基于多层次机会预防性的林区风力发电机维护策略研究[D].长沙:中南林业科技大学,2017.

[56]谢鲁冰.海上风电机组动态机会成组维修策略的研究[D].北京:华北电力大学(北京),2022.

[57]Wu J, Ng T S A, Xie M, et al. Analysis of maintenance policies for finite life-cycle multi-state systems[J]. Computers & Industrial Engineering, 2010, 59(4): 638-646.

[58]Van Dijkhuizen G, van Harten A. Optimal clustering of frequency-constrained maintenance jobs with shared set-ups[J]. European Journal of Operational Research, 1997, 99(3): 552-564.

[59]Agushaka J O, Ezugwu A E, Abualigah L. Gazelle optimization algorithm: a novel nature-inspired metaheuristic optimizer[J]. Neural Computing and Applications, 2023, 35(5): 4099-4131.

[60]Malve S, Uzsoy R. A genetic algorithm for minimizing maximum lateness on parallel identical batch processing machines with dynamic job arrivals and incompatible job families[J]. Computers & Operations Research, 2007, 34(10): 3016-3028.

[61]Humphries N E, Queiroz N, Dyer J R M, et al. Environmental context explains Lévy and Brownian movement patterns of marine predators[J]. Nature, 2010, 465(7301): 1066-1069.

[62]Mantegna R N. Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes[J]. Physical Review E, 1994, 49(5): 4677.

[63]于丰源.基于遗传算法与粒子群算法的供水管网水力模型校核对比研究[D].邯郸:河北工程大学,2022.

[64]李娜娜.基于改进粒子群算法的多目标优化问题研究[D].贵阳:贵州民族大学,2023.