Abstract
As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision- and policy-making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This second paper presents a literature review of key enabling technologies of digital twins, with an emphasis on uncertainty quantification, optimization methods, open-source datasets and tools, major findings, challenges, and future directions. Discussions focus on current methods of uncertainty quantification and optimization and how they are applied in different dimensions of a digital twin. Additionally, this paper presents a case study where a battery digital twin is constructed and tested to illustrate some of the modeling and twinning methods reviewed in this two-part review. Code and preprocessed data for generating all the results and figures presented in the case study are available on Github.
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Change history
07 January 2023
A Correction to this paper has been published: https://doi.org/10.1007/s00158-022-03476-7
References
Abdar M, Pourpanah F, Hussain S, Rezazadegan D, Liu L, Ghavamzadeh M, Fieguth P, Cao X, Khosravi A, Acharya UR (2021) A review of uncertainty quantification in deep learning: techniques, applications and challenges. Inf Fusion 76:243–297
Adnan MA, Razzaque MA, Ahmed I, Isnin IF (2013) Bio-mimic optimization strategies in wireless sensor networks: a survey. Sensors 14(1):299–345
Advantage Magazine A (2021) Kärcher cleans up with ansys twin builder. https://www.ansys.com/advantage-magazine/volume-xv-issue-2-2021/karcher-cleans-up-with-ansys-twin-builder
AllahBukhsh Z, Stipanovic I, Klanker G, O’Connor A, Doree AG (2019) Network level bridges maintenance planning using multi-attribute utility theory. Struct Infrastruct Eng 15(7):872–885
Allemang RJ (2003) The modal assurance criterion-twenty years of use and abuse. Sound Vib 37(8):14–23
Alliance GB (2020) The global battery alliance battery passport: giving an identity to the ev’s most important component. Glob. Batter, Alliance
Alsheikh MA, Hoang DT, Niyato D, Tan H-P, Lin S (2015) Markov decision processes with applications in wireless sensor networks: a survey. IEEE Commun Surv Tutor 17(3):1239–1267
An H, Youn BD, Kim HS (2022a) A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty. Compos Struct 279:114863
An H, Youn BD, Kim HS (2022b) Optimal sensor placement considering both sensor faults under uncertainty and sensor clustering for vibration-based damage detection. Struct Multidisc Optim 65(3):1–32
Anand M, Ives Z, Lee I (2005) Quantifying eavesdropping vulnerability in sensor networks. In: Proceedings of the 2nd International Workshop on Data Management for Sensor Networks, pp 3–9
Andrieu C, De Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50(1):5–43
Ao D, Hu Z, Mahadevan S (2017a) Design of validation experiments for life prediction models. Reliab Eng Syst Saf 165:22–33
Ao D, Hu Z, Mahadevan S (2017b) Dynamics model validation using time-domain metrics. J Verif Valid Uncertain Quantif 2(1):011004
ARC (2022) Automotive research center at the university of michigan. https://arc.engin.umich.edu/. Accessed 6 May 2022
Arendt PD, Apley DW, Chen W (2012) Quantification of model uncertainty: calibration, model discrepancy, and identifiability
Asorey-Cacheda R, Garcia-Sanchez A-J, García-Sánchez F, García-Haro J (2017) A survey on non-linear optimization problems in wireless sensor networks. J Netw Comput Appl 82:1–20
Astroza R, Alessandri A, Conte JP (2019) A dual adaptive filtering approach for nonlinear finite element model updating accounting for modeling uncertainty. Mech Syst Signal Process 115:782–800
Attia PM, Chueh WC, Harris SJ (2020) Revisiting the t0. 5 dependence of sei growth. J Electrochem Soc 167(9):090535
Augustine P (2020) The industry use cases for the digital twin idea. In: Advances in Computers, vol 117. Elsevier, pp 79–105
Aydemir H, Zengin U, Durak U (2020) The digital twin paradigm for aircraft review and outlook. In: AIAA Scitech 2020 Forum, p 0553
Ayerbe E, Berecibar M, Clark S, Franco AA, Ruhland J (2021) Digitalization of battery manufacturing: current status, challenges, and opportunities. Adv Energy Mater 12(17):2102696
Bai Y, Muralidharan N, Sun Y-K, Passerini S, Whittingham MS, Belharouak I (2020) Energy and environmental aspects in recycling lithium-ion batteries: concept of battery identity global passport. Mater Today 41:304–315
Bao N, Wang C (2015) A monte carlo simulation based inverse propagation method for stochastic model updating. Mech Syst Signal Process 60:928–944
Barbehenn M (1998) A note on the complexity of Dijkstra’s algorithm for graphs with weighted vertices. IEEE Trans Comput 47(2):263
Barzegar V, Laflamme S, Hu C, Dodson J (2022) Ensemble of recurrent neural networks with long short-term memory cells for high-rate structural health monitoring. Mech Syst Signal Process 164:108201
Basagni S, Bölöni L, Gjanci P, Petrioli C, Phillips CA, Turgut D (2014) Maximizing the value of sensed information in underwater wireless sensor networks via an autonomous underwater vehicle. In: IEEE INFOCOM 2014-IEEE Conference on Computer Communications, pp 988–996. IEEE
Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461
Behmanesh I, Moaveni B, Papadimitriou C (2017) Probabilistic damage identification of a designed 9-story building using modal data in the presence of modeling errors. Eng Struct 131:542–552
Bellamy III W (2018) Boeing ceo talks ’digital twin’ era of aviation. https://www.aviationtoday.com/2018/09/14/boeing-ceo-talks-digital-twin-era-aviation/
Bing L, Meilin Z, Kai X (2000) A practical engineering method for fuzzy reliability analysis of mechanical structures. Reliab Eng Syst Saf 67(3):311–315
Birkl CR, Roberts MR, McTurk E, Bruce PG, Howey DA (2017) Degradation diagnostics for lithium ion cells. J Power Sources 341:373–386
Bisdikian C, Kaplan LM, Srivastava MB (2013) On the quality and value of information in sensor networks. ACM Trans Sens Netw 9(4):1–26
Błachowski B, Świercz A, Ostrowski M, Tauzowski P, Olaszek P, Jankowski Ł (2020) Convex relaxation for efficient sensor layout optimization in large-scale structures subjected to moving loads. Comput-Aided Civil Infrastruct Eng 35(10):1085–1100
Boers Y, Driessen JN (2003) Interacting multiple model particle filter. IEEE Proc-Radar Sonar Navig 150(5):344–349
Boscaglia L, Bonsanto F, Boglietti A, Nategh S, Scema C (2019) Conjugate heat transfer and cfd modeling of self-ventilated traction motors. In: 2019 IEEE Energy Conversion Congress and Exposition (ECCE), pp 3103–3109. IEEE
Bousdekis A, Lepenioti K, Apostolou D, Mentzas G (2019) Decision making in predictive maintenance: literature review and research agenda for industry 4.0. IFAC-PapersOnLine 52(13):607–612
Bruynseels K, Santoni de Sio F, Van den Hoven J (2018) Digital twins in health care: ethical implications of an emerging engineering paradigm. Front Genet 31
Bukhsh ZA, Stipanovic I, Doree AG (2020) Multi-year maintenance planning framework using multi-attribute utility theory and genetic algorithms. Eur Transp Res Rev 12(1):1–13
Burns JA, Cliff EM, Farlow K (2014) Parameter estimation and model discrepancy in control systems with delays. IFAC Proc Vol 47(3):11679–11684
Burns JA, Cliff EM, Herdman TL (2018) Identification of dynamical systems with structured uncertainty. Inverse Probl Sci Eng 26(2):280–321
Camci F (2009) System maintenance scheduling with prognostics information using genetic algorithm. IEEE Trans Reliab 58(3):539–552
Camci F (2015) Maintenance scheduling of geographically distributed assets with prognostics information. Eur J Oper Res 245(2):506–516
Cantero-Chinchilla S, Chiachío J, Chiachío M, Chronopoulos D, Jones A (2020) Optimal sensor configuration for ultrasonic guided-wave inspection based on value of information. Mech Syst Signal Process 135:106377
Careless J (2021) Digital twinning: The latest on virtual models. https://www.aerospacetechreview.com/digital-twinning-the-latest-on-virtual-models/
Carne TG, Dohrmann CR (1994) A modal test design strategy for model correlation. Technical report, Sandia National Labs., Albuquerque, NM (United States)
Casals LC, García BA, Canal C (2019) Second life batteries lifespan: rest of useful life and environmental analysis. J Environ Manag 232:354–363
Caulfield B (2022) Nvidia, bmw blend reality, virtual worlds to demonstrate factory of the future. https://blogs.nvidia.com/blog/2021/04/13/nvidia-bmw-factory-future/
Cha S-H (2007) Comprehensive survey on distance/similarity measures between probability density functions. City 1(2):1
Chadha M, Hu Z, Todd MD (2021) An alternative quantification of the value of information in structural health monitoring. Struct Health Monit 14759217211028439
Chen G-S, Bruno RJ, Salama M (1991) Optimal placement of active/passive members in truss structures using simulated annealing. AIAA J 29(8):1327–1334
Chen X, Kang E, Shiraishi S, Preciado VM, Jiang Z (2018) Digital behavioral twins for safe connected cars. In: Proceedings of the 21th ACM/IEEE international conference on model driven engineering languages and systems, p 144–153
Chrono P Chrono. https://projectchrono.org/. Accessed 17 April 2022
Consortium DT Digital twin open-source repository. https://www.digitaltwinconsortium.org/initiatives/open-source.htm/. Accessed 17 April 2022
De Angelis V, Preger Y, Chalamala BR (2021) Battery lifecycle framework: a flexible repository and visualization tool for battery data from materials development to field implementation
Der Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105–112
Diao W, Saxena S, Pecht M (2019) Accelerated cycle life testing and capacity degradation modeling of licoo2-graphite cells. J Power Sources 435:226830
Digital Engineering M (2021) Engie lab crigen and ansys accelerate zero carbon energy. https://www.digitalengineering247.com/article/engie-lab-crigen-and-ansys-accelerate-zero-carbon-energy/
Dodson J, Downey A, Laflamme S, Todd MD, Moura AG, Wang Y, Mao Z, Avitabile P, Blasch E (2022) High-rate structural health monitoring and prognostics: an overview. Data Sci Eng 9:213–217
Dowding KJ, Pilch M, Hills RG (2008) Formulation of the thermal problem. Comput Methods Appl Mech Eng 197(29–32):2385–2389
Downey A, Hu C, Laflamme S (2018) Optimal sensor placement within a hybrid dense sensor network using an adaptive genetic algorithm with learning gene pool. Struct Health Monit 17(3):450–460
Duchoň F, Babinec A, Kajan M, Beňo P, Florek M, Fico T, Jurišica L (2014) Path planning with modified a star algorithm for a mobile robot. Procedia Eng 96:59–69
Durão LF, Haag S, Anderl R, Schützer K, Zancul E (2018) Digital twin requirements in the context of industry 4.0. In: IFIP international conference on product lifecycle management. Springer, pp 204–214
Ehsani N, Afshar A (2010) Optimization of contaminant sensor placement in water distribution networks: multi-objective approach. Water Distrib Syst Anal 2010:338–346
Eindhoven. Prom tools, eindhoven university of technology. http://www.promtools.org/doku.php/. Accessed 17 April 2022
Engel Y, Wellman MP (2010) Multiattribute auctions based on generalized additive independence. J Artif Intell Res 37:479–525
Engel H, Hertzke P, Siccardo G (2019) Second-life ev batteries: the newest value pool in energy storage. McKinsey & Company
Epic Games I Unreal engine 5. http://www.unrealengine.com/en-US/unreal-engine-5. Accessed 27 May 2022
Eshghi AT, Lee S, Jung H, Wang P (2019) Design of structural monitoring sensor network using surrogate modeling of stochastic sensor signal. Mech Syst Signal Process 133:106280
Feng X, Gu J, Guan X (2018) Optimal allocation of hybrid energy storage for microgrids based on multi-attribute utility theory. J Mod Power Syst Clean Energy 6(1):107–117. https://doi.org/10.1007/s40565-017-0310-3
Ferson S, Oberkampf WL, Ginzburg L (2008) Model validation and predictive capability for the thermal challenge problem. Comput Methods Appl Mech Eng 197(29–32):2408–2430
Flynn EB, Todd MD (2010) A bayesian approach to optimal sensor placement for structural health monitoring with application to active sensing. Mech Syst Signal Process 24(4):891–903
Foundation E Eclipse ditto: open-source framework for digital twins in the iot. https://www.eclipse.org/ditto/. Accessed 23 April 2022
Frazier W (2014) Metal additive manufacturing: a review. J Mater Eng Perform 23:1917–1928
Froger A, Gendreau M, Mendoza JE, Pinson E, Rousseau L-M (2016) Maintenance scheduling in the electricity industry: a literature review. Eur J Oper Res 251(3):695–706
Gal Y, Ghahramani Z (2015) Bayesian convolutional neural networks with bernoulli approximate variational inference. arXiv preprint arXiv:1506.02158
Gal Y, Ghahramani Z (2016a) Dropout as a bayesian approximation: representing model uncertainty in deep learning. In: International Conference on Machine Learning, pp 1050–1059. PMLR
Gal Y, Ghahramani Z (2016b) A theoretically grounded application of dropout in recurrent neural networks. Adv Neural Inf Process Syst 29
Gammell JD, Srinivasa SS, Barfoot TD (2014) Informed rrt*: optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 2997–3004. IEEE
Gao W, Song C, Tin-Loi F (2010) Probabilistic interval analysis for structures with uncertainty. Struct Saf 32(3):191–199
Garmabaki A, Ahmadi A, Ahmadi M (2016) Maintenance optimization using multi-attribute utility theory. In: Current trends in reliability, availability, maintainability and safety. Springer, pp 13–25
Gawlikowski J, Tassi CRN, Ali M, Lee J, Humt M, Feng J, Kruspe A, Triebel R, Jung P, Roscher R, Shahzad M (2021) A survey of uncertainty in deep neural networks. arXiv preprint arXiv:2107.03342
Github. Link to github repository where the preprocessed data and python scripts used to generate all the results and figures in the case study section reside. https://github.com/acthelen/battery_digital_twin
Glaessgen E, Stargel D (2012) The digital twin paradigm for future nasa and us air force vehicles. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference 20th AIAA/ASME/AHS adaptive structures conference 14th AIAA, p 1818
Goebel K, Saha B, Saxena A, Celaya JR, Christophersen JP (2008) Prognostics in battery health management. IEEE Instrum Meas Mag 11(4):33–40
Gomes GF, de Almeida FA, da Silva Lopes Alexandrino P, da Cunha SS, de Sousa BS, Ancelotti AC (2019) A multiobjective sensor placement optimization for SHM systems considering fisher information matrix and mode shape interpolation. Eng Comput 35(2):519–535
Graham N 3d data model resources for dublin docklands sdz. https://data.smartdublin.ie/dataset/3d-data-hack-dublin-resources/. Accessed 23 April 2022
Grall A, Dieulle L, Bérenguer C, Roussignol M (2002) Continuous-time predictive-maintenance scheduling for a deteriorating system. IEEE Trans Reliab 51(2):141–150
Gupta V, Sharma M, Thakur N (2010) Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: a technical review. J Intell Mater Syst Struct 21(12):1227–1243
Guratzsch RF, Mahadevan S (2010) Structural health monitoring sensor placement optimization under uncertainty. AIAA J 48(7):1281–1289
He W, Williard N, Osterman M, Pecht M (2011) Prognostics of lithium-ion batteries based on Dempster-Shafer theory and the bayesian Monte Carlo method. J Power Sources 196(23):10314–10321
Heimes FO (2008) Recurrent neural networks for remaining useful life estimation. In: 2008 international conference on prognostics and health management, pp 1–6. IEEE
Heydari A, Aghabozorgi M, Biguesh M (2020) Optimal sensor placement for source localization based on RSSD. Wireless Netw 26(7):5151–5162
Hills R, Dowding K, Swiler L (2008) Thermal challenge problem: summary. Comput Methods Appl Mech Eng 197(29–32):2490–2495
Honkura K, Takahashi K, Horiba T (2011) Capacity-fading prediction of lithium-ion batteries based on discharge curves analysis. J Power Sources 196(23):10141–10147
Hsu M-H (2021) Machine learning-based non-destructive evaluation of fatigue damage in metals. PhD thesis
Hu Z, Mahadevan S (2017) Uncertainty quantification and management in additive manufacturing: current status, needs, and opportunities. Int J Adv Manuf Technol 93(5):2855–2874
Hu C, Youn BD, Wang P, Yoon JT (2012) Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life. Reliab Eng Syst Saf 103:120–135
Hu C, Jain G, Tamirisa P, Gorka T (2014) Method for estimating capacity and predicting remaining useful life of lithium-ion battery. In: 2014 international conference on prognostics and health management, pp 1–8. IEEE
Hu C, Ye H, Jain G, Schmidt C (2018) Remaining useful life assessment of lithium-ion batteries in implantable medical devices. J Power Sources 375:118–130
Hu X, Xu L, Lin X, Pecht M (2020) Battery lifetime prognostics. Joule 4(2):310–346
Hu Z, Ao D, Mahadevan S (2017) Calibration experimental design considering field response and model uncertainty. Comput Methods Appl Mech Eng 318:92–119
Hu Z, Hu C, Mourelatos ZP, Mahadevan S (2019) Model discrepancy quantification in simulation-based design of dynamical systems. J Mech Des 141(1)
Huan X, Marzouk YM (2013) Simulation-based optimal Bayesian experimental design for nonlinear systems. J Comput Phys 232(1):288–317
Huan X, Marzouk Y (2014) Gradient-based stochastic optimization methods in bayesian experimental design. Int J Uncertain Quantif 4(6)
Huber GP (1974) Multi-attribute utility models: a review of field and field-like studies. Manag Sci 20(10):1393–1402
IBM Blog I (2019) How to create a twin to improve your own performance. https://www.ibm.com/blogs/internet-of-things/iot-digital-twin-rotterdam/
IBM Blog I (2020) Profile: Ucsf health and maximo lead the way on smart medical buildings. https://www.ibm.com/blogs/internet-of-things/iot-ucsf-health-and-maximo-smart-medical-buildings/
IBM Newsletter I (2020) Siemens and ibm deliver service lifecycle management solution. https://newsroom.ibm.com/2020-06-17-Siemens-and-IBM-Deliver-Service-Lifecycle-Management-Solution
IBM White Paper I (2020) Digital twin technologies for high-performance manufacturing. https://www.ibm.com/downloads/cas/KX8A3MWX
ICSHM (2020) International project competition for structural health monitoring. http://www.schm.org.cn/#/IPC-SHM,2020. Accessed 24 May 2022
Ijomah WL, Childe S, McMahon C (2004) Remanufacturing: a key strategy for sustainable development
ISA (2010) Ansi/isa-95.00.01-2010 (iec 62264-1 mod) enterprise-control system integration—part 1: models and terminology. https://www.isa.org/products/ansi-isa-95-00-01-2010-iec-62264-1-mod-enterprise. Accessed 29 May 2022
Jiang X, Mahadevan S (2009) Bayesian inference method for model validation and confidence extrapolation. J Appl Stat 36(6):659–677
Jiang C, Hu Z, Liu Y, Mourelatos ZP, Gorsich D, Jayakumar P (2020) A sequential calibration and validation framework for model uncertainty quantification and reduction. Comput Methods Appl Mech Eng 368:113172
Jiang C, Hu Z, Mourelatos ZP, Gorsich D, Jayakumar P, Fu Y, Majcher M (2021) R2-RRT*: reliability-based robust mission planning of off-road autonomous ground vehicle under uncertain terrain environment. IEEE Trans Autom Sci Eng 19(2):1030–1046
Jiang C, Liu Y, Mourelatos ZP, Gorsich D, Fu Y, Hu Z (2022a) Efficient reliability-based mission planning of off-road autonomous ground vehicles using an outcrossing approach. J Mech Des 144(4)
Jiang C, Vega MA, Ramancha MK, Todd MD, Conte JP, Parno M, Hu Z (2022b) Bayesian calibration of multi-level model with unobservable distributed response and application to miter gates. Mech Syst Signal Process 170:108852
Jiang C, Vega MA, Todd MD, Hu Z (2022c) Model correction and updating of a stochastic degradation model for failure prognostics of miter gates. Reliab Eng Syst Saf 218:108203
Johnson JB, Kulchitsky AV, Duvoy P, Iagnemma K, Senatore C, Arvidson RE, Moore J (2015) Discrete element method simulations of mars exploration rover wheel performance. J Terrramech 62:31–40
Kammer DC (1991) Sensor placement for on-orbit modal identification and correlation of large space structures. J Guid Control Dyn 14(2):251–259
Kapteyn MG, Pretorius JV, Willcox KE (2021) A probabilistic graphical model foundation for enabling predictive digital twins at scale. Nat Comput Sci 1(5):337–347
Kaveh A, Dadras Eslamlou A, Rahmani P, Amirsoleimani P (2022) Optimal sensor placement in large-scale dome trusses via q-learning-based water strider algorithm. Struct Control Health Monit e2949
Kendall A, Gal Y (2017) What uncertainties do we need in bayesian deep learning for computer vision? Adv Neural Inf Process Syst 30
Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B 63(3):425–464
Kim T, Youn BD, Oh H (2018) Development of a stochastic effective independence (sefi) method for optimal sensor placement under uncertainty. Mech Syst Signal Process 111:615–627
Kim W, Yoon H, Lee G, Kim T, Youn BD (2020) A new calibration metric that considers statistical correlation: marginal probability and correlation residuals. Reliab Eng Syst Saf 195:106677
Kuffner JJ, LaValle SM (2000) Rrt-connect: an efficient approach to single-query path planning. In: Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No. 00CH37065), vol 2, pp 995–1001. IEEE
Kuleshov V, Fenner N, Ermon S (2018) Accurate uncertainties for deep learning using calibrated regression. In: International conference on machine learning, pp 2796–2804. PMLR
Kulkarni RV, Venayagamoorthy GK (2010) Particle swarm optimization in wireless-sensor networks: a brief survey. IEEE Trans Syst Man Cybern Part C 41(2):262–267
Lakshminarayanan B, Pritzel A, Blundell C (2017) Simple and scalable predictive uncertainty estimation using deep ensembles. Adv Neural Inf Process Syst 30
Lee J, Lapira E, Bagheri B, Kao H-A (2013a) Recent advances and trends in predictive manufacturing systems in big data environment. Manuf Lett 1(1):38–41
Lee J, Lapira E, Yang S, Kao A (2013b) Predictive manufacturing system-trends of next-generation production systems. Ifac Proc Vol 46(7):150–156
Lehner H, Dorffner L (2020) Digital geotwin vienna: towards a digital twin city as geodata hub
Lei X, Sandborn PA (2018) Maintenance scheduling based on remaining useful life predictions for wind farms managed using power purchase agreements. Renew Energy 116:188–198
Li J, Zhang X, Xing J, Wang P, Yang Q, He C (2015) Optimal sensor placement for long-span cable-stayed bridge using a novel particle swarm optimization algorithm. J Civ Struct Heal Monit 5(5):677–685
Li M, Nemani VP, Liu J, Lee MA, Ahmed N, Kremer GE, Hu C (2021a) Reliability-informed life cycle warranty cost and life cycle analysis of newly manufactured and remanufactured units. J Mech Des 143(11)
Li S, Fang H, Shi B (2021b) Remaining useful life estimation of lithium-ion battery based on interacting multiple model particle filter and support vector regression. Reliab Eng Syst Saf 210:107542
Li W, Chen W, Jiang Z, Lu Z, Liu Y (2014) New validation metrics for models with multiple correlated responses. Reliab Eng Syst Saf 127:1–11
Li Y, Sui S, Tong S (2016) Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics. IEEE Trans Cybern 47(2):403–414
Ling Y, Mahadevan S (2013) Quantitative model validation techniques: new insights. Reliab Eng Syst Saf 111:217–231
Liu Y, Li X-Y (2002) Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics. IEEE Trans Autom Control 47(5):848–856
Liu W, Gao W-C, Sun Y, Xu M-J (2008) Optimal sensor placement for spatial lattice structure based on genetic algorithms. J Sound Vib 317(1–2):175–189
Liu Y, Chen W, Arendt P, Huang H-Z (2011) Toward a better understanding of model validation metrics. J Mech Des 133(7)
Liu Y, Zhang L, Yang Y, Zhou L, Ren L, Wang F, Liu R, Pang Z, Deen MJ (2019) A novel cloud-based framework for the elderly healthcare services using digital twin. IEEE Access 7:49088–49101
Liu J, Lin Z, Padhy S, Tran D, Bedrax Weiss T, Lakshminarayanan B (2020) Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. Adv Neural Inf Process Syst 33:7498–7512
Liu X, Gao M, Zhao J, Sun X, Li Z, Li Q, Wang L, Wang J, Zhuang W (2021a) Effects of charging protocols on the cycling performance for high-energy lithium-ion batteries using a graphite-siox composite anode and li-rich layered oxide cathode. J Power Sources 495:229793
Liu Y, Jiang C, Mourelatos ZP, Gorsich D, Jayakumar P, Fu Y, Majcher M, Hu Z (2021b) Simulation-based mission mobility reliability analysis of off-road ground vehicles. J Mech Des 143(3)
Liu Y, Jiang C, Zhang X, Mourelatos ZP, Barthlow D, Gorsich D, Singh A, Hu Z (2021c) Reliability-based multi-vehicle path planning under uncertainty using a bio-inspired approach. J Mech Des 1–44
Long Q, Scavino M, Tempone R, Wang S (2013) Fast estimation of expected information gains for bayesian experimental designs based on laplace approximations. Comput Methods Appl Mech Eng 259:24–39
Lu L, Han X, Li J, Hua J, Ouyang M (2013) A review on the key issues for lithium-ion battery management in electric vehicles. J Power Sources 226:272–288
Lu Q, Parlikad AK, Woodall P, Don Ranasinghe G, Xie X, Liang Z, Konstantinou E, Heaton J, Schooling J (2020) Developing a digital twin at building and city levels: case study of west cambridge campus. J Manag Eng 36(3):05020004
Lui YH, Li M, Downey A, Shen S, Nemani VP, Ye H, VanElzen C, Jain G, Hu S, Laflamme S, Hu C (2021) Physics-based prognostics of implantable-grade lithium-ion battery for remaining useful life prediction. J Power Sources 485:229327
Mahadevan S, Nath P, Hu Z (2022) Uncertainty quantification for additive manufacturing process improvement: recent advances. ASCE-ASME J Risk Uncertain Eng Syst Part B 8(1):010801
Malik AA (2021) Framework to model virtual factories: a digital twin view. arXiv preprint arXiv:2104.03034
Malik AA, Brem A (2021) Digital twins for collaborative robots: a case study in human-robot interaction. Robot Comput-Integr Manuf 68:102092
Malings C, Pozzi M (2016) Value of information for spatially distributed systems: application to sensor placement. Reliab Eng Syst Saf 154:219–233
Malings C, Pozzi M, Velibeyoglu I (2015) Sensor placement optimization for structural health monitoring. In: Proceedings of the 10th International Workshop on Structural Health Monitoring
Mandelbaum A, Weinshall D (2017) Distance-based confidence score for neural network classifiers. arXiv preprint arXiv:1709.09844
Markets, Markets M (2020) Digital twin market. https://www.marketsandmarkets.com/Market-Reports/digital-twin-market-225269522.html
Meo M, Zumpano G (2005) On the optimal sensor placement techniques for a bridge structure. Eng Struct 27(10):1488–1497
Miao Q, Xie L, Cui H, Liang W, Pecht M (2013) Remaining useful life prediction of lithium-ion battery with unscented particle filter technique. Microelectron Reliab 53(6):805–810
Moghaddass R, Zuo MJ (2014) An integrated framework for online diagnostic and prognostic health monitoring using a multistate deterioration process. Reliab Eng Syst Saf 124:92–104
Mousazadeh H (2013) A technical review on navigation systems of agricultural autonomous off-road vehicles. J Terrramech 50(3):211–232
Mukhoti J, Kirsch A, van Amersfoort J, Torr PH, Gal Y (2021) Deterministic neural networks with appropriate inductive biases capture epistemic and aleatoric uncertainty. arXiv e-prints, p-2102
Nado Z, Band N, Collier M, Djolonga J, Dusenberry MW, Farquhar S, Feng Q, Filos A, Havasi M, Jenatton R, Jerfel G (2021) Uncertainty baselines: benchmarks for uncertainty & robustness in deep learning. arXiv preprint arXiv:2106.04015
NASA (2008) Standard for models and simulation-nasa technical standard. National Aeronautics and Space Administration, Washington (DC): Standard No.NASA–STD–7009
Nath P, Hu Z, Mahadevan S (2017) Sensor placement for calibration of spatially varying model parameters. J Comput Phys 343:150–169
Nemani VP, Lu H, Thelen A, Hu C, Zimmerman AT (2021) Ensembles of probabilistic lstm predictors and correctors for bearing prognostics using industrial standards. Neurocomputing
Niculescu-Mizil A, Caruana R (2005) Predicting good probabilities with supervised learning. In: Proceedings of the 22nd International Conference on Machine Learning, pp 625–632
Ostachowicz W, Soman R, Malinowski P (2019) Optimization of sensor placement for structural health monitoring: a review. Struct Health Monit 18(3):963–988
Papamarkou T, Hinkle J, Young MT, Womble D (2021) Challenges in markov chain monte carlo for bayesian neural networks. Stat Sci
PCoE NA Prognostics center of excellence - data repository. https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/. Accessed 23 April 2022
PHM (2022) Phm society data challenge. https://data.phmsociety.org/. Accessed 24 April 2022
PHMAP (2021) Data challenge at phmap 2021. http://phmap.org/data-challenge/. Accessed 24 May 2022
PHME (2022) The annual phme data challenge. https://phm-europe.org/data-challenge. Accessed 24 May 2022
Plett GL (2004) Extended kalman filtering for battery management systems of lipb-based hev battery packs: Part 3. State and parameter estimation. J Power Sources 134(2):277–292
Plett GL (2006) Sigma-point kalman filtering for battery management systems of lipb-based hev battery packs: Part 2: Simultaneous state and parameter estimation. J Power Sources 161(2):1369–1384
Prudencio EE, Schulz KW (2012) The parallel C++ statistical library ‘QUESO’: quantification of uncertainty for estimation, simulation and optimization. In: Euro-Par 2011: Parallel Processing Workshops. Springer, pp 398–407http://dx.doi.org/10.1007/978-3-642-29737-3_44
Ramancha MK, Conte JP, Parno MD (2022) Accounting for model form uncertainty in bayesian calibration of linear dynamic systems. Mech Syst Signal Process 171:108871
Rebba R, Mahadevan S (2008) Computational methods for model reliability assessment. Reliab Eng Syst Saf 93(8):1197–1207
Ricker NL Te code. http://depts.washington.edu/control/LARRY/TE/download.html. Accessed 17 April 2022
Ricker NL, Lee J (1995) Nonlinear model predictive control of the tennessee eastman challenge process. Comput Chem Eng 19(9):961–981
Rohrs CE, Valavani L, Athans M, Stein G (1982) Robustness of adaptive control algorithms in the presence of unmodeled dynamics. In: 1982 21st IEEE Conference on Decision and Control, pp 3–11. IEEE
Rohrs C, Valavani L, Athans M, Stein G (1985) Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics. IEEE Trans Autom Control 30(9):881–889
Sabatino S, Frangopol DM, Dong Y (2015) Sustainability-informed maintenance optimization of highway bridges considering multi-attribute utility and risk attitude. Eng Struct 102:310–321
Sachan VK, Imam SA, Beg M (2012) Energy-efficient communication methods in wireless sensor networks: a critical review. Int J Comput Appl 39(17):35–48
Saha B, Goebel K (2007) Battery data set. NASA AMES prognostics data repository
Saha B, Goebel K, Poll S, Christophersen J (2008) Prognostics methods for battery health monitoring using a bayesian framework. IEEE Trans Instrum Meas 58(2):291–296
Saha B, Goebel K, Christophersen J (2009) Comparison of prognostic algorithms for estimating remaining useful life of batteries. Trans Inst Meas Control 31(3–4):293–308
Salvatier J, Wiecki TV, Fonnesbeck C (2016) Probabilistic programming in python using pymc3. PeerJ Comput Sci 2:e55
Saxena A, Goebel K (2008a) Phm08 challenge data set. NASA Ames Prognostics Data Repository
Saxena A, Goebel K (2008b) Turbofan engine degradation simulation data set. NASA Ames Prognostics Data Repository, pp 1551–3203
Scott E, Brown J, Schmidt C, Howard W (2005) A practical longevity model for lithium-ion batteries: de-coupling the time and cycle-dependence of capacity fade. In: 208th ECS Meeting
Sela L, Amin S (2018) Robust sensor placement for pipeline monitoring: mixed integer and greedy optimization. Adv Eng Inform 36:55–63
Severson KA, Attia PM, Jin N, Perkins N, Jiang B, Yang Z, Chen MH, Aykol M, Herring PK, Fraggedakis D, Bazant MZ (2019) Data-driven prediction of battery cycle life before capacity degradation. Nat Energy 4(5):383–391
Sharma M, George J (2018) Digital twin in the automotive industry: Driving physical-digital convergence. Tata Consultancy Services White Paper
Shen W, Huan X (2021) Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning. arXiv preprint arXiv:2110.15335
Siemens Newsletter S (2020) Digitalization in industry: twins with potential. https://new.siemens.com/global/en/company/stories/industry/the-digital-twin.html
Sisson W, Karve P, Mahadevan S (2022) Digital twin approach for component health-informed rotorcraft flight parameter optimization. AIAA J 60(3):1923–1936
Sjarov M, Lechler T, Fuchs J, Brossog M, Selmaier A, Faltus F, Donhauser T, Franke J (2020) The digital twin concept in industry—a review and systematization. In: 2020 25th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), vol 1, pp 1789–1796. IEEE
Skardal A, Shupe T, Atala A (2016) Organoid-on-a-chip and body-on-a-chip systems for drug screening and disease modeling. Drug Discov Today 21(9):1399–1411
Smith RC (2013) Uncertainty quantification: theory, implementation, and applications, vol 12. Siam
SNL D. Battery archive. https://www.batteryarchive.org/. Accessed 23 April 2022
Snoek J, Larochelle H, Adams RP (2012) Practical bayesian optimization of machine learning algorithms. Adv Neural Inf Process Syst 25
Song M, Moaveni B, Papadimitriou C, Stavridis A (2019) Accounting for amplitude of excitation in model updating through a hierarchical bayesian approach: application to a two-story reinforced concrete building. Mech Syst Signal Process 123:68–83
Soundappan P, Nikolaidis E, Haftka RT, Grandhi R, Canfield R (2004) Comparison of evidence theory and bayesian theory for uncertainty modeling. Reliab Eng Syst Saf 85(1–3):295–311
Subramanian A, Mahadevan S (2019) Error estimation in coupled multi-physics models. J Comput Phys 395:19–37
Suresh K, Kumarappan N (2013) Hybrid improved binary particle swarm optimization approach for generation maintenance scheduling problem. Swarm Evol Comput 9:69–89
Tan Y, Zhang L (2020) Computational methodologies for optimal sensor placement in structural health monitoring: A review. Struct Health Monit 19(4):1287–1308
Tasora A, Serban R, Mazhar H, Pazouki A, Melanz D, Fleischmann J, Taylor M, Sugiyama H, Negrut D (2015) Chrono: an open source multi-physics dynamics engine. In: International Conference on High Performance Computing in Science and Engineering. Springer, pp 19–49
T. Q. D. Team. Pymc3. https://docs.pymc.io/en/v3/, a. Accessed 17 April 2022
T. Q. D. Team. Queso. https://github.com/libqueso/queso/, b. Accessed 17 April 2022
T. S. D. Team. Shm data sets and software. https://www.lanl.gov/projects/national-security-education-center/engineering/software/shm-data-sets-and-software.php, 2022. Accessed 24 May 2022
Thelen A, Zhang X, Fink O, Lu Y, Ghosh S, Youn BD, Todd MD, Mahadevan S, Hu C, Hu Z (2022) A comprehensive review of digital twin—part 1: modeling and twinning enabling technologies. Struct Multidisc Optim
Tong K, Bakhary N, Kueh A, Yassin A (2014) Optimal sensor placement for mode shapes using improved simulated annealing. Smart Struct Syst 13(3):389–406
Van Amersfoort J, Smith L, Teh YW, Gal Y (2020) Uncertainty estimation using a single deep deterministic neural network. In: International conference on machine learning, pp 9690–9700. PMLR
Van Dongen BF, de Medeiros AKA, Verbeek H, Weijters A, van Der Aalst WM (2005) The prom framework: a new era in process mining tool support. In: International conference on application and theory of petri nets. Springer, pp 444–454
VanDerHorn E, Mahadevan S (2021) Digital twin: generalization, characterization and implementation. Decis Support Syst 145:113524
Vega MA, Hu Z, Fillmore TB, Smith MD, Todd MD (2021) A novel framework for integration of abstracted inspection data and structural health monitoring for damage prognosis of miter gates. Reliab Eng Syst Saf 211:107561
Verbeek H, Buijs J, Van Dongen B, van der Aalst WM (2010) Prom 6: the process mining toolkit. Proc. BPM Demonstration Track 615:34–39
Viana FA, Nascimento RG, Dourado A, Yucesan YA (2021) Estimating model inadequacy in ordinary differential equations with physics-informed neural networks. Comput Struct 245:106458
Walker E, Rayman S, White RE (2015) Comparison of a particle filter and other state estimation methods for prognostics of lithium-ion batteries. J Power Sources 287:1–12
Wang P, Wang T (2006) Adaptive routing for sensor networks using reinforcement learning. In: The Sixth IEEE International Conference on Computer and Information Technology (CIT’06), pp 219–219. IEEE
Wang T, Yu J, Siegel D, Lee J (2008) A similarity-based prognostics approach for remaining useful life estimation of engineered systems. In: 2008 international conference on prognostics and health management, pp 1–6. IEEE
Wang S, Chen W, Tsui K-L (2009) Bayesian validation of computer models. Technometrics 51(4):439–451
Wang D, Miao Q, Pecht M (2013) Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model. J Power Sources 239:253–264
Wang P, Youn BD, Hu C, Ha JM, Jeon B (2015) A probabilistic detectability-based sensor network design method for system health monitoring and prognostics. J Intell Mater Syst Struct 26(9):1079–1090
Wang Z, Li H-X, Chen C (2019) Reinforcement learning-based optimal sensor placement for spatiotemporal modeling. IEEE Trans Cybern 50(6):2861–2871
Ward R, Choudhary R, Gregory A, Jans-Singh M, Girolami M (2021) Continuous calibration of a digital twin: Comparison of particle filter and bayesian calibration approaches. Data-Centric Eng 2
Weigert M, Schmidt U, Boothe T, Müller A, Dibrov A, Jain A, Wilhelm B, Schmidt D, Broaddus C, Culley S, Rocha-Martins M (2018) Content-aware image restoration: pushing the limits of fluorescence microscopy. Nat Methods 15(12):1090–1097
White G, Zink A, Codecá L, Clarke S (2021) A digital twin smart city for citizen feedback. Cities 110:103064
Wilkinson RD, Vrettas M, Cornford D, Oakley JE (2011) Quantifying simulator discrepancy in discrete-time dynamical simulators. J Agric Biol Environ Stat 16(4):554–570
Williams C, Rasmussen C (1995) Gaussian processes for regression. Adv Neural Inf Process Syst 8
Winterfeldt DV, Fischer GW (1975) Multi-attribute utility theory: models and assessment procedures. Util Probab Hum Decis Making 47–85
Xi Z, Dahmardeh M, Xia B, Fu Y, Mi C (2019) Learning of battery model bias for effective state of charge estimation of lithium-ion batteries. IEEE Trans Veh Technol 68(9):8613–8628
Xiong Y, Chen W, Tsui K-L, Apley DW (2009) A better understanding of model updating strategies in validating engineering models. Comput Methods Appl Mech Eng 198(15–16):1327–1337
Yan J, Laflamme S, Hong J, Dodson J (2021) Online parameter estimation under non-persistent excitations for high-rate dynamic systems. Mech Syst Signal Process 161:107960
Yang C, Liang K, Zhang X (2020a) Strategy for sensor number determination and placement optimization with incomplete information based on interval possibility model and clustering avoidance distribution index. Comput Methods Appl Mech Eng 366:113042
Yang Z, Lu Y, Yeung H, Kirishnamurty S (2020b) 3d build melt pool predictive modeling for powder bed fusion additive manufacturing. 22662: V009T09A046
Yang Y, Chadha M, Hu Z, Vega MA, Parno MD, Todd MD (2021) A probabilistic optimal sensor design approach for structural health monitoring using risk-weighted f-divergence. Mech Syst Signal Process 161:107920
Yao L, Sethares WA, Kammer DC (1993) Sensor placement for on-orbit modal identification via a genetic algorithm. AIAA J 31(10):1922–1928
Ye M, Guo H, Xiong R, Yu Q (2018) A double-scale and adaptive particle filter-based online parameter and state of charge estimation method for lithium-ion batteries. Energy 144:789–799
Yeung H, Yang Z, Lu Y (2020) A meltpool prediction based scan strategy for powder bed fusion additive manufacturing. J Addit Manuf 35:101383
Yi T-H, Li H-N, Gu M (2011) Optimal sensor placement for structural health monitoring based on multiple optimization strategies. Struct Des Tall Spec Build 20(7):881–900
Yucesan YA, Viana FA (2020) A physics-informed neural network for wind turbine main bearing fatigue. Int J Prognostics Health Manag 11(1)
Zacharaki A, Vafeiadis T, Kolokas N, Vaxevani A, Xu Y, Peschl M, Ioannidis D, Tzovaras D (2021) Reclaim: toward a new era of refurbishment and remanufacturing of industrial equipment. Front Art Intell 101
Zhang J, Lee J (2011) A review on prognostics and health monitoring of li-ion battery. J Power Sources 196(15):6007–6014
Zhang X, Li J, Xing J, Wang P, Yang Q, Wang R, He C (2014) Optimal sensor placement for latticed shell structure based on an improved particle swarm optimization algorithm. Math Probl Eng
Zhang C, Lim P, Qin AK, Tan KC (2016) Multiobjective deep belief networks ensemble for remaining useful life estimation in prognostics. IEEE Trans Neural Netw Learn Syst 28(10):2306–2318
Zhang X, Mahadevan S, Deng X (2017) Reliability analysis with linguistic data: an evidential network approach. Reliab Eng Syst Saf 162:111–121
Zhang Q, Shi L, Holzman M, Ye M, Wang Y, Carmona F, Zha Y (2019) A dynamic data-driven method for dealing with model structural error in soil moisture data assimilation. Adv Water Resour 132:103407
Zhao Y, Pandey V, Kim H, Thurston D (2010) Varying lifecycle lengths within a product take-back portfolio
Zhao Z, Liang B, Wang X, Lu W (2017) Remaining useful life prediction of aircraft engine based on degradation pattern learning. Reliab Eng Syst Saf 164:74–83
Zhu J, Mathews I, Ren D, Li W, Cogswell D, Xing B, Sedlatschek T, Kantareddy SNR, Yi M, Gao T, Xia Y (2021) End-of-life or second-life options for retired electric vehicle batteries. Cell Rep Phys Sci 2(8):100537
Acknowledgements
Adam Thelen and Chao Hu would like to thank the financial support from the U.S. National Science Foundation under Grant No. ECCS-2015710. Xiaoge Zhang is supported by a grant from the Research Committee of The Hong Kong Polytechnic University under project code 1-BE6V. Sankaran Mahadevan acknowledges the support of the National Institute of Science and Technology. Michael D. Todd and Zhen Hu received financial support from the U.S. Army Corps of Engineers through the U.S. Army Engineer Research and Development Center Research Cooperative Agreement W912HZ-17-2-0024.
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All authors read and approved the final manuscript. CH and ZH devised the original concept of the review paper. ZH, AT, and XZ were responsible for the literature review. AT was responsible for geometric modeling. CH, AT, and ZH were responsible for physics-based modeling. ZH was responsible for data-driven modeling. CH and ZH were responsible for physics-informed ML. XZ was responsible for system modeling. CH and ZH were responsible for probabilistic model updating. XZ was responsible for ML model updating. CH and ZH were responsible for fault diagnostics, failure prognostics, and predictive maintenance. YL was responsible for MPC. OF was responsible for federated learning and domain adaptation. XZ, ZH, and OF were responsible for deep reinforcement learning. CH was responsible for UQ of ML models. ZH was responsible for UQ of dynamic system models, optimization for sensor placement, and optimization for physical system modeling. YL was responsible for the optimization of additive manufacturing processes. XZ and ZH were responsible for real-time mission planning. AT and CH were responsible for the case study and predictive maintenance scheduling. CH was responsible for open-source software and data. SG was responsible for the industry demonstration. CH, MT, and SM were responsible for perspectives. All authors participated in manuscript writing, review, editing, and comment. All correspondence should be addressed to Chao Hu (e-mails: chao.hu@uconn.edu; huchaostu@gmail.com) and Zhen Hu (e-mail: zhennhu@umich.edu).
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The Python code and preprocessed dataset used for the battery case study are available for download on Githubhttps://github.com/acthelen/battery_digital_twin.
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Thelen, A., Zhang, X., Fink, O. et al. A comprehensive review of digital twin—part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives. Struct Multidisc Optim 66, 1 (2023). https://doi.org/10.1007/s00158-022-03410-x
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DOI: https://doi.org/10.1007/s00158-022-03410-x