{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T14:45:33Z","timestamp":1784904333185,"version":"3.55.0"},"reference-count":41,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Laboratory Directed Research and Development Program at Oak Ridge National Laboratory (ORNL)","award":["DE-FG2-13ER41967"],"award-info":[{"award-number":["DE-FG2-13ER41967"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cyber-physical system security presents unique challenges to conventional measurement science and technology. Anomaly detection in software-assisted physical systems, such as those employed in additive manufacturing or in DNA synthesis, is often hampered by the limited available parameter space of the underlying mechanism that is transducing the anomaly. As a result, the formulation of anomaly detection for such systems often leads to inverse or ill-posed problems, requiring statistical treatments. Here, we present Bayesian inference of unknown parameters associated with a generic actuator considered as a representative vital element of a cyber-physical system. Via a series of experimental input-output measurements, a transfer function for the actuator is obtained numerically, which serves as our model for the proposed method. Linear, nonlinear, and delayed dynamics may be assumed for the actuator response. By devising a code-based malicious signal, we study the efficacy of Bayesian inference for its potential to produce a detection, including uncertainty quantification, with a remarkably small number of input data points. Our approach should be adaptable to a variety of real-time cyber-physical anomaly detection scenarios.<\/jats:p>","DOI":"10.3390\/s22166112","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T03:15:27Z","timestamp":1660706127000},"page":"6112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian Estimation of Oscillator Parameters: Toward Anomaly Detection and Cyber-Physical System Security"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9650-4462","authenticated-orcid":false,"given":"Joseph M.","family":"Lukens","sequence":"first","affiliation":[{"name":"Quantum Information Science Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4736-4157","authenticated-orcid":false,"given":"Ali","family":"Passian","sequence":"additional","affiliation":[{"name":"Quantum Information Science Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Srikanth","family":"Yoginath","sequence":"additional","affiliation":[{"name":"Systems and Decision Sciences Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3133-2537","authenticated-orcid":false,"given":"Kody J. H.","family":"Law","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Manchester, Manchester M13 9PL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joel A.","family":"Dawson","sequence":"additional","affiliation":[{"name":"Energy and Control Systems Security Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Passian, A., and Imam, N. (2019). Nanosystems, edge computing, and the next generation computing systems. Sensors, 19.","DOI":"10.3390\/s19184048"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7804","DOI":"10.1016\/j.egyr.2021.05.037","article-title":"A review of transactive energy systems: Concept and implementation","volume":"7","author":"Huang","year":"2021","journal-title":"Energy Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1109\/TSG.2019.2928168","article-title":"Cyber Physical Security Analytics for Transactive Energy Systems","volume":"11","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s11416-020-00349-9","article-title":"Analytical modelling of cyber-physical systems: Applying kinetic gas theory to anomaly detection in networks","volume":"16","author":"Tavolato","year":"2020","journal-title":"J. Comput. Virol. Hacking Tech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/TASE.2019.2918562","article-title":"Context-Sensitive Modeling and Analysis of Cyber-Physical Manufacturing Systems for Anomaly Detection and Diagnosis","volume":"17","author":"Saez","year":"2020","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_6","unstructured":"National Academies of Sciences, Engineering, and Medicine (2018). Biodefense in the Age of Synthetic Biology, National Academies Press."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Faezi, S., Chhetri, S.R., Malawade, A.V., Chaput, J.C., Grover, W., Brisk, P., and Al Faruque, M.A. (2019, January 24\u201327). Oligo-Snoop: A Non-Invasive Side Channel Attack Against DNA Synthesis Machines. Proceedings of the Network and Distributed Systems Security Symposium (NDSS 2019), San Diego, CA, USA.","DOI":"10.14722\/ndss.2019.23544"},{"key":"ref_8","unstructured":"Ney, P., Koscher, K., Organick, L., Ceze, L., and Kohno, T. (2017, January 16\u201318). Computer Security, Privacy, and DNA Sequencing: Compromising Computers with Synthesized DNA, Privacy Leaks, and More. Proceedings of the 26th USENIX Security Symposium (USENIX Security 17), Vancouver, BC, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"133421","DOI":"10.1109\/ACCESS.2019.2928005","article-title":"Detecting Sabotage Attacks in Additive Manufacturing Using Actuator Power Signatures","volume":"7","author":"Gatlin","year":"2019","journal-title":"IEEE Access"},{"key":"ref_10","first-page":"431","article-title":"Security of additive manufacturing: Attack taxonomy and survey","volume":"21","author":"Yarnpolskiy","year":"2018","journal-title":"Addit. Manuf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100301","DOI":"10.1016\/j.ijcip.2019.05.004","article-title":"Optimal sabotage attack on composite material parts","volume":"26","author":"Ranabhat","year":"2019","journal-title":"Int. J. Crit. Infrastruct. Protect."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"102138","DOI":"10.1016\/j.cose.2020.102138","article-title":"Quantitative cyber-physical security analysis methodology for industrial control systems based on incomplete information Bayesian game","volume":"102","author":"Liu","year":"2021","journal-title":"Comput. Secur."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1109\/TCSS.2018.2858440","article-title":"Dynamic Security Risk Evaluation via Hybrid Bayesian Risk Graph in Cyber-Physical Social Systems","volume":"5","author":"Li","year":"2018","journal-title":"IEEE Trans. Comput. Soc. Syst."},{"key":"ref_14","unstructured":"Kornecki, A.J., Subramanian, N., and Zalewski, J. (2013, January 8\u201311). Studying Interrelationships of Safety and Security for Software Assurance in Cyber-Physical Systems: Approach Based on Bayesian Belief Networks. Proceedings of the 2013 Federated Conference on Computer Science and Information Systems, Krakow, Poland."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"233403","DOI":"10.1103\/PhysRevB.75.233403","article-title":"Stochastic excitation and delayed oscillation of a micro-oscillator","volume":"75","author":"Passian","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114314","DOI":"10.1063\/1.2365378","article-title":"Fluctuation and dissipation of a stochastic micro-oscillator under delayed feedback","volume":"100","author":"Passian","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"113206","DOI":"10.1088\/1742-5468\/aa9346","article-title":"Energetics of a driven Brownian harmonic oscillator","volume":"2017","author":"Yaghoubi","year":"2017","journal-title":"J. Stat. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102030L","DOI":"10.1117\/12.2264588","article-title":"An approach to detecting deliberately introduced defects and microdefects in 3D printed objects","volume":"10203","author":"Straub","year":"2017","journal-title":"Proc. SPIE"},{"key":"ref_19","unstructured":"Srinivasan, S. (2022, July 07). Duffing Oscillator. Available online: www.mathworks.com\/matlabcentral\/fileexchange\/44987-duffing-oscillator."},{"key":"ref_20","unstructured":"Ralich, R. (2022, July 07). Stochastic Resonance in the Duffing Oscillator with MATLAB. Available online: https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/35479-stochastic-resonance-in-the-duffing-oscillator-with-matlab."},{"key":"ref_21","unstructured":"Heng, J., Jasra, A., Law, K.J.H., and Tarakanov, A. (2021). On Unbiased Estimation for Discretized Models. arXiv."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Jasra, A., Law, K.J., and Yu, F. (2021). Randomized multilevel Monte Carlo for embarrassingly parallel inference. arXiv.","DOI":"10.1007\/978-3-030-96498-6_1"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Martins, G., Bhatia, S., Koutsoukos, X., Stouffer, K., Tang, C., and Candell, R. (2015, January 18\u201320). Towards a systematic threat modeling approach for cyber-physical systems. Proceedings of the Resilience Week (RWS), Philadelphia, PA, USA.","DOI":"10.1109\/RWEEK.2015.7287428"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lazarova-Molnar, S., Niloofar, P., and Barta, G.K. (2020, January 14\u201318). Data-driven fault tree modeling for reliability assessment of cyber-physical systems. Proceedings of the Winter Simulation Conference (WSC), Orlando, FL, USA.","DOI":"10.1109\/WSC48552.2020.9383882"},{"key":"ref_25","unstructured":"MacKay, D.J.C. (2003). Information Theory, Inference, and Learning Algorithms, Cambridge University Press."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Smith, C.R., and Erickson, G.J. (1987). Bayesian Spectrum and Chirp Analysis. Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems, Reidel.","DOI":"10.1007\/978-94-009-3961-5"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Robert, C.P., and Casella, G. (1999). Monte Carlo Statistical Methods, Springer.","DOI":"10.1007\/978-1-4757-3071-5"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1214\/13-STS421","article-title":"MCMC methods for functions: Modifying old algorithms to make them faster","volume":"28","author":"Cotter","year":"2013","journal-title":"Stat. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of State Calculations by Fast Computing Machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"Monte Carlo sampling methods using Markov chains and their applications","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"063038","DOI":"10.1088\/1367-2630\/ab8efa","article-title":"A practical and efficient approach for Bayesian quantum state estimation","volume":"22","author":"Lukens","year":"2020","journal-title":"New J. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"053501","DOI":"10.1103\/PhysRevA.104.053501","article-title":"Bayesian inference for plasmonic nanometrology","volume":"104","author":"Lukens","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1137\/130929904","article-title":"Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors","volume":"3","author":"Vollmer","year":"2015","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"ref_34","unstructured":"MathWorks (2022, July 07). tfest. Available online: www.mathworks.com\/help\/ident\/ref\/tfest.html."},{"key":"ref_35","unstructured":"MathWorks (2022, July 07). ksdensity. Available online: www.mathworks.com\/help\/stats\/ksdensity.html."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Bretthorst, G.L. (1988). Bayesian Spectrum Analysis and Parameter Estimation, Springer.","DOI":"10.1007\/978-1-4684-9399-3"},{"key":"ref_37","unstructured":"Casella, G., and Berger, R.L. (2002). Statistical Inference, Duxbury. [2nd ed.]."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"102236","DOI":"10.1016\/j.peva.2021.102236","article-title":"Fundamental scaling laws of covert DDoS attacks","volume":"151","author":"Ramtin","year":"2021","journal-title":"Perform. Eval."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1111\/rssb.12336","article-title":"Unbiased Markov chain Monte Carlo methods with couplings","volume":"82","author":"Jacob","year":"2020","journal-title":"J. R. Stat. Soc. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2140\/camcos.2010.5.65","article-title":"Ensemble samplers with affine invariance","volume":"5","author":"Goodman","year":"2010","journal-title":"Commun. Appl. Math. Comput. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Huang, D.Z., Huang, J., Reich, S., and Stuart, A.M. (2022). Efficient derivative-free Bayesian inference for large-scale inverse problems. arXiv.","DOI":"10.1088\/1361-6420\/ac99fa"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:09:18Z","timestamp":1760141358000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,16]]},"references-count":41,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166112"],"URL":"https:\/\/doi.org\/10.3390\/s22166112","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,16]]}}}