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Probabilistic Boolean network modeling of an industrial machine

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Abstract

Theoretical modeling of manufacturing processes assists the design of new systems for predictions of future behavior, identifies improvement areas, and evaluates changes to existing systems. A novel approach is proposed to model industrial machines using probabilistic Boolean networks (PBNs) to study the relationship between machine components, their reliability and function. Once a machine is modeled as a PBN, through identification of regulatory nodes, predictors and selection probabilities, simulation and property verification are used to verify model correctness and behavior. Using real machine data, model parameters are estimated and a PBN is built to describe the machine, and formulate valid predictions about probability of failure through time. Two models were established: one with non-deterministic inputs (proposed), another with components’ MTBFs inputs. Simulations were used to generate data required to conduct inferential statistical tests to determine the level of correspondence between predictions and real machine data. An ANOVA test shows no difference between expected and observed values of the two models (p value = 0.208). A two-sample T test demonstrates the proposed model provides values closer to expected values; consequently, it can model observable phenomena (p value \(=\) 0.000). Simulations are used to generate data required to conduct inferential statistical tests to determine the level of correspondence between model prediction and real machine data. This research demonstrates that using PBNs to model manufacturing systems provides a new mechanism for the study and prediction of their future behavior at the design phase, assess future performance and identify areas to improve design reliability and system resilience.

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References

  • Akutsu, T., Kosub, S., Melkman, A., & Tamura, T. (2012). Finding a periodic attractor of a Boolean network. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9(5), 1410–1421.

    Article  Google Scholar 

  • Anghinolfi, D., Boccalante, A., Grosso, A., Paolucci, M., Passadore, A., & Vecchiola, C. (2007). A swarm intelligence method applied to manufacturing scheduling. In Proceedings of the WOA (pp. 65–70).

  • Arnosti, D. N., & Ay, A. (2012). Boolean modeling of gene regulatory networks: Driesch redux. Proceedings of the National Academy of Sciences, 109(45), 18239–18240.

    Article  Google Scholar 

  • Assef, Y., Bastard, P., & Meunier, M. (1996). Artificial neural networks for single phase fault detection in resonant grounded power distribution sytems. In Proceedings of the 1996 transmission and distribution conference. http://ieeexplore.ieee.org.ezproxy.library.wisc.edu/xpls/abs_all.jsp?arnumber=547573.

  • Ayhan, M. B., Aydin, M. E., & Öztemel, E. (2013). A multi-agent based approach for change management in manufacturing enterprises. Journal of Intelligent Manufacturing. doi:10.1007/s10845-013-0794-2.

  • Babiceanu, R. F., & Chen, F. F. (2006). Development and applications of holonic manufacturing systems: A survey. Journal of Intelligent Manufacturing, 17(1), 111–131.

    Article  Google Scholar 

  • Bane, V., Ravanmehr, V., & Krishnan, A. R. (2012). An information theoretic approach to constructing robust Boolean gene regulatory networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9(1), 52–65.

    Article  Google Scholar 

  • Barbosa, J. & Leitão, P. (2011). Simulation of multi-agent manufacturing systems using agent-based modelling platforms. In Proceedings of the 9th IEEE international conference on industrial informatics (INDIN), Lisbon, Portugal (pp. 477–482).

  • Barghash, M. A., & Santarisi, N. S. (2004). Pattern recognition of control charts using artificial neural networks—Analyzing the effect of the training parameters. Journal of Intelligent Manufacturing, 15(5), 635–644.

    Article  Google Scholar 

  • Beaudin, M. (1990). Manufacturing systems analysis. Englewood Cliffs, NJ: Yourdon Press.

    Google Scholar 

  • Berntensis, N., & Ebeling, M. (2013). Detection of attractors of large Boolean networks via exhaustive enumeration of appropriate subspaces of the state space. BMC Bioinformatics, 14, 361.

    Article  Google Scholar 

  • Booker, L., Goldberg, D., & Holland, J. H. (1989). Clasifier systems and genetic algorithms. Artificial Intelligence, 40(1–3), 235–282.

    Article  Google Scholar 

  • Chaib-Draa, B., Moulin, B., Mandiau, R., & Millot, P. (1992). Trends in distributed artificial intelligence. Artificial Intelligence Review, 6, 35–66.

    Article  Google Scholar 

  • Chaouiya, C., Ourrad, O., & Lima, R. (2013). Majority rules with random tie-breaking in Boolean gene regulatory networks. PLoS ONE, 8(7), e69626.

    Article  Google Scholar 

  • Chen, H., & Sun, J. (2014). Stability and stabilisation of context-sensitive probabilistic Boolean networks. IET Control Theory & Applications, 8(17), 2115–2121.

    Article  Google Scholar 

  • Chen, X., Jiang, H., & Ching, W.-K. (2012). On construction of sparse probabilistic Boolean Networks. East Asian Journal on Applied Mathematics. doi:10.4208/eajam.030511.060911a.

  • Cheng, X., Sun, M., & Socolar, J. E. S. (2013). Autonomous Boolean modelling of developmental gene regulatory networks. Journal of the Royal Society Interface, 10(78), 20120574.

    Article  Google Scholar 

  • Ching, W.-K., Chen, X., & Tsing, N.-K. (2009). Generating probabilistic Boolean networks from a prescribed transition probability matrix. IET Systems Biology, 3, 453–464.

    Article  Google Scholar 

  • Ching, W.-K., Zhang, S.-Q., Jiao, Y., Akutsu, T., Tsing, N.-K., & Wong, A.-S. (2009). Optimal control policy for probabilistic Boolean networks with hard constraints. IET Systems Biology, 3(2), 90–99.

    Article  Google Scholar 

  • Cicirello, V., & Smith, S. (2001a). Improved routing wasps for distributed factory control. In Proceedings of the workshop on artificial intelligence and manufacturing. Presented at the workshop on artificial intelligence and manufacturing.

  • Cicirello, V., & Smith, S. (2001b). Wasp nests for self-configurable factories. In Proceedings of the 5th international conference on autonomous agents.

  • Corry, P., & Kozan, E. (2004). Ant colony optimisation for machine kayout problems. Computational Optimization and Applications, 28(3), 287–310.

    Article  Google Scholar 

  • Didier, G., & Remy, E. (2012). Relations between gene regulatory networks and cell dynamics in Boolean models. Discrete Applied Mathematics, 160(15), 2147–2157.

    Article  Google Scholar 

  • Dorigo, M. (1992). Optimization, learning, and natural algorithms (Doctoral Thesis). Politecnico di Milano, Milan, Italy.

  • Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical Computer Science, 344(2–3), 243–278.

    Article  Google Scholar 

  • Dougherty, E. R. (2011). Validation of gene regulatory networks: Scientific and inferential. Briefings in Bioinformatics, 12(3), 245–252.

    Article  Google Scholar 

  • Dougherty, E. R., Kim, S., & Chen, Y. (2000). Coefficient of determination in nonlinear signal processing. Signal Processing, 80, 2219–2235.

    Article  Google Scholar 

  • Dubrova, E., & Teslenko, M. (2011). A SAT-based algorithm for finding attractors in synchronous Boolean networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8(5), 1393–1399. doi:10.1109/TCBB.2010.20.

    Article  Google Scholar 

  • Ebeling, C. E. (1997). An introduction to reliability and maintainability engineering. New York: McGraw-Hill.

    Google Scholar 

  • Gao, Y., Xu, P., Wang, X., & Liu, W. (2013). The complex fluctuations of probabilistic Boolean networks. BioSystems, 114(1), 78–84.

    Article  Google Scholar 

  • Gershenson, C. (2007). Design and control of self-organizing systems. CopIt Arxives, Mexico. http://tinyurl.com/DCSOS2007.

  • Ghanbarnejad, F. (2012). Perturbations in Boolean networks as model of gene regulatory dynamics (doctoral thesis). Leipzig: University of Leipzig.

    Google Scholar 

  • Gu, J.-W., Ching, W.-K., Siu, T.-K., & Zheng, H. (2013). On modeling credit defaults: A probabilistic Boolean network approach. Risk and Decision Analysis, 4(2), 119–129.

    Google Scholar 

  • Guo, W., Yang, G., Wu, W., He, L., & Sun, M. (2014). A parallel attractor finding algorithm based on Boolean satisfiability for genetic regulatory networks. PLoS One .

  • Hopfensitz, M., Müssel, C., & Maucher, M. (2012). Attractors in Boolean networks: a tutorial. Computational Statistics. http://www.springerlink.com.ezproxy.library.wisc.edu/index/NR1671N55Q3365Q5.pdf

  • Hsieh, F.-S., & Lin, J.-B. (2013). A self-adaptation scheme for workflow management in multi-agent systems. Journal of Intelligent Manufacturing.

  • Hsieh, F.-S., & Lin, J.-B. (2014). Context-aware workflow management for virtual enterprises based on coordination of agents. Journal of Intelligent Manufacturing, 25(3), 393–412.

    Article  Google Scholar 

  • Huang, Y., McMurran, R., Dhadyalla, G., & Jones, R. P. (2008). Probability based vehicle fault diagnosis: Bayesian network method. Journal of Intelligent Manufacturing, 19(3), 301–311.

    Article  Google Scholar 

  • Jamhour, A., & García, C. (2012). Automation of industrial serial processes based on finite state machines. Presented at the 20th international congress of chemical and process engineering, Prague, Czech Republic.

  • Kauffman, S. A. (1969a). Homeostasis and differentitation in random genetic control networks. Nature, 224, 177–178.

    Article  Google Scholar 

  • Kauffman, S. A. (1969b). Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22, 437–467.

    Article  Google Scholar 

  • Kauffman, S. A. (1993). The origins of order: Self-organization and selection in evolution. NewYork: Oxford University Press.

    Google Scholar 

  • Kobayashi, K., & Hiraishi, K. (2010). Reachability analysis of probabilistic Boolean networks using model checking. Presented at the SICE annual conference 2010, proceedings of (pp. 829–832). http://library.uprm.edu:2055/stamp/stamp.jsp?tp=&arnumber=5604207.

  • Koestler, A. (1967). The ghost in the machine. New York: Macmillan.

    Google Scholar 

  • Kumar, A., & Dhingra, A. K. (2012). Optimization of scheduling problems: A genetic algorithm survey. International Journal of Applied Science and Engineering Research, 1(1), 11–25.

    Google Scholar 

  • Kwiatkowska, M. Z., Norman, G., & Parker, D. (2011). PRISM 4.0: Verification of probabilistic real-time systems. In G. Gopalakrishnan & S. Qadeer (Eds.), Computer Aided Verification. Lecture Notes in Computer Science (Vol. 6806, pp. 585–591). Berlin, Heidelberg: Springer.

  • Leger, R., Garland, W., & Poehlman, W. F. S. (1998). Fault detection and diagnosis using statistical control charts and artificial neural networks. Artificial Intelligence in Engineering. http://www.sciencedirect.com.ezproxy.library.wisc.edu/science/article/pii/S0954181096000398.

  • Leitão, P. (2008). Self-organization in manufacturing systems: Challenges and opportunities. In Procedings of the second IEEE international conference on self-adaptive and self-organizing systems workshops (pp. 174–179). Presented at the 2nd IEEE international conference on self-adaptive and self-organizing systems.

  • Leitão, P., & Restivo, F. (2002). Agent-based holonic production control. In Proceedings of the 13th international workshop on database and expert systems applications (pp. 589–596).

  • Li, P., Zhang, C., Perkins, E. J., Gong, P., & Deng, Y. (2007). Comparison of probabilistic Boolean network and dynamic Bayesian network approaches for inferring gene regulatory networks. BMC Bioinformatics, 8(13).

  • Liang, R., Qiu, Y., & Ching, W.-K. (2014). Construction of Probabilistic Boolean Network for Credit Default Data. In Proceedings of the seventh international joint conference on computational science and optimization. Presented at the Seventh International Joint Conference on Computational Science and Optimization.

  • Liu, X., Yi, H., & Zhong-hua, N. (2013). Application of ant colony optimization algorithm in process planning optimization. Journal of Intelligent Manufacturing, 24(1), 1–13.

    Article  Google Scholar 

  • Liu, Y., Ling, X., Zhewen, S., Mingwei, L., Fang, J., & Zhang, L. (2011). A survey on particle swarm optimization algorithms for multimodal function optimization. Journal of Software, 6(12), 2449.

    Google Scholar 

  • Markov, A. A. (1954). The theory of algorithms. Academy of Sciences of the USSR, 42, 3–375.

    Google Scholar 

  • Moon, I., Lee, S., Shin, M., & Ryu, K. (2014). Evolutionary resource assignment for workload-based production scheduling. Journal of Intelligent Manufacturing.

  • Moore, K., & Gupta, S. M. (1996). Petri net models of flexible and automated manufacturing systems: A survey. International Journal of Production Research, 34(11), 3001–3035.

    Article  Google Scholar 

  • Mosallam, A., Medjaher, K., & Zerhouni, N. (2014). Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction. Journal of Intelligent Manufacturing. doi:10.1007/s10845-014-0933-4.

  • Nouiri, M., Bekrar, A., Jemai, A., Niar, S., & Ammari, A. C. (2015). An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem. Journal of Intelligent Manufacturing. doi:10.1007/s10845-015-1039-3.

  • Pal, R., Ivanov, I., Datta, A., Bittner, M. L., & Dougherty, E. R. (2006). Synthesizing Boolean networks with a given attractor structure. Genomic Signal Processing and Statistics, 2006. GENSIPS’06. IEEE International Workshop on, 73–74, doi:10.1109/GENSIPS.2006.353162.

  • Park, H.-S., & Tran, N.-H. (2010). An intelligent manufacturing system with biological principles. International Journal of CAD/CAM, 10(1), 39–50.

    Google Scholar 

  • Prokopenko, M. (2009). Guided self-organization. HFSP Journal, 3(5), 287–289.

    Article  Google Scholar 

  • Qiu, Y., Tamura, T., Ching, W.-K., & Akutsu, T. (2014). On control of singleton attractors in multiple Boolean networks: Integer programming-based method. BMC Systems Biology, 8, S7.

    Article  Google Scholar 

  • Rausand, M., & Høyland, A. (2004). Systems reliability theory: Models, statistical methods, and applications (2nd ed.). Hoboken, NJ: Wiley.

    Google Scholar 

  • Ristevski, B. (2013). A survey of models for inference of gene regulatory networks. Nonlinear Analysis-Modeling and Control, 18(24), 444–465.

    Google Scholar 

  • Sahin, C., Demitras, M., Erol, R., Baykasoğlu, A., & Kaplanoğlu, V. (2015). A multi-agent based approach to dynamic scheduling with flexible processing capabilities. Journal of Intelligent Manufacturing. doi:10.1007/s10845-015-1069-x.

  • Samanta, B., & Nataraj, C. (2009). Application of particle swarm optimization and proximal support vector machines for fault detection. Swarm Intelligence, 3(4), 303–325.

  • Shmulevich, I., Dougherty, E., & Kim, S. (2002). Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks. Bioinformatics. http://bioinformatics.oxfordjournals.org.ezproxy.library.wisc.edu/content/18/2/261.short

  • Shmulevich, I., & Dougherty, E. R. (2010). Probabilistic boolean networks: Modeling and control of gene regulatory networks. Philadelphia, PA: SIAM.

    Book  Google Scholar 

  • Shmulevich, I., Dougherty, E. R., Kim, S., & Zhang, W. (2002). From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proceedings of the IEEE, 90, 1778–1792.

    Article  Google Scholar 

  • Skitt, P. J. C., Javed, M. A., Sanders, S. A., & Higginson, A. M. (1993). Process monitoring using auto-associative, feed-forward artificial neural networks. Journal of Intelligent Manufacturing, 4(1), 79–94.

    Article  Google Scholar 

  • Sood, A. (2013). Artificial neural networks-growth & learn: A survey. International Journal of Soft Computing and Engineering, 3(3), 103–104.

    Google Scholar 

  • Sun, T.-H., Tien, F.-C., Tien, F.-C., & Kuo, R.-J. (2014). Automated thermal fuse inspection using machine vision and artificial neural networks. Journal of Intelligent Manufacturing. doi:10.1007/s10845-014-0902-y.

  • Tchangani, A. P. (2004). Decision-making with uncertain data: Bayesian linear programming approach. Journal of Intelligent Manufacturing, 15(1), 17–27.

    Article  Google Scholar 

  • Trairatphisan, P., Mizera, A., Pang, J., Tantar, A. A., Schneider, J., & Sauter, T. (2013). Recent development and biomedical applications of probabilistic Boolean networks. Cell Communication and Signaling, 11, 46.

    Article  Google Scholar 

  • Ueda, K. (1992). A concept for bionic manufacturing systems based on DNA-type information. In Proceedings of the 8th international PROLAMAT conference (pp. 853–863).

  • Ueda, K. (1993). A genetic approach toward future manufacturing systems. In J. Peklenik (Ed.), Flexible manufacturing systems: Past–present–future (p. 211). Ljubljana, Slovenia: CIRP.

  • Ueda, K. (1994). Biological manufacturing systems. Tokyo: Kogyochosakai.

    Google Scholar 

  • Ueda, K., Vaario, J., & Ohkura, K. (1997). Modelling of biological manufacturing systems for dynamic reconfiguration. Annals of the CIRP, 46(1), 343–346.

    Article  Google Scholar 

  • Vahedi, G. (2009). An engineering approach towards personalized cancer therapy. Retrieved from http://gradworks.umi.com.ezproxy.library.wisc.edu/33/84/3384337.html

  • Wang, X., Wang, H., & Qi, C. (2014). Multi-agent reinforcement learning based maintenance policy for a resource constrained flow line system. Journal of Intelligent Manufacturing. doi:10.1007/s10845-013-0864-5.

  • Wooldridge, M. (2002). An introduction to multi-agent systems. New York: Wiley.

    Google Scholar 

  • Wu, C.-H., Wang, D.-Z., Ip, A., Wang, D.-W., Chan, C.-Y., & Wang, H.-F. (2009). A particle swarm optimization approach for components placement inspection on printed circuit boards. Journal of Intelligent Manufacturing, 20(5), 535–549.

    Article  Google Scholar 

  • Xiong, W., & Fu, D. (2015). A new immune multi-agent system for the flexible shop scheduling problem. Journal of Intelligent Manufacturing. doi:10.1007/s10845-015-1137-2.

  • Zainal, N., Zain, A. M., Razi, N. H. M., & Othman, M. R. (2014). Glowworm swarm optimization (GSO) for optimization of machining parameters. Journal of Intelligent Manufacturing. doi:10.1007/s10845-014-0914-7.

  • Zheng, D., Yang, G., Li, X., Wang, Z., Liu, F., & He, L. (2013). An efficient algorithm for computing attractors of sychronous and asynchronous Boolean networks. PLoS One, 8(4), e60593. doi:10.1371/journal.pone.0060593.

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Authors and Affiliations

  1. ETSET-Universidade de Vigo, Campus Universitario, s/n, 36310, Vigo, Spain

    Pedro J. Rivera Torres & Luis Anido Rifón

  2. Polytechnic University of Puerto Rico, 377 Ponce De Leon Ave., San Juan, PR, 00918, USA

    E. I. Serrano Mercado

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  1. Pedro J. Rivera Torres
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Rivera Torres, P.J., Serrano Mercado, E.I. & Anido Rifón, L. Probabilistic Boolean network modeling of an industrial machine. J Intell Manuf 29, 875–890 (2018). https://doi.org/10.1007/s10845-015-1143-4

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