**A dedicated sensitivity analysis and optimization application for industrial processes**

**A dedicated sensitivity analysis and optimization application for industrial processes**

**Kamila Myczkowska****, Danuta Szeliga**

AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland.

**DOI:**

https://doi.org/10.7494/cmms.2021.4.0775

**Abstract:**

The paper describes the architecture and the use case of the developed Modelbox system for sensitivity analysis (SA), uncertainty analysis (UA) and the subsequent optimization of industrial processes. The proposed solution addresses the most common practical and technical problems encountered by researchers and engineers when performing sensitivity analysis. It combines the functions from the numerical toolbox with a simulation management system. Maintaining usability and a good user experience while managing complex investigations of time-consuming industrial process simulations is a very important feature of the system. Several improvements were introduced to optimize the computation time of analysis/modelling tasks, including the automatization of distributed calculations, persistent, transparent caching of simulation data and duration estimations from collected statistics. The system has the ability to perform remote, parallel, asynchronous computations of both analytic algorithms and numerical simulations. The system is dynamically scalable horizontally by using serverless computing endpoints and thus it can be easily adapted to the user’s current needs in a flexible way. Modelbox provides web-based access to analysis/modelling tasks from sampling, SA/UA, optimization to metamodelling. It is extended with numerous interactive visualization components for effective results control. In addition, to access data from the completed analysis, the system supports convergence tracking for SA estimates and intermediate optimization results.

The process of controlled cooling of rails was considered as a case study. The formulated optimization task was to find a combination of process parameters that ensures a minimum volume fraction of bainite along with required interlamellar spacing and optimal homogeneity of hardness. Different sensitivity analysis methods were used to evaluate the significance of all variables with respect to their influence on the model output.

**Cite as:**

Myczkowska, K., & Szeliga, D. (2021). A dedicated sensitivity analysis and optimization application for industrial processes.

Computer Methods in Materials Science, 21(4), 219–232. https://doi.org/10.7494/cmms.2021.4.0775

**Article (PDF)**:

**Keywords:**

Sensitivity analysis, Modelling of industrial process, Optimization, Model validation, Cooling of rails

**References:**

Apache Commons (2021). Commons Math: The Apache Commons Mathematics Library. http://commons.apache.org/proper/commons-math/.

AWS (n.d.). AWS Lambda. Run code without thinking about servers or clusters. https://aws.amazon.com/lambda/.

Ciepela, E., Nowakowski, P., Kocot, J., Harężlak, D., Gubała, D., Meizner, J., Kasztelnik, M., Bartyński, T., Malawski, M., Bubak, M. (2012). Managing entire lifecycles of e-Science applications in the GridSpace2 Virtual Laboratory – from motivation through idea to operable web-accessible environment built on top of PL-Grid e-Infrastructure. In M. Bubak, T. Szepieniec, K. Wiatr (Eds.), Building a National Distributed e-Infrastructure – PL-Grid (pp. 228–239). Springer Berlin, Heidelberg.

Douglas-Smith, D., Iwanaga, T., Croke, B.F.W., Jakeman, A.J. (2020). Certain trends in uncertainty and sensitivity analysis: An overview of software tools and techniques. Environmental Modelling & Software, 124, https://doi.org/10.1016/j.envsoft.2019.104588.

EJML (2015). Efficient Java Matrix Library. https://code.google.com/p/efficient-java-matrix-library/.

Exp4j (2017). http://www.objecthunter.net/exp4j/.

JSON JavaScript Object Notation (n.d.). Introducing JSON. Retrieved 2021 from http://www.json.org/.

Jython (n.d.). What is Jython?. Retrieved 2020 from http://www.jython.org/.

Kochenderfer, M.J., Wheeler, T.A. (2019). Algorithms for Optimization, The MIT Press.

Kodein (n.d.). Retrieved 2021 from https://github.com/Kodein-Framework/Kodein-DI/.

Kotlin (2021). Coroutines. https://kotlinlang.org/docs/reference/coroutines-overview.html.

Ktor (n.d.). Retrieved 2021 from https://github.com/Kotlin/ktor.

Kuziak, R., Pietrzyk, M. (2012). Numerical simulation of controlled cooling of rails as a tool for optimal design of this process. Computer Methods in Materials Science, 12(4), 233–243.

MathJax (n.d.). Retrieved 2020 from https://www.mathjax.org.

Milenin, A., Zalecki, W., Pernach, M., Rauch, Ł, Kuziak, R., Zygmunt, T., Pietrzyk, M. (2020). Numerical simulation of manufacturing process chain for pearlitic and bainitic steel rails. Archives of Civil and Mechanical Engineering, 20(4), 107, doi.org/10.1007/s43452-020-00107-0.

MongoDB (n.d.). Retrieved 2021 from https://www.mongodb.com/.

Morris, M.D. (1991). Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2), 161–174.

Pianosi, F., Beven, K., Freer, J., Hall, J., Rougier, J., Stephenson, D.B., Wagener, T. (2016). Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modelling and Software, 79, 214–232.

Plotly (n.d.). Retrieved 2020 from https://plot.ly/.

Prasanna, D.R. (2009). Dependency Injection. Design Patterns Using Spring and Guide. Manning.

Project Reactor (n.d.). Retrieved 2021 from https://projectreactor.io.

Radecki, M., Szymocha, T., Harężlak, D., Pawlik, M., Andrzejewski, J., Ziajka, W., Szelc, M. (2012). Integrating various grid middleware components and user services into a single platform. In M. Bubak, T. Szepieniec, K. Wiatr (Eds.), Building a National Distributed e-Infrastructure – PL-Grid (pp. 15–26). Springer Berlin, Heidelberg.

Rauch, Ł., Szeliga, D., Bachniak, D., Bzowski, K., Pietrzyk, M. (2014). Application of sensitivity analysis to grid-based procedure dedicated to creation of SSRVE. In M. Bubak, J. Kitowski, K. Wiatr (Eds.), eScience on Distributed Computing Infrastructure. Achievements of PLGrid Plus Domain-Specific Services and Tools (pp. 364–377). Springer Cham.

Razavi, S., Gupta, H.V. (2016). A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory. Water Resources Research, 52(1), 423–439.

React (n.d.). React. A JavaScript library for building user interfaces. Retrieved 2021 from https://facebook.github.io/react/.

ReactiveX (n.d.). Retrieved 2021 from http://reactivex.io/documentation/operators.html.

Redux (n.d.). Retrieved 2021 from https://github.com/reactjs/redux.

SALib (n.d.). SALib. Sensitivity Analysis Library in Python (Numpy). Contains Sobol, Morris, and FAST methods. Retrieved 2020 from http://salib.github.io/SALib/.

Saltelli, A., Chan, K., Scott, E.M. (2009). Sensitivity Analysis, Wiley.

Saltelli, A., Aleksankina, K., Becker, W., Fennell, P., Ferretti, F., Holst, N., Li, S., Wu, Q. (2019). Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices. Environmental Modelling and Software, 114, 29–39.

Scalarm (n.d.). Retrieved 2017 from https://github.com/Scalarm/scalarm.

Sheikholeslami, R., Razavi, S., Gupta, H.V., Becker, W., Haghnegahdar, A. (2019). Global sensitivity analysis for high-dimensional problems: How to objectively group factorsand measure robustness and convergence while reducing computational cost. Environmental Modelling and Software, 111, 282–299.

SimLab (n.d.). SIMLAB and other software. Retrieved 2020 from https://ec.europa.eu/jrc/en/samo/simlab.

Szeliga, D., Kusiak, J., Rauch, Ł. (2012). Sensitivity analysis as support for design of hot rolling technology of dual phase steel strips. In J. Kusiak, J. Majta, D. Szeliga (Eds.), Metal Forming 2012. Proceedings of the 14th International Conference on Metal Forming (pp. 1275–1278). Wiley-VCH.

Szeliga, D., Sztangret, Ł., Kusiak, J., Pietrzyk, M. (2013). Optimization as a support for design of hot rolling technology of dual phase steel strips. In S.-H. Zhang, X.-H. Liu, M. Cheng, J. Li (Eds.), AIP Proceedings of the 11th International Conference on Numerical Methods in Industrial Forming Processes: NUMIFORM (pp. 183–191).

Xiong, Y., Chen, W.D., Apley, D., Ding, X. (2006). A non-stationary covariance-based Kriging method for metamodelling in engineering design. International Journal for Numerical Methods in Engineering, 71(6), 733–756, https://doi.org/10.1002/nme.1969.