Galvanin, Federico

Quaglio, Marco

Sangoi, Enrico

English

UCL Discovery

520 560 600 640 680 72050110170230290350Sampling time [s]Temperature [K]26.4028.9731.5534.1336.7039.2741.8544.4247.00ANN test-accuracy [%]05010015020025052056060064068072010152025303540455055Temperature [K]ANN test-accuracy [%]Initial concentration of A [mol/m3 ]Optimal Design of Experiments for Artificial Neural Network-based Kinetic Model RecognitionEnrico Sangoi, Marco Quaglio, Federico GalvaninDepartment of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UKCorresponding Author: f.galvanin@ucl.ac.ukEnrico Sangoi Prof. Federico GalvaninThe problem of kinetic model selectionSeries mechanism:   𝐴 ՜𝑘1𝐵, 𝐵՜𝑘3𝐶Parallel mechanism: 𝐴 ՜𝑘1B, 𝐴՜𝑘2𝐶Material balancesd𝐶𝑖d𝑡= σ𝑗=13 ν𝑖𝑗𝑟𝑗 ∀𝑖 = 𝐴, 𝐵, 𝐶Arrhenius-type kinetic factors𝑘𝑗 = 𝐴𝑗𝑒−𝐸𝑎,𝑗/𝑅𝑇 ∀𝑗=1, 2, 3Series mechanism Parallel mechanismLabel: 1 2 3 4 5 6 7 8𝒓𝟏 𝑘1 ∙ 𝐶𝐴 𝑘1 ∙ 𝐶𝐴 𝑘1 ∙ 𝐶𝐴2 𝑘1 ∙ 𝐶𝐴2 𝑘1 ∙ 𝐶𝐴 𝑘1 ∙ 𝐶𝐴 𝑘1 ∙ 𝐶𝐴2 𝑘1 ∙ 𝐶𝐴2𝒓𝟐 𝑘2 ∙ 0 𝑘2 ∙ 0 𝑘2 ∙ 0 𝑘2 ∙ 0 𝑘2 ∙ 𝐶𝐴 𝑘2 ∙ 𝐶𝐴2 𝑘2 ∙ 𝐶𝐴 𝑘2 ∙ 𝐶𝐴2𝒓𝟑 𝑘3 ∙ 𝐶𝐵 𝑘3 ∙ 𝐶𝐵2 𝑘3 ∙ 𝐶𝐵 𝑘3 ∙ 𝐶𝐵2 𝑘3 ∙ 0 𝑘3 ∙ 0 𝑘3 ∙ 0 𝑘3 ∙ 0Objective function to be maximised: Artificial Neural Network accuracy on unseen dataAccΨtest =𝑖 ∈ 1,… , 𝑁Ψtest s. t. n𝑖 , 𝑙𝑖 ∈ Ψtest ∧መ𝑙𝑖 = 𝑙𝑖𝑖 ∈ 1, … , 𝑁Ψtest s. t. n𝑖 , 𝑙𝑖 ∈ Ψtest∙ 100%where Ψtest is the testing-set of data (size 𝑁Ψtest), n𝑖 experimental data and 𝑙𝑖 the label of the model used to generate the data and መ𝑙𝑖 the label predicted by the ANN. 1 2 3 4 5 630405060708090100Artificial neural network test-accuracy, (%)Number of experiments s=1.00  Temperature, reactant concentration and sampling time s=4.00   Temperature and reactant concentration s=10.00  Temperature and sampling timeThe proposed approach has been tested on a case study with in silico generated experimental data. The system considered was an isothermal batch reactor, where the experimental conditions were defined by:➢ Initial concentration of reactant A➢ Temperature➢ Sampling timesThe reacting system was characterised by three species: A, B, CWe aimed at discriminating among 8 candidate model structures, assuming the reactions could take place either in series or parallel, and being described either by 1st or 2ndorder power law kinetic equations.  Kinetic models formulation520 540 560 580 600 620 640 660 680 700 72050100150200250300350Sampling time (s)Temperature (K)520 540 560 580 600 620 640 660 680 700 72050100150200250300350Sampling time (s)Temperature (K) 1 exp  4 exp 2 exp  5 exp 3 exp  6 expArtificial neural network for kinetic model recognitionA different approach may be considered to discriminate among the models by means of Artificial Neural Network classifiers. [2]The advantages are▲ Small amount of experimental data required (in silico dataset generation)▲ No structural identifiability test → no rejection of any model a priori[1] S.P. Asprey and S. Macchietto, 2000, Statistical Tools for Optimal Dynamic ModelBuilding, Computers & Chemical Engineering, 24, 1261-1267[2] M. Quaglio, L. Roberts, M.S. Bin Japaar, E.S. Fraga, V. Dua, F. Galvanin, 2020, AnArtificial Neural Network Approach to Recognise Kinetic Models from Experimental Data,Computers & Chemical Engineering, 135We propose to couple the ANN application to model recognition with a population algorithm for optimizing the experimental conditions, aiming to improve the ANN performance. ➢ The number of experiments is provided as an input to the algorithm➢ The ANN training is performed with simulated experimental data, which include parameter uncertainty within feasibility regions.➢ Physical experiments are only required to be conducted at the identified optimal conditions, then the acquired experimental data is fed to the trained ANN.The classical model discrimination approach [1]is characterised by several steps. The modelling process may require a significant amount of time and the quantity of experimental data may be limited due to cost and time limitations. Low experimental errorHigh experimental errorThe limitations are:▼ No information about the model parameters from the discrimination▼ Experimental design is fixedSENSITIVITY ANALYSIS➢ The choice of the experimental conditions has a strong impact on the ANN performance. ➢ Using a fixed experimental design may lead to suboptimal performance or to conduct unnecessary experiments.Experimental errorε~𝒩 0, 𝜎2OPTIMAL DESIGN OF EXPERIMENTS➢ The optimization algorithm performance was satisfactory both in the case of low and high noise on experimental data.➢ High levels of accuracy were obtained with just a few experiments required even in the high experimental error scenario. ➢ The choice of which experimental variables to manipulate affected the outcome in terms of ANN accuracy.➢ When the optimal ANN failed, the correct model was always among the top 3 ranked models. 1 exp  4 exp 2 exp  5 exp 3 exp  6 exp➢ The identification of kinetic model structures using ANNs was improved by optimizing the experimental design.➢ Steep increase in ANN accuracy with respect to the number of experiments.➢ High levels of accuracy were obtained with a minimal number of experiments to be conducted.➢ The proposed approach is promising for conducting a first discrimination among many candidate kinetic models.Noise σMax ANN accuracyN exp.1.00 100 % 44.00 97 % 510.00 92 % 5I wish to thank UCL’s Department of Chemical Engineering and the EU Erasmus+ Study Abroad project that allowed me to study and do research at UCL during my Masters.  Symbol Lower bound Upper bound𝐶𝐴0 0 𝑚𝑜𝑙/𝑚3 250 𝑚𝑜𝑙/𝑚3𝑇 520 K 720 K𝑡 50 sec 350 secGitHub repository for the Python code

Optimal Design of Experiments for Artificial Neural Network-based Kinetic Model Recognition

https://discovery.ucl.ac.uk/10173050/1/Poster_Sangoi_Enrico_industrial_consortium.pdf

Optimal Design of Experiments for Artificial Neural Network-based Kinetic Model Recognition

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