Application of Model Order Reduction to an Industrial-scale Natural Gas Boiler

Abstract

Reduced order models (ROMs) were constructed as a possible digital twin for real time monitoring and prediction of an industrial natural gas boiler. Proper guidelines for optimal setups of ROMs are derived through a series of parametric studies on major factors directly related to the performances of the ROMs. The training samples and validation samples for ROMs are configured with the scalar fields from the steady-state numerical simulations with various excess air ratios (EARs) and swirl vane angles (SVAs). EAR and SVA of each sample is selected by Latin Hypercube sampling (LHS) and the adaptive sampling. The model order was reduced by selecting a limited number of eigenmodes of the largest singular values in proper orthogonal decomposition (POD).

The surrogate model and the sparse reconstruction method are both employed as the ROMs. In Kriging as the surrogate model, the performance of Kriging is directly affected by the distribution of each parameter grid. A sensitivity study was performed in Kriging on the effects of the number of parameter grids. As the number of parameter grids increases, Kriging followed the training samples more precisely. However, the prediction performance did not improve beyond a certain level. The number of parameter grids need to be predetermined between the computational cost and the prediction accuracy.

In order for gappy-POD to be practically applied as an effective digital twin tool, the sensors should be located where real sensors can be placed. In this regard, the performance of gappy-POD with sensors on the 2D wall was evaluated as a realistic measurement option. The results with the 2D wall sensors show lower but comparable accuracy compared to the results with the 3D domain. Two new methods were tried in this study as a way to improve the practicality of gappy-POD with the 2D wall sensors. First, the sensor location optimizations were performed for the optimal locations of the 2D wall sensors. Second, a deep neural network (DNN) was applied to predict virtual sensor data as input of gappy-POD.

The optimized locations of the 2D wall sensors show improved accuracy as compared with those by LHS in the mass fraction field of nitric oxide, but no meaningful influence on temperature by two genetic algorithms with the objective functions given by the minimization of the condition number and the best point interpolation method. The 2D wall sensor data was taken as input of a DNN and corresponding virtual sensor data are predicted. The new method provided promising prediction accuracy and is proven to have high potential in fusion of virtual systems and online data for smart operation for the digital twin.