Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

A Generalized Fuzzy Linguistic Model for Predicting Component Concentrations in an Optical Gas Sensing System

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NOx, SO2 etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

A generalized fuzzy linguistic model for predicting component concentrations in an optical gas sensing system

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NO_x, SO₂ etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.