Reduced-Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Noncompact Gas Turbine Combustors

2015 ◽  
Vol 138 (5) ◽  
Author(s):  
Tobias Hummel ◽  
Constanze Temmler ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Gas Turbine ◽  
Time Domain ◽  
Stokes Equations ◽  
Order Reduction ◽  
High Order ◽  
Essential Information ◽  
Reduced Order ◽  
Stability Analyses ◽  
Modal Reduction ◽  
Low Order

A methodology is presented to model noncompact thermoacoustic phenomena using reduced-order models (ROMs) based on the linearized Navier–Stokes equations (LNSEs). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSEs, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow and are hence capable of describing propagation and (e.g., vortical) damping of the acoustic fluctuations within the considered volume. Such an ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools and is conceptually based on three core features: First, the multidimensional and volumetric nature of the ROM establishes access to account spatial variability and noncompact effects on heat-release fluctuations. As a result, it is particularly useful for high-frequency phenomena such as screech. Second, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Third, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, nonlinear saturation mechanisms can be included, which reproduce the nonlinear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM's underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain and discretized via the finite element method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order (N∼ 200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr∼ 100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE–FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of noncompact thermoacoustic systems using the herein presented ROMs.

Reduced Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Non-Compact Gas Turbine Combustors

2015 ◽  
Author(s):  
Tobias Hummel ◽  
Constanze Temmler ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Gas Turbine ◽  
Time Domain ◽  
Order Reduction ◽  
High Order ◽  
Essential Information ◽  
Reduced Order ◽  
Stability Analyses ◽  
Modal Reduction ◽  
Non Linear ◽  
Low Order

A methodology is presented to model non-compact thermoacoustic phenomena using Reduced Order Models (ROM) based on the Linearized Navier-Stokes Equations (LNSE). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSE, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow, and are hence capable of describing propagation and (e.g. vortical) damping of the acoustic fluctuations within the considered volume. Such a ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools, and is conceptually based on three core features: Firstly, the multi-dimensional and volumetric nature of the ROM establishes access to account spatial variability and non-compact effects on heat release fluctuations. As a result, it is particularly useful for high frequency phenomena such as screech. Secondly, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Thirdly, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, non-linear saturation mechanisms can be included, which reproduce the non-linear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM’s underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice-tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain, and discretized via the Finite Element Method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order (N ∼200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr ∼100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice-tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE-FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of non-compact thermoacoustic systems using the herein presented ROMs.

A correlation-based model order reduction approach for a diesel engine NOx and brake mean effective pressure dynamic model using machine learning

2020 ◽  
pp. 146808742093694
Author(s):  
Armin Norouzi ◽  
Masoud Aliramezani ◽  
Charles Robert Koch
Keyword(s):  
Support Vector Machine ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Support Vector ◽  
Effective Pressure ◽  
Reduction Algorithm ◽  
Order Model ◽  
Model Order ◽  
Low Order

A correlation-based model order reduction algorithm is developed using support vector machine to model [Formula: see text] emission and break mean effective pressure of a medium-duty diesel engine. The support vector machine–based model order reduction algorithm is used to reduce the number of features of a 34-feature full-order model by evaluating the regression performance of the support vector machine–based model. Then, the support vector machine–based model order reduction algorithm is used to reduce the number of features of the full-order model. Two models for [Formula: see text] emission and break mean effective pressure are developed via model order reduction, one complex model with high accuracy, called high-order model, and the other with an acceptable accuracy and a simple structure, called low-order model. The high-order model has 29 features for [Formula: see text] and 20 features for break mean effective pressure, while the low-order model has nine features for [Formula: see text] and six features for break mean effective pressure. Then, the steady-state low-order model and high-order model are implemented in a nonlinear control-oriented model. To verify the accuracy of nonlinear control-oriented model, a fast response electrochemical [Formula: see text] sensor is used to experimentally study the engine transient [Formula: see text] emissions. The high-order model and low-order model support vector machine models of [Formula: see text] and break mean effective pressure are compared to a conventional artificial neural network with one hidden layer. The results illustrate that the developed support vector machine model has shorter training times (5–14 times faster) and higher accuracy especially for test data compared to the artificial neural network model. A control-oriented model is then developed to predict the dynamic behavior of the system. Finally, the performance of the low-order model and high-order model is evaluated for different rising and falling input transients at four different engine speeds. The transient test results validate the high accuracy of the high-order model and the acceptable accuracy of low-order model for both [Formula: see text] and break mean effective pressure. The high-order model is proposed as an accurate virtual plant while the low-order model is suitable for model-based controller design.

scholarly journals Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System

2021 ◽  
Vol 5 (5) ◽  
pp. 598-618
Author(s):  
Vu Ngoc Kien ◽  
Nguyen Hien Trung ◽  
Nguyen Hong Quang
Keyword(s):  
Model Order Reduction ◽  
Design Method ◽  
Order Reduction ◽  
High Order ◽  
Optimal Order ◽  
Robust Controller ◽  
Model Order ◽  
Rotor Angle ◽  
Load Angle ◽  
Low Order

The electrical system's problem stabilizes the electrical system with three primary parameters: rotor angle stability, frequency stability, and voltage stability. This paper focuses on the problem of designing a low-order stable optimal controller for the generator rotor angle (load angle) stabilization system with minor disturbances. These minor disturbances are caused by lack of damping torque, change in load, or change in a generator during operation. Using the RH∞optimal robust design method for the Power System Stabilizer (PSS) to stabilize the generator’s load angle will help the PSS system work sustainably under disturbance. However, this technique's disadvantage is that the controller often has a high order, causing many difficulties in practical application. To overcome this disadvantage, we propose to reduce the order of the higher-order optimal robust controller. There are two solutions to reduce order for high-order optimal robust controller: optimal order reduction according to the given controller structure and order reduction according to model order reduction algorithms. This study selects the order reduction of the controller according to the model order reduction algorithms. In order to choose the most suitable low-order optimal robust controller that can replace the high-order optimal robust controller, we have compared and evaluated the order-reducing controllers according to many model order reduction algorithms. Using robust low-order controllers to control the generator’s rotor angle completely meets the stabilization requirements. The research results of the paper show the correctness of the controller order reduction solution according to the model order reduction algorithms and open the possibility of application in practice. Doi: 10.28991/esj-2021-01299 Full Text: PDF

Iterative-learning procedures for nonlinear-model-order reduction in discrete time

2019 ◽  
Vol 37 (3) ◽  
pp. 953-986
Author(s):  
Salim Ibrir
Keyword(s):  
Nonlinear Model ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Approximation Error ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Dimensional System ◽  
Model Order ◽  
Reduced Order ◽  
Low Order

Abstract Efficient numerical procedures are developed for model-order reduction of a class of discrete-time nonlinear systems. Based on the solution of a set of linear-matrix inequalities, the Petrov–Galerkin projection concept is utilized to set up the structure of the reduced-order nonlinear model that preserves the input-to-state stability while ensuring an acceptable approximation error. The first numerical algorithm is based on the construction of a constant optimal projection matrix and a constant Lyapunov matrix to form the reduced-order dynamics. The second proposed algorithm aims to incorporate the output of the original system to correct the instantaneous value of the truncation matrix and maintain an acceptable approximation error even with low-order systems. An extension to uncertain systems is provided. The usefulness and the efficacy of the developed procedures are approved by the consideration of two numerical examples treating a nonlinear low-order system and a high-dimensional system, issued from the discretization of the damped heat-transfer partial-differential equation.

Self-Adaptive Firefly Algorithm with Pole Zero Cancellation Method for Controlling SMIB Power System

2019 ◽  
Vol 18 (02) ◽  
pp. 1950013
Author(s):  
Sawsan Morkos Gharghory ◽  
Azza Elsayed Ebrahim
Keyword(s):  
Firefly Algorithm ◽  
Controller Design ◽  
Global Optimum ◽  
High Order ◽  
Step Response ◽  
Accurate Analysis ◽  
Reduced Order ◽  
Response Characteristics ◽  
Self Adaptive ◽  
Low Order

The accurate analysis and controller design for high-order systems are important issues. In this paper, a design of controller is suggested to Single Machine Infinite Bus (SMIB) System in which its order is reduced by the proposed self-adaptive Firefly Algorithm (FA). First, the dynamic adaption to the dominant parameters of the standard FA is proposed for overcoming its disadvantages and improving its ability in searching the global optimum solution with application to reduce the model order of SMIB. The parameters which are proposed to self-adaption are both of the light absorption based on the mean distance of fireflies’ positions and the step setting based on the fitness information to the status of preceding firefly and the current fireflies. Second, proportional–integral–derivative (PID) controller is suggested to be designed by pole zero cancellation method via the step response characteristics of the reduced-order SMIB to be applied to its high order. The efficiency of the proposed methods is tested on high-order SMIB to get its corresponding low order and to control it. The experimental results prove the efficacy of self-adaptive FA compared to the standard FA and the methods in the literature in terms of step response characteristics using error indices. The proposed methods assure the stability of the reduced order and the ability of the designed controller to handle both high and low-order model.

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

Improved extrapolation of steady turbulent aerodynamics using a non-linear POD-based reduced order model

2012 ◽  
Vol 116 (1184) ◽  
pp. 1079-1100 ◽  
Author(s):  
R. Zimmermann ◽  
S. Görtz
Keyword(s):  
Fluid Dynamics ◽  
Stokes Equations ◽  
Solution Space ◽  
Order Reduction ◽  
Navier Stokes ◽  
Space Representation ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Non Linear ◽  
The Cost

AbstractA reduced-order modelling (ROM) approach for predicting steady, turbulent aerodynamic flows based on computational fluid dynamics (CFD) and proper orthogonal decomposition (POD) is presented. Model-order reduction is achieved by parameter space sampling, solution space representation via POD and restriction of a CFD solver to the POD subspace. Solving the governing equations of fluid dynamics is replaced by solving a non-linear least-squares optimisation problem. The method will be referred to as LSQ-ROM method. Two approaches of extracting POD basis information from CFD snapshot data are discussed: POD of the full state vector (global POD) and POD of each of the partial states separately (variable-by-variable POD). The method at hand is demonstrated for a 2D aerofoil (NACA 64A010) as well as for a complete industrial aircraft configuration (NASA Common Research Model) in the transonic flow regime by computing ROMs of the compressible Reynolds-averaged Navier-Stokes equations, pursuing both the global and the variable-by-variable POD approach. The LSQ-ROM approach is tried for extrapolatory flow conditions. Results are juxtaposed with those obtained by POD-based extrapolation using Kriging and the radial basis functions spline method. As a reference, the full-order CFD solutions are considered. For the industrial aircraft configuration, the cost of computing the reduced-order solution is shown to be two orders of magnitude lower than that of computing the reference CFD solution.

Calibrated POD Reduced-Order Models of Massively Separated Flows in the Perspective of Their Control

2006 ◽  
Author(s):  
J. Favier ◽  
L. Cordier ◽  
A. Kourta ◽  
A. Iollo
Keyword(s):  
Optimal Control ◽  
Stokes Equations ◽  
Optimization Problems ◽  
Active Flow Control ◽  
Boundary Layer Separation ◽  
Wake Flow ◽  
Control Procedure ◽  
Reduced Order ◽  
Fidelity Model ◽  
Low Order

Lots of studies have been performed to control boundary layer separation. In order to develop a control procedure that is energetically efficient, it is interesting to formulate active flow control problems like optimization problems [1]. To reduce the numerical costs associated to this approach, a POD Reduced-Order Model is used instead of the high-fidelity model formed by the Navier-Stokes equations. Resolving this low-order dynamical system provides the dynamics of the flow on the POD subspace and using the optimal control theory, it is possible to find the optimal control law determined on the low-fidelity model [2]. In the present paper, DNS velocity fields of the wake flow behind a circular cylinder and PIV measurements of a separated flow around an airfoil are used to build and calibrate low order models.

scholarly journals Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Ngoc Kien Vu ◽  
Hong Quang Nguyen
Keyword(s):  
Inverted Pendulum ◽  
Order Reduction ◽  
Variable Load ◽  
Operating Environment ◽  
Robust Controller ◽  
Reduced Order ◽  
Actual Operating ◽  
Load Variable ◽  
Actual Control ◽  
Low Order

When there is no driver, balancing the two-wheel vehicle is a challenging but fascinating problem. There are various solutions for maintaining the balance of a two-wheel vehicle. This article presents a solution for balancing a two-wheel vehicle using a flywheel according to the inverted pendulum principle. Since uncertainties influence the actual operating environment of the vehicle, we have designed a robust controller RH∞ to maintain the vehicle equilibrium. Robust controllers often have a high order that can affect the actual control performance; therefore, order reduction algorithms are proposed. Using Matlab/Simulink, we compared the performance of the control system with different reduced-order controllers to choose a suitable low-order controller. Finally, experimental results using a low-order robust controller show that the vehicle balances steadily in different scenarios: no-load, variable load, stationary, and moving.

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