Reduced-order models based on CFD impulse and step responses

Two reduced-order modeling approaches for the evaluation of nonlinear aerodynamic forces based on CFD computations are presented. These reducedorder models (ROMs) provide a means for rapid calculation of frequency-domain generalized aerodynamic forces, which can be used in traditional flutter analysis scheme, to calculate flutter characteristics about nonlinear steady flows. Two ROMs are presented, one that is based on the Volterra theory for nonlinear systems, and a new ROM that is based on step (indicial) responses. ROM kernels are identified directly from input-output relations, and the study focuses on issues of kernel identification and their effect on the quality of the ROM. First- and second-order ROMs are generated for the response of the AGARD 445.6 wing to forced-harmon ic excitation of its elastic modes. Responses computed from the ROMs are compared to responses obtained directly from a CFD analysis in which the boundary conditions are excited harmonically. Results show that the quality of the Volterra ROM is very sensitive to the amplitudes of the impulse inputs used for identification. The step-response ROM is shown to be more accurate than the Volterra ROM and less sensitive to the amplitude used for its identification.

Two reduced-order modeling approaches for the evaluation of nonlinear aerodynamic forces based on CFD computations are presented. These reducedorder models (ROMs) provide a means for rapid calculation of frequency-domain generalized aerodynamic forces, which can be used in traditional flutter analysis scheme, to calculate flutter characteristics about nonlinear steady flows. Two ROMs are presented, one that is based on the Volterra theory for nonlinear systems, and a new ROM that is based on step (indicial) responses. ROM kernels are identified directly from input-output relations, and the study focuses on issues of kernel identification and their effect on the quality of the ROM. First- and second-order ROMs are generated for the response of the AGARD 445.6 wing to forced-harmon ic excitation of its elastic modes. Responses computed from the ROMs are compared to responses obtained directly from a CFD analysis in which the boundary conditions are excited harmonically. Results show that the quality of the Volterra ROM is very sensitive to the amplitudes of the impulse inputs used for identification. The step-response ROM is shown to be more accurate than the Volterra ROM and less sensitive to the amplitude used for its identification.

During the past decades, modern control theory has become an effective analysis and design tool for various applications, especially in aerospace engineering. Many user-friendly software packages have become available. Probably due to the fact that the time-domain approach is more popular than the frequency domain approach among control engineers, software users are often required to input state space model data {A, B, C, D) to initiate their tasks. However, state-space data is not always available to software users. More specifically, the data which is made available to engineers might be in the form of time-series (e.g., unit step responses, impulse responses, and frequency responses). The objective of this paper is to present a technique which enables one to generate reduced-order state-space model data (A, B, C, D) from time-domain data (impulse and unit step response). Computational examples of flight control systems will be presented herein to demonstrate the merit of this proposed technique. Generation of State Space Models from the Impulse and Unlt Step Responses To identify a partially known system, test signals such as a unit step function or approximate impulsive function are frequently used to generate system responses. Based on these system responses, (i.e., unit step and impulse responses) a state space model (A, B. C, D) can be generated. This section is concerned with a approach for generating (A, B, C, D) from either an impulse or unit step response. The realization approach adopted here has a built-in capability for providing reduced order models. The impulse response h(t) specifies a linear SISO system which has the following state-space representation where the state vector x (t) is an n x 1 vector and the system matrix A is n x n. The dimension n is to be determined. From linear system theory (Chen, 19841, it is well known that any impulse response h(t) can be expressed in terms of A, b and namely where the state-transition matrix e*t denotes the exponential of the matrix At. In the sequel, focus will be placed on the problem of finding A, b and c from a known impulse response h(t). A numerical procedure will be developed along with computational results. A set of sampled data (time series) h ( k ~ ) is first obtained by sampling the impulse response h(t), where T is the sampling period. Recalling that h(t) = c eAt b then

A methodology for efe cient evaluation of generalized aerodynamic forces (GAFs) in transonic e ows for use in e utter analysis is presented. GAF matrices are evaluated from a reduced-order model (ROM), which comprises the generalized aerodynamic forces recorded from a time-accurate computational e uid dynamics (CFD) analysis in response to a modal step excitation in each structural mode. With the step response database, that is, the ROM, the comprehensive CFD analysis is replaced by a simple convolution scheme to compute the GAFs. The forces due to excitation of one mode at a given Mach number for all reduced frequencies can be computed from a single step response. Comparison of the GAFs computed from the ROM to those computed by direct sinusoidal excitation of the boundary conditions in a CFD run demonstrate, that for small amplitudes of excitation, the ROM is capable of predicting the unsteady aerodynamic forces very accurately. The use of ROM offers a signie cant reduction in computational time and makes the calculation of CFD-based unsteady aerodynamic forces for e utter analysis feasible. The CFD-based GAFs are used to conduct a e utter analysis of the AGARD 445.6 wing at several Mach numbers, and the results are compared to wind tunnel test results.

Aeroservoelastic Analysis for Transonic Missile Based on Computational Fluid Dynamics

Order reduction via balancing and suboptimal control of a fuel cell – Reformer system

The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood occur in the airways whose dimensions vary from several centimeters to micrometers. Organization of about 60,000 conducting airways and 33 million respiratory airways in a limited space results in a complex structure. Due to this inherent complexity and a high number of airways, using target-oriented dimensional reduction is inevitable. In addition, there is no general reduced-order model for various types of problems. This necessitates coming up with an appropriate model from a variety of different reduced-order models to solve the desired problem. Lumped formulation, trumpet, or typical path model of whole or parts of bronchial tree are frequently used reduced-order models. On the other hand, using any of these models results in underestimation of flow heterogeneity leading to inaccurate prediction of the systems whose mechanisms depend on the fluid heterogeneity. In this study, a simple robust model combining mechanistic and non-mechanistic modeling approaches of the bronchial tree is proposed which overcomes the limitations of the previous reduced-order models and gives the same results of a detailed mechanistic model for the first time. This model starts from an accurate multi-branching model of conducting and respiratory airways (i.e., the base model) and suggests a proxy model of conducting airway and reduced-order model of respiratory airways based on the base model to significantly reduce computational cost while retaining the accuracy. The combination of these models suggests various reduced-order surrogate models of the human bronchial tree for different problems. The applications and limitations of each reduced-order model are also discussed. The accuracy of the proposed model in the prediction of fluid heterogeneity has been examined by the simulation of multi-breath inert gas washout because the alveolar slope is the reflection of fluid heterogeneity where the computational time decreases from 121h (using the base model) to 4.8s (using the reduced-order model). A parallel strategy for solving the equations is also proposed which decreases run time by 0.18s making the model suitable for real-time applications. Furthermore, the ability of the model has been evaluated in the modeling of asthmatic lung as an instance of abnormal lungs, and in the modeling of O2-CO2 exchange as an instance of nonlinear reacting systems. The results indicate that the proposed model outperforms previous models based on accuracy, robustness, and run time.

In recent years, autonomously guided parachute systems have been developed with the goal of increasing the landing accuracy of airdrop operations. These precision airdrop systems utilize an onboard global positioning system (GPS) coupled with a guidance, navigation and control (GNC) system to continuously monitor and correct the flight path of the parachute system during descent. A critical component of the GNC system is an algorithm that predicts the response of the system to various aerodynamic forces in real-time that are typically based on a low-order multi-degree of freedom (DOF) dynamics model. Reduced order modeling is the process of representing a complex dynamic system with many DOF with a model having relatively few DOF. The goal of this study is to examine the use of large scale finite element models to construct and calibrate Reduced Order Models (ROM) for parachute systems. The resulting ROM would provide parachute designers with a simple tool to examine parachute behavior under various operating conditions. The use of numerical simulations to calibrate the ROM would help to eliminate the number of physical tests needed to characterize a parachute system’s properties. In this study, a 6 degree of freedom ROM is adopted. The system dynamic properties for the ROM and the resultant forces and moments acting on the ROM are obtained from finite element simulations. The 6 DOF model originally proposed by Cockrell and Doherr and later used by Dobrokhodov is adopted for the ROM. The finite element (FE) code, TENSION, is used to perform the large scale simulations and extract the ROM dynamic properties and resultant forces. Several examples are performed that verify the ROM procedure by comparing ROM predictions to FE simulations for various parachute system trajectories. The performance of the ROM is shown to be excellent for in-plane motion under an oscillating wind field. It is shown, however, that the ROM procedure deteriorates as the FE model is refined by adding more DOF. It is demonstrated that, for highly deformable FE models with many DOF, more sophisticated ROM procedures are needed.

Reduced order model (ROM) of a pouch type lithium polymer battery based on electrochemical thermal principles for real time applications

Step responses for two-dimensional electromagnetic models

Systematically derived weights based order diminution of continuous systems using GWO algorithm

This article presents an approach based on numerical reduced-order modeling to analyze the thermal behavior of electric traction motors. In this article, a single conjugate heat transfer analysis provides the possibility to accurately predict thermal performances by incorporating both computational fluid dynamic and heat transfer modules. Then, the developed model is used as the basis for deriving a fast reduced-order model of the traction motor enabling prediction of motor thermal behavior in duty cycles with a high number of operating points. All the results achieved are verified using flow and temperature measurements carried out on a traction motor designed and built for a traction application. A good agreement between the measured and estimated values of flows and temperatures is achieved while keeping the computation time within a reasonable range for both the full-order and reduced-order conjugate heat transfer models. The optimized full-order model can be run in minutes and the reduced-order model computation time is less than one second per operating point. The transient simulation based on the reduced-order model is conducted and both the learning phase and validation results are well illustrated. It is shown than the deviation of the reduced-order model in estimating the motor thermal performance is less than one celsius degree from the full-order model.

Nonlinear unsteady aerodynamic forces prediction and aeroelastic analysis of wind-induced bridge response at multiple wind speeds: A deep learning-based reduced-order model

Reliable and computationally affordable aeroelastic simulations of compressor blades are of capital relevance today, as modern turbomachinery for aircraft propulsion are expected to meet stricter goals on weight saving and fuel efficiency through slender and highly-loaded geometries with a reduced number of blades, that may ultimately lead to a higher flutter susceptibility. In this paper, an aeroelastic reduced order model (ROM) based on the aerodynamic influence coefficient (AIC) technique for flutter simulation in transonic compressor blades is adopted to compute the aerodynamic damping for two resonance conditions. The ROM is capable of performing flutter simulations in both an uncoupled and a coupled way. In the former, the motion of blades is imposed as a travelling wave vibration pattern, with constant amplitude, frequency and phase, and the exchanged work between the fluid and the blade is used to assess stability; in the latter, a structural and an aerodynamic subsystem are built for each blade, exchanging displacements and forces respectively at the blade surface in a time-marching model. The key point in model order reduction is the accurate representation of unsteady aerodynamic forces. To this purpose a training simulation is setup, which relates the displacement of a blade to the induced aerodynamic loads on the neighbouring ones, called aerodynamic influence coefficients. In the uncoupled model the unsteady pressure field on the blade surface is adopted as AIC, while in the coupled version the AIC are the modal aerodynamic forces, related to the motion of blades with system identification techniques. The ROM is applied to the TU-Darmstadt Open Test Rotor geometry, a representative case of modern transonic compressor designs. Two resonance conditions are selected, where the crossing between a natural frequency and the rotational speed allows the experimental measurement of aerodynamic damping of the selected mode at several mass flows through a blade tip-timing system. Validation of the CFD model is performed by computing the compressor map in steady conditions and comparing the data against experimental measurements. After that, the uncoupled ROM accuracy is assessed, by comparing the aerodynamic damping for the two resonances at different mass flows and IBPA to full order flutter simulations adopting Fourier transformation and harmonic balance methods. The coupled ROM is then setup and compared to experimental data on damping ratio at the same conditions. The results prove the accuracy of the developed ROM, as well as a consistent reduction in computational cost compared to full order calculations.

Microgrids (MGs) concepts are a systematic way to integrate the supply and demand side along with the storage devices. These mostly use renewable energy resources (RESs) viz. solar PV and wind turbines, interfaced to the low voltage distribution network via an inverter. As several components are involved, MGs has a system of systems (SoSs) architecture and its modeling leads to form a high order system. Hence, for the controllers' design purposes, these models had to be brought down to a reduced lower order system. This paper performs a comparative study of various model order reduction (MOR) techniques viz. aggregation, balanced truncation (BT), singular perturbation (SP) and Hankel norm approximation (HNA) on a two-source autonomous MG system. The standard performance evaluation methods used for a multi-input multi-output (MIMO) system i.e. the step and impulse responses, eigenvalue analysis and Bode plots were considered to determine the effectiveness of these MOR method.