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Reduced order feedback control equations for linear time and frequency domain analysis

An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized.

Frisch, H. P.↗

User's Guide for MSAP2D: A Program for Unsteady Aerodynamic and Aeroelastic (Flutter and Forced Response) Analysis of Multistage Compressors and Turbines

This guide describes the input data required for using MSAP2D (Multi Stage Aeroelastic analysis Program - Two Dimensional) computer code. MSAP2D can be used for steady, unsteady aerodynamic, and aeroelastic (flutter and forced response) analysis of bladed disks arranged in multiple blade rows such as those found in compressors, turbines, counter rotating propellers or propfans. The code can also be run for single blade row. MSAP2D code is an extension of the original NPHASE code for multiblade row aerodynamic and aeroelastic analysis. Euler equations are used to obtain aerodynamic forces. The structural dynamic equations are written for a rigid typical section undergoing pitching (torsion) and plunging (bending) motion. The aeroelastic equations are solved in time domain. For single blade row analysis, frequency domain analysis is also provided to obtain unsteady aerodynamic coefficients required in an eigen analysis for flutter. In this manual, sample input and output are provided for a single blade row example, two blade row example with equal and unequal number of blades in the blade rows.

Reddy, T. S. R.↗

Sensor selection and tool wear prediction with data‐driven models for precision machining

Abstract Estimation of tool wear in precision machining is vital in the traditional subtractive machining industry to reduce processing cost, improve manufacturing efficiency and product quality. In this vein, fusion of time and frequency‐domain features of commonly sensed signals can provide an early indication of tool wear and improve its prediction accuracy for prognostics and health management. This paper presents a data‐driven methodology and a complete tool chain for the inference of precision machining tool wear from fused machine measurements, such as cutting force, power, audio and vibration signals, and quantify the usefulness of each measurement. Indicators of tool wear are extracted from time‐domain signal statistics, frequency‐domain analysis, and time‐frequency domain analysis. Correlation coefficients between the extracted features (indicators) and the tool wear are used to select the most informative features. Principal Component Analysis and Partial Least‐Squares are used to reduce the dimensionality of the feature space. Regression models, including linear regression, support vector regression, Decision tree regression, neural network regression and Gaussian process regression, are used to predict the tool wear using data from a Haas milling machine performing spiral boss face milling. The performance of the regression models based on subsets of sensors validates the preliminary estimates about the saliency of the sensors. The experimental results show that the proposed methods can predict the machine tool wear precisely, with readily available sensor measurements. Neural network and Gaussian process regression were able to achieve good estimates of tool wear at different machine operating conditions. The most informative signal in predicting tool wear was shown to be the vibration signal. Time‐frequency domain features were the most informative features among the combination of features of three domains. In addition, using partial least squares components extracted from the original features of signals led to higher prediction accuracy.

Han, Seulki↗

PLATSIM: An efficient linear simulation and analysis package for large-order flexible systems

PLATSIM is a software package designed to provide efficient time and frequency domain analysis of large-order generic space platforms implemented with any linear time-invariant control system. Time domain analysis provides simulations of the overall spacecraft response levels due to either onboard or external disturbances. The time domain results can then be processed by the jitter analysis module to assess the spacecraft's pointing performance in a computationally efficient manner. The resulting jitter analysis algorithms have produced an increase in speed of several orders of magnitude over the brute force approach of sweeping minima and maxima. Frequency domain analysis produces frequency response functions for uncontrolled and controlled platform configurations. The latter represents an enabling technology for large-order flexible systems. PLATSIM uses a sparse matrix formulation for the spacecraft dynamics model which makes both the time and frequency domain operations quite efficient, particularly when a large number of modes are required to capture the true dynamics of the spacecraft. The package is written in MATLAB script language. A graphical user interface (GUI) is included in the PLATSIM software package. This GUI uses MATLAB's Handle graphics to provide a convenient way for setting simulation and analysis parameters.

Maghami, Periman↗

Characterizing patterns and variability of building electric load profiles in time and frequency domains

The rapid development of advanced metering infrastructure provides a new data source—building electrical load profiles with high temporal resolution. Electric load profile characterization can generate useful information to enhance building energy modeling and provide metrics to represent patterns and variability of load profiles. Such characterizations can be used to identify changes to building electricity demand due to operations or faulty equipment and controls. In this study, we proposed a two-path approach to analyze high temporal resolution building electrical load profiles: (1) time-domain analysis and (2) frequency-domain analysis. Furthermore, the commonly adopted time-domain analysis can extract and quantify the distribution of key parameters characterizing load shape such as peak-base load ratio and morning rise time, while a frequency-domain analysis can identify major periodic fluctuations and quantify load variability. We implemented and evaluated both paths using whole-year 15-minute interval smart meter data of 188 commercial office building in Northern California. The results from these two paths are consistent with each other and complementary to represent full dynamics of load profiles. The time- and frequency-domain analyses can be used to enhance building energy modeling by: (1) providing more realistic assumptions about building operation schedules, and (2) validating the simulated electric load profiles using the developed variability metrics against the real building load data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

Maghami, Peiman G.↗

Linearized Frequency-Domain Gust Analysis and Adjoint-Based Sensitivities

Gust analysis is added to a linearized frequency-domain method in FUN3D, a NASA computational fluid dynamics solver. The method linearizes about a nonlinear static equilibrium condition and is therefore appropriate for problems with small perturbations such as transonic stochastic gust analysis. In addition to the gust analysis, adjoint-based sensitivities of stochastic gust constraints are implemented for multidisciplinary design optimization. The linearized frequency-domain gust model and adjoint-based sensitivities are described and verified. The method is applied to an optimization for mass minimization of the AGARD 445.6 wing subject to a stochastic gust constraint limiting the displacement of the wing tip.

Aeroelasticity↗

Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

36 MATERIALS SCIENCE↗

Asymptotic Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis

The Asymptotic Waveform Evaluation (AWE) technique is applied to a generalized frequency domain electromagnetic problem. Most of the frequency domain techniques in computational electromagnetics result in a matrix equation, which is solved at a single frequency. In the AWE technique, the Taylor series expansion around that frequency is applied to the matrix equation. The coefficients of the Taylor's series are obtained in terms of the frequency derivatives of the matrices evaluated at the expansion frequency. The coefficients hence obtained will be used to predict the frequency response of the system over a frequency range. The detailed derivation of the coefficients (called 'moments') is given along with an illustration for electric field integral equation (or Method of Moments) technique. The radar cross section (RCS) frequency response of a square plate is presented using the AWE technique and is compared with the exact solution at various frequencies.

Cockrell, C. R.↗

A frequency domain stability analysis of a phase plane control system

A describing function is used to model a phase plane controller which is part of the Space Shuttle on-orbit Reaction Control System autopilot. A frequency domain stability analysis of the closed-loop control system is applied to a study of potential flight control system interaction with the Orbiter and a class of payloads deployed from a tilt table. Phase-gain plot techniques are used to show that expansion of phase plane angular rate limits and stiffening of the tilt table pivot do not always enhance system stability. Instability region approximations are mapped as a function of rate limit, payload geometry, jet used, and natural frequency of the pivot. Comparison of the describing function analysis with simulation results shows excellent correlation.

Hattis, P. D.↗

Submerged Pressure Differential Plate Wave Energy Converter with Variable Geometry: Preprint

This work presents a novel wave energy converter device concept that combines a submerged pressure differential plate with variable geometry modules. The two variable geometry sections, placed at the force and aft locations on the plate, consist of five identical flaps that are opened in ascending order starting with the flaps closest to the edges of the plate and moving inward. The variable geometry modules act as control surfaces that allow for the hull geometry to be adjusted leading to changes in the hydrodynamics. The device geometry is controlled in a quasi-static fashion while the power-take off (PTO) unit would be controlled on a wave-to-wave time scale. The submerged plate is tethered directly to the seabed by integrated mooring and PTO lines eliminating the need for a second reaction body. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, PTO force, and absorber body motion. The frequency domain analysis required the linearization of the PTO dynamics to couple the fore and aft PTOs to the motion of the absorber body. The inclusion of the variable geometry modules was shown to be effective at altering the device geometry to provide changes in the absorber hydrodynamics to produce measurable reductions in structural and PTO loading.

16 TIDAL AND WAVE POWER↗

Flight-Time Identification of a UH-60A Helicopter and Slung Load

This paper describes a flight test demonstration of a system for identification of the stability and handling qualities parameters of a helicopter-slung load configuration simultaneously with flight testing, and the results obtained.Tests were conducted with a UH-60A Black Hawk at speeds from hover to 80 kts. The principal test load was an instrumented 8 x 6 x 6 ft cargo container. The identification used frequency domain analysis in the frequency range to 2 Hz, and focussed on the longitudinal and lateral control axes since these are the axes most affected by the load pendulum modes in the frequency range of interest for handling qualities. Results were computed for stability margins, handling qualities parameters and load pendulum stability. The computations took an average of 4 minutes before clearing the aircraft to the next test point. Important reductions in handling qualities were computed in some cases, depending, on control axis and load-slung combination. A database, including load dynamics measurements, was accumulated for subsequent simulation development and validation.

Cicolani, Luigi S.↗

Flight-Time Identification of a UH-60A Helicopter and Slung Load

This paper describes a flight test demonstration of a system for identification of the stability and handling qualities parameters of a helicopter-slung load configuration simultaneously with flight testing, and the results obtained. Tests were conducted with a UH-60A Black Hawk at speeds from hover to 80 kts. The principal test load was an instrumented 8 x 6 x 6 ft cargo container. The identification used frequency domain analysis in the frequency range to 2 Hz, and focussed on the longitudinal and lateral control axes since these are the axes most affected by the load pendulum modes in the frequency range of interest for handling qualities. Results were computed for stability margins, handling qualities parameters and load pendulum stability. The computations took an average of 4 minutes before clearing the aircraft to the next test point. Important reductions in handling qualities were computed in some cases, depending on control axis and load-sling combinations. A database, including load dynamics measurements, was accumulated for subsequent simulation development and validation.

Cicolani, Luigi S.↗

A harmonic balance method for PDEs

In this report, we describe some approaches to calculate the non-linear system of equations prescribed by the harmonic balance method (HB), a frequency domain analysis technique for modelling a non-linear system of partial differential equations (PDEs). The approach which we ultimately pursue can be seen as a time-collocation approach, except that the harmonic balance equations are obtained weakly (in the sense used in the calculus of variations). This weak formulation allows us to adapt existing transient or stationary PDEs models in the Panzer/Trilinos framework for frequency domain analysis via the harmonic balance method. We begin with a motivatation for the harmonic balance method and outline its mathematical formulation. We then describe some approaches to calculate the harmonic balance formulae, and their means of implementation through the modification of a Panzer tutorial problem - a stationary Helmholtz equation with a constant Dirichlet boundary condition and a non-linear source. For each of these approaches, we outline the necessary adaptations to solve the corresponding (periodically) transient Helmholtz equation with a (temporally) periodic Dirichlet boundary condition and non-linear source.

97 MATHEMATICS AND COMPUTING↗