An Efficient Iterative Algorithm for Accurately Calculating Impulse Response Functions

This paper investigates the measurement errors involved in estimating frequency response functions (FRFs) - and related quantities such as the coherence function - from weighted overlapped segment averaging, a technique that has become a standard in modern data analyzers due to its computational advantages. Particular attention is paid to leakage errors, for which this technique has frequently been criticized. Our main result is that a half-sine or diff window with about 2/3 overlap achieves the best compromise to reduce leakage errors in the case of stationary random excitations, and this is independently of the system FRF. This conclusion is to be contrasted with the customary habit of using a Hanning window with 1/2 overlap. The same reasoning confirms that a rectangular window without overlap minimizes measurement errors in the special case of multisine excitations. Moreover, practical formulas are provided to the reader for computing the bias and variance of the frequency response and coherence functions in the general case.

Errors involved in computing impulse response functions via frequency response functions

The demand for ubiquitous telecommunications services forces operators to have a special concern about signal quality and the coverage area they offer to their customers. This was usually checked by using suitable propagation models for Single Input Single Output (SISO) systems, which are no longer the case for new and future mobile generations, such as 5G and beyond. To guarantee good signal quality coverage, operators started to replace these models with Multiple Input Multiple Output (MIMO) ones. To achieve the best results, these models are usually calibrated with Drive Test (DT) measures; however, the DTs available for MIMO propagation models are sparse, in contrast to SISO ones. The main contribution presented in this paper is a methodology to extend the propagation models of SISO systems so they can be applied in MIMO sytems with Single-Carrier and Frequency-Domain Equalization (SC-FDE), while still using DTs acquired for SISO systems. This paper presents the impact on Bit Error Rate (BER) performance and its coverage area resulting from the application of our proposed method. We consider a MIMO SC-FDE system with an Iterative Block Decision Feedback Equalization (IB-DFE) receiver and we present the improvement expressions for the BER that we illustrate with some simulations.

Frequency response function estimation techniques and the corresponding coherence functions: A review and update

Modal parameters, i.e., modal frequencies, damping ratios, and mode shapes of a two disk-shaft system are estimated in Multiple Input/Multiple Output (MIMO) scheme. The response at the output degrees of freedom (dof) of the considered structure due to the excitation at the input dofs is estimated from theoretical analysis. The generated theoretical data is used to estimate the Frequency Response Function (FRF) matrix, which relates the output (vibration) at response points with the input at the excitation points in the frequency domain. The corresponding Impulse Response Function (IRF) matrix, which relates response and excitation in the time domain, is obtained by Inverse Fast Fourier Transform (IFFT) of the FRF matrix. The unified Matrix Polynomial Approach (UMPA) is employed in the frequency and time domains with the estimated FRF and IRF matrices, respectively, to estimate the desired modal parameters. The obtained results are compared with results from Theoretical Modal Analysis (TMA).

Vehicle–road coupled system is inherently time–varying, and its responses are traditionally calculated using time–domain methods which involves significant computational effort. Aiming to improve the efficiency of response calculation for the coupled system, this paper proposes a fast calculation method in frequency domain, based on the newly developed moving frequency response function (FRF). Firstly, considering the vibration characteristics of an infinitely long road, the road response is straightforwardly expressed using the road impulse response function (IRF). Subsequently, the concept of the road moving IRF is proposed and derived with respect to the moving observation points. The moving FRF is then obtained by applying Fourier transform, which allows the responses of the road moving observation points to be established in frequency domain for fast calculation under moving loads. Furthermore, by analyzing the vehicle–road coupled vibrations, based on the vehicle FRF and road moving FRF, a formula for the vehicle–road coupling force is derived in frequency domain, along with an expression for the responses at the vehicle–road contact points. Finally, the approach is illustrated in numerical simulations of vehicle–road coupled systems, and its computational efficiency and accuracy are verified through comparison with currently popular methods.

The design of a multi-level fuzzy-logic control system for the control of turbine engines using type-1 fuzzy-logic is presented in this paper. A Matlab-Simulink model of an advanced turbine engine was used to test and validate the performance of the developed fuzzy control system. The model provided comprehensive and complex model of a turbine engine. As with most modeling of turbine engines, it was assumed that the fundamental dynamic characteristics of a turbine engine can be achieved by control of the engine fuel flow. In this model a single input single output (SISO) system is used to control the engine fuel flow, where the input to the SISO system is the low spool speed error signal and the output is the fuel flow actuator control signal. A fuzzy controller was developed for the SISO system and its performance is compared with that of the existing proportional integral (PI) controller. Both controllers were tested under normal operating conditions and with introduction of engine faults embedded in the model.

Stability properties of regenerative cutting processes, based on impulse response functions expressed in the impulse dynamic subspace

Given a SISO (single-input single-output) system with arbitrary poles and zeros in the closed right half plane and having time delay uncertainty, the question arises as to the maximum time delay margin available before the closed-loop system becomes unstable when an arbitrary controller is connected to the SISO system in the closed loop. The authors provide a solution to this problem and show how to derive the controller corresponding to the optimum condition. The method of solution is based on general framework of P.P. Khargonekar and R. Tannenbaum (1985) for the robust stabilization of SISO systems with parameter uncertainty using Nevanlinna-Pick interpolation theory and the theory of conformal mapping. >

This chapter introduces the terminology of random processes and their properties; stationarity, correlation function, power spectral density, and the Wiener–Khinchin theorem. The theory of linear, causual, and time-invariant systems is presented, as is and their characterization in terms of impulse response and frequency response function. Response to random input is next examined. The correlation functions and power spectral densitites of output in terms of those of input are given.

Investigated are modeling and control approaches for vibration analysis of two identical beams which are coupled with fluid and active mechanical links. In the modeling of the coupled beam system, orthogonal functions are used to represent vibration of the beams and the fluid-structure interaction is considered. Frequency Response Functions (FRFs) are derived from the coupled governing equations and the superposition principle for linear vibration systems. In the control of vibration of the beams, impulse response functions corresponding to the FRFs and an adaptive control algorithm are employed to attenuate vibration transmission between the two beams. Natural frequencies, mode shapes as well as the pressure distribution in the fluid are computed. The results obtained by the proposed modeling method are in good consistency with those obtained by the finite element analysis. Moreover, it is demonstrated that the active mechanical link is able to reduce vibration transmission and change the deformation of beams as well as the distribution of fluid pressure.

Nonstationary response statistics of structures with hysteretic damping to evolutionary stochastic excitation

New Coherence Function with Measurements of One Sampling Period

During the operation process of turbine blades in aero-engine, the exhaust gas flow generates complex interaction with the blade surfaces. When the excitation frequency induced by the airflow approaches the inherent natural frequency of the blade structure, resonance phenomenon occurs. This resonance not only leads to performance degradation of the engine but may also result in structural damage or even fracture of the blades, posing serious threats to the safety and reliability of the engine. Therefore, precise measurement and analysis of blade modal parameters hold significant importance. This study establishes a methodology for measuring blade modal parameters. The proposed approach employs the Single Input Single Output (SISO) technique, applying sinusoidal sweep-frequency excitation to measure blade responses, and ultimately calculates the Frequency Response Function (FRF). Additionally, the Matrix Pencil Method (MPM) is utilized to perform matrix decomposition on the FRF, thereby extracting modal characteristic parameters within the sweep frequency range of the blades. Experimental results demonstrate that the measurement method adopted in this study can accurately obtain blade modal parameters, providing valuable reference for optimizing the dynamic design of turbine blades.

Frequency response functions (FRFs) can be calculated from a composite function of other FRFs composition and decomposition problems. Considering that an experimentally measured FRF has an uncertainty in its magnitude and phase, what would be the uncertainty of the magnitude and phase of an FRF calculated from a composite function of experimentally measured FRFs? This work derives analytical expressions for the uncertainty of magnitude and phase of FRFs calculated from functions composed of the basic arithmetic operations involving measured FRFs and their inherent uncertainties. The derivation of the uncertainty values comes from the application of multivariable error analysis to the basic arithmetic operations considering the real and the imaginary parts of the FRFs involved. The resultant uncertainty of the composite FRF is obtained by applying the methodology to every operation in the composite function. Hence, an analytical method is proposed for applying to both composition and decomposition problems. An example of a decomposition problem is presented, and the calculated uncertainty of the magnitude and the phase of the composite FRF showed good agreement with results obtained from Monte Carlo simulation. In addition, it is shown that the blind application of the root-mean-square rule to the composite function written in terms of magnitude is not an appropriate procedure. The proposed methodology is accurate in predicting the uncertainty of composite FRFs.