Polynomial Transfer Function Research Articles

Short time step heat flow calculation of building constructions based on frequency-domain regression method

Short time step heat flow calculation of building constructions is often needed for practical applications. Conventional methods such as state-space method and root-finding method may produce unstable conduction transfer function (CTF) coefficients at short time steps, and thus result in unstable heat flow calculation through building constructions. Frequency-domain regression (FDR) method is a newly developed method for computing CTF coefficients efficiently by representing the real building construction system with equivalent polynomial s-transfer functions. Previous studies on this method mainly addressed CTF coefficients at the conventional time step of 3600 s and the performance of heat flow calculation using these coefficients. This paper presents the investigation on the performance of CTF coefficients at various short time steps based on FDR method, and the performance of the heat flow calculation using these coefficients. The results show that FDR method can produce stable CTF coefficients at various time steps for most building constructions, and the calculated heat flows using these coefficients are of high accuracy.

Loss-efficiency model of single and variable-speed compressors using neural networks

Compressor is the critical component to the performance of a vapor-compression refrigeration system. The loss-efficiency model including the volumetric efficiency and the isentropic efficiency is widely used for representing the compressor performance. A neural network loss-efficiency model is developed to simulate the performance of positive displacement compressors like the reciprocating, screw and scroll compressors. With one more input, frequency, it can be easily extended to the variable speed compressors. The three-layer polynomial perceptron network is developed because the polynomial transfer function is found very effective in training and free of over-learning. The selection of input parameters of neural networks is also found critical to the network prediction accuracy. The proposed neural networks give less than 0.4% standard deviations and ±1.3% maximum deviations against the manufacturer data.

Neural-Network-Based Polynomial Correlation of Single- and Variable-Speed Compressor Performance

The compressor is one of the major components in a vapor-compression refrigeration system. A neural-network-based polynomial correlation method of positive-displacement compressor performance has been developed that can be applied to both single-speed and variable-speed compressor families. The multi-layer perceptron neural network was used as a universal function approximator. To align with and extend the ARI ten-coefficient correlation method (ARI 1999), the third-order polynomial transfer function is customized in the hidden layer and the pure linear function is adopted in the output layer of the neural network. The ARI ten-coefficient correlation has been proven as a special case of the proposed neural network. The new neural network method can be easily extended to multi-input/multi-output cases. In particular, in modeling the performance of a single-speed or variable-speed compressor family, this method gives less than 1% standard deviations and ±3% maximum deviations against manufacturer data.

A z -domain transfer function solution to the non-minimum phase acoustic beamformer

The two input Griffiths–Jim acoustic beamformer is analysed in the frequency domain using a causal Wiener z-transfer function formulation. Unlike previous solutions the approach here examines the particular problem of non-minimum phase acoustic transfer functions which are encountered in many real filtering problems. The polynomial transfer function approach gives an elegant way of obtaining the frequency response of the beamformer. The effect of signal leakage is also considered and a general polynomial solution is given.

An improvement to frequency-domain regression method for calculating conduction transfer functions of building walls

An improvement is proposed for the frequency-domain regression (FDR) method to calculate CTF (conduction transfer function) coefficients of multilayer constructions. This improvement aims at providing complete CTF coefficients with a unique set of d values. In the improvement, the external and internal polynomial s-transfer functions of heat conduction of a wall are identified based on equivalent frequency response characteristics by constraining their denominators equal to that of the cross polynomial s-transfer function while this cross polynomial s-transfer function of this wall is identified using FDR method in advance. The complete CTF coefficients of this wall (i.e., external CTF values a, cross CTF values b, internal CTF values c and a unique set of heat flow rate history coefficients d) can be easily calculated from these identified polynomial s-transfer functions. Examples and comparisons show that this improvement of the frequency-domain regression method works well.

Approximation of amplitude-frequency responses of minimum-phase low-frequency recursive digital filters for shaping and reception of elements of data signals

The paper considers methods of treatment and examples to the problem of approximation of AFR of digital recursive low-pass filters with any ratio between the powers of the numerator and denominator of the transfer function polynomials and for a prescribed cutoff function of AFR in the transitional domain of frequencies.

해석적인 정보를 고려한 다중입력을 받는 다자유도계 구조물의 시스템 규명 기법 개발

This paper presents a system identification method for multi-input, multi-output (MIMO) systems, by which a rational polynomial transfer function model is identified from experimentally determined frequency response function data. Analytically determined information is incorporated in this method to obtain a more reliable model, even in the frequency range where the excitation energy is limited. To verify the suggested method, shaking table test for an actively controlled two-story, bench-scale building employing an active mass damper is conducted. The results show that the proposed method is quite effective and robust for system identification of MIMO systems.

Frequency Domain Identification of Multi-Input, Multi-Output Systems Considering Physical Relationships between Measured Variables

This paper presents a new frequency domain identification method for multi-input, multi-output (MIMO) systems. Based on experimentally determined frequency response function data, rational polynomial transfer function models of structural systems are identified. Known physical relationships between the measured variables are incorporated in this MIMO frequency domain identification method. The method has three stages: (1) an initial estimation model is generated using a linear least-squares method, (2) the Steiglitz–McBride method is applied to improve the initial estimation model, and (3) a maximum likelihood estimator is optimized using the Levenberg–Marquardt method. For verification of the method, two experimental studies are conducted using shaking table tests; one is the system identification of a smart base-isolated structure employing a magnetorheological (MR) damper, and the other is for an actively controlled two-story, bench-scale building employing an active mass driver. Using the developed me...

A Comparative Study of Modelling Techniques for Laminar Flow Transients in Hydraulic Pipelines

Accurate predictions of pressure surges are crucial in many fluid-line systems. There are several techniques available for modelling flow transients in hydraulic pipelines, offering different advantages and disadvantages and therefore suiting different applications. In this paper four modelling methods are evaluated in terms of accuracy, computational efficiency and flexibility for laminar, single-phase flow in circular, rigid pipes. These are the method of characteristics (MOC), the finite element method (FEM), the transmission line method (TLM), and the rational polynomial transfer function approximation (RPTFA) method, which is a form of modal approximation method. All four methods were implemented in MATLAB/Simulink. It was found that the RPTFA model potentially gives the most accurate solution, while the MOC and TLM models are the most computationally efficient. The FEM is the least accurate out of the four methods, but it can be used with varying parameters and time steps thus providing the most modelling flexibility.

HMM-Based Fault Detection and Diagnosis Scheme for Rolling Element Bearings

In this paper, we introduce a new bearing fault detection and diagnosis scheme based on hidden Markov modeling (HMM) of vibration signals. Features extracted from amplitude demodulated vibration signals from both normal and faulty bearings were used to train HMMs to represent various bearing conditions. The features were based on the reflection coefficients of the polynomial transfer function of an autoregressive model of the vibration signals. Faults can be detected online by monitoring the probabilities of the pretrained HMM for the normal case given the features extracted from the vibration signals. The new technique also allows for diagnosis of the type of bearing fault by selecting the HMM with the highest probability. The new scheme was also adapted to diagnose multiple bearing faults. In this adapted scheme, features were based on the selected node energies of a wavelet packet decomposition of the vibration signal. For each fault, a different set of nodes, which correlates with the fault, is chosen. Both schemes were tested with experimental data collected from an accelerometer measuring the vibration from the drive-end ball bearing of an induction motor (Reliance Electric 2 HP IQPreAlert) driven mechanical system and have proven to be very accurate.

Unsteady aerodynamic model of a cargo container for slung-load simulation

AbstractThe problem of simulation models capable of predicting the aerodynamic instability of helicopter slung-load cargo containers and bluff bodies is addressed. Instability for these loads is known to depend on unsteady frequency-dependent aerodynamics, but simulation models that include the unsteady aerodynamics do not currently exist. This paper presents a method for generating such models using computational fluid dynamics (CFD) to generate forced-oscillation aerodynamic data and frequency domain system identification techniques to generate a frequency response from the CFD data and to identify a transfer function fit to the frequency response. The method is independent of the responsible flow phenomenon and is expected to apply to bluff-bodies generally. Preliminary results are presented for the case of the 6- by 6- by 8-ft CONEX (container express) cargo container. The present work is based on two-dimensional (2D) aerodynamic data for the CONEX side force and yaw moment generated by a forced oscillation in which frequency is varied smoothly over the range of interest. A first-order rational polynomial transfer function is found adequate to fit the aerodynamics, and this is shown to provide a good match with flight test data for the yawing motion of the CONEX.

Measuring the Coupling of Hormone Concentration Time Series Using Polynomial Transfer Functions

This chapter discusses use of polynomial transfer functions for measuring the coupling of hormone concentration time series. A method for estimating the strength of coupling and the relationship between two hormones is outlined. The performance of polynomial transfer functions is reported as a tool to reconstruct the coupling between various combinations of hormone concentration–time series data derived from a known mathematical construct that describes certain hypothetical endocrine feedback networks. The use of synthetic data allows comparison between method-predicted coupling and known (model-defined) hormone interactions. The measurement of the percent of the variance accounted for by the polynomial transfer function was consistent. The measurement is affected by the number of hormones (or inputs) involved in the control of a given hormone. It is shown that polynomial transfer functions can consistently describe the strength of the relationship between two hormones, and that the ability to measure this coupling decreases with increasing data noise and with increasing error in the estimated hormone half-lives. This technique is expected to be useful for the investigation of normal hormonal physiology and pathophysiology.

Approximation of amplitude-frequency responses of minimum-phase recursive digital band-pass filters

The paper considers a method of treatment and an example to the problem of approximation of AFR of digital recursive band-pass filters with any ratio between powers of the numerator and denominator of the transfer function polynomials and for a prescribed function of guaranteed attenuation in the rejection band.

A procedure for calculating transient thermal load through multilayer cylindrical structures

This paper presents the transmission matrix and frequency characteristics of transient heat conduction through a multilayer cylindrical structure. The frequency-domain regression method [Appl. Thermal Eng. 21 (6) (2000) 683] is introduced to estimate some simple polynomial s-transfer functions from the frequency characteristics and further calculate the transient heat flow of the cylindrical structure including its thermal response factors and Z-conduction transfer function coefficients. The calculation examples and comparisons have fully demonstrated that the developed procedure is not only easy and simple, but also has high computation accuracy and efficiency.

An approach to calculate transient heat flow through multilayer spherical structures

The transmission matrix and frequency characteristics of transient heat conduction through a multilayer spherical structure are presented by applying Laplace transforms in this paper. The frequency domain regression (FDR) [S.W. Wang, Y.M. Chen, Appl. Thermal Engrg. 21 (6) (2000) 683] method is introduced to construct some simple polynomial s-transfer functions from the frequency characteristics. The polynomial s-transfer functions are further used to calculate the transient heat flow of the spherical structure including its thermal response factors and Z-conduction transfer function (CTF) coefficients. This approach is very easy and simple to implement in programming and avoids the case of missing roots in finding the roots of characteristic equation. The examples and comparisons have demonstrated that this approach has high computation accuracy.

Shunted piezoelectric patches in elastic and aeroelastic vibrations

A procedure for a modal-based modeling and analysis of the effectiveness of shunted piezoelectric devices in increasing passive damping of elastic and aeroelastic systems is presented. Dynamical models with different levels of complexity, including both elastic and aeroelastic systems, have been considered in order to show the capability of the proposed approach. The numerical tests presented concern the description of several systems of aeronautical interest with piezoelectric devices to achieve a selective control of different modes. The linear aeroelastic modeling has been reduced to a rational polynomial transfer function, i.e., it has been represented in a linear state–space form which has allowed to extend the proposed piezo modeling to a general linear aeroelastic system. In particular, the aeroelastic application showed a weak capability of improving the stability margin, but a significant performance in the reduction of the gust response level in proximity of the critical condition of the system (e.g., when the flight speed is close to the flutter speed). Thus, a suitable performance of the piezo damper should be designed for any flight speed, altitude and Mach number. An optimal strategy to evaluate the electrical load for the tuning of piezo devices, as function of the flight speed (semi-active control), has been also proposed.

Flexible Bearing Supports, Using Experimental Data

Abstract A laboratory rotor, representing a scaled-down model of a three-stage compressor supported by fluid film bearings on anisotropic flexible supports was analyzed. The support characteristics were measured at the bearing locations by exciting the bearing housings with electromechanical shakers and measuring the acceleration. Direct, cross-coupled, and cross-talk accelerance between supports were measured. Unbalance response and stability analyses of the rotor were performed using polynomial transfer functions extracted from the measured accelarance data. The predicted critical speeds and instability threshold agree with measured data. Predictions using other support models are included to show the effectiveness of this method.

Scattering Theory for Quantum Fields¶with Indefinite Metric

In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of Haag--Ruelle theory do not carry over to the case of indefinite metric, we propose an axiomatic framework for the construction of in- and out- states, such that the LSZ asymptotic condition can be derived from the assumptions. The central mathematical object for this construction is the collection of mixed vacuum expectation values of local, in- and out- fields, called the ``form factor functional'', which is required to fulfill a Hilbert space structure condition. Given a scattering matrix with polynomial transfer functions, we then construct interpolating, local, relativistic quantum fields with indefinite metric, which fit into the given scattering framework.

A novel and simple building load calculation model for building and system dynamic simulation

Based on polynomial s-transfer functions of transient heat conduction through a building construction, a novel and simple model is developed for building thermal load calculation. The polynomial s-transfer functions are estimated from the theoretical frequency responses of the building construction by frequency-domain regression method. The simple polynomial s-transfer functions are completely equivalent to the hyperbolic s-transfer functions in terms of frequency characteristics. First, the frequency responses of the total transmission matrix are calculated within the frequency range concerned. Then, a set of linear equations is solved yielding a simple polynomial s-transfer function for cross and internal heat conduction. Finally, simple recursive formulae are obtained by inverse Laplace transforms and discretization of the convolution integrals. The coefficients of the model are independent from time step and the time step can be varied according to the requirement during simulation. Validations and comparisons show that this model has fast computation speed and no numerical unstability, and provides high accuracy and good flexibility to the requirement of variable time step.

Including the Effects of Flexible Bearing Supportsin Rotating Machinery

Unbalance response and stability analyses of a flexible rotor on three lobe journal bearings on flexible supports are presented. The influence of the support structure was included in the analyses using polynomial transfer functions. These transfer functions were extracted from measured dynamic compliance data of the support structure, measured at the bearing locations. Numerical predictions using polynomial transfer functions and single mass supports are compared to the experimental data. Predictions using the transfer function representation of the support structure show a clear improvement over the predictions using single mass supports without over‐complicating the problem. The predicted critical speeds are within 2.9% of the measured critical speeds. The predicted stability threshold agrees with the measured stability threshold within 1%. The effects of cross talk between supports and cross coupling between horizontal and vertical directions are investigated. The cross talk between supports was found to have a strong influence in the results while the influence of cross coupling between the vertical and horizontal directions is negligible.