Ceri Evans

Periodic signals for measuring nonlinear Volterra kernels

The frequency-domain measurement of the Volterra kernels of a nonlinear system using periodic multisine signals is now a practical possibility. An analysis is presented of the harmonic output of a Volterra kernel when excited with a multiharmonic signal, which lays the basis for the design of such signals. This is followed by a review of previous work in this area, after which a range of new periodic signals is defined. The minimization of the signal crest factors is then examined, along with the practical problems associated with their application. Practical results are presented which illustrate the application of the signals to testing a reference nonlinear circuit and a servo motor system.

Nonlinear gas turbine modeling using NARMAX structures

The estimation of a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model of an aircraft gas turbine is presented. A method is proposed whereby periodic signals with certain harmonic content are used to qualify the nature of the nonlinearity of the engine in the frequency domain. The static behavior of the engine is investigated in the time domain to approximate the order of nonlinearity and this information is used a priori to restrict the search space of the potential NARMAX models. A forward-regression orthogonal estimation algorithm is then employed to select the model terms using the error reduction ratio. The performance of the estimated NARMAX model is illustrated against a range of small- and large-signal engine tests.

Nonlinear distortions and multisine signals. I. Measuring the best linear approximation

This paper examines the effects of nonlinearities on frequency response function measurements using periodic multifrequency signals. A class of broadband pilot test signals is proposed, termed sparse odd multisines, which can be used to establish the system bandwidth and detect nonlinearities. Signals are then defined within this class which allow the measurement of the best linear approximation of a nonlinear system. A comparison is made with related work in this area.

Nonlinear disturbance errors in system identification using multisine test signals

The errors introduced into linear system identification by nonlinear distortions are examined. A theoretical framework is presented for the distortion generated by odd power nonlinearities when using multisine test signals for frequency domain identification. It is shown that the distortion is a function of the number of test harmonics, their harmonic values and their phases. An explanation of previously published practical results is then given. This leads to the definition of a novel class of signals, termed no interharmonic distortion (NID) multisines, with interesting properties. The application of NID multisines to system testing with a recently proposed method of compensating for nonlinearities is examined. This allows the identification of the linear system and the straightforward calculation of the coefficient of the nonlinear term. >

Frequency-domain identification of gas turbine dynamics

The identification of the fuel flow to shaft speed dynamics of a twin-shaft gas turbine is addressed, with the aim of validating thermodynamic engine models. A measured input signal must be used in estimation in order to exclude the fuel feed dynamics from the model. This has been shown to present problems when fitting discrete models to engine data, and this paper examines the direct estimation of s-domain models in the frequency domain. A number of different multisine test signals were applied to the engine for the purposes of model estimation and nonlinear detection. The use of frequency-domain techniques is shown to produce high-quality models, and the tests also yield information on the levels of noise and nonlinearity and the length of the pure time delay. This work illustrates the potential of frequency-domain techniques for modeling systems where a physical interpretation is to be made of the model and where the need for accuracy requires that a measured input signal be used in estimation.

Application of system identification techniques to aircraft gas turbine engines

Abstract A variety of system identification techniques are applied to the modelling of aircraft gas turbine dynamics. The motivation behind the study is to improve the efficiency and cost-effectiveness of system identification techniques currently used in the industry. Three system identification approaches are outlined in this paper. They are based upon: multisine testing and frequency-domain identification, time-varying models estimated using extended least squares with optimal smoothing, and multiobjective genetic programming to select model structure.

Identification of aircraft gas turbine dynamics using frequency-domain techniques

Abstract This paper describes the estimation of parametric and nonparametric models of the fuel feed to shaft speed dynamics of a twin-shaft gas turbine engine, using frequency-domain techniques. Data gathered from practical testing of the turbine are presented and shown to be of high quality. Accurate models are then estimated at several points along the turbine operating curve. The results of the parametric estimations are used to verify theoretical models derived from the thermodynamic relations of the gas turbine.

Frequency domain analysis of nonlinear systems driven by multiharmonic signals

This paper examines the output properties of static power-series nonlinearities driven by periodic multiharmonic signals with emphasis given to their effect on linear frequency response function (FRF) measurements. The analysis is based on the classification of nonlinear distortions into harmonic and interharmonic contributions. The properties of harmonic contributions are examined in detail and explicit formulae are derived, by which the number of harmonic contributions generated at the test frequencies can be calculated for odd-order nonlinearities up to, and including, the ninth order. Although an analytic solution for any odd-order nonlinearity is still under investigation, a heuristic methodology is developed that solves this problem. It is shown that the derived formulae provide a useful tool in the examination of the behavior of FRF measurements in the presence of nonlinear distortions. Based on these formulae, different approaches in classifying nonlinear distortions are then compared with respect to their suitability in assessing the influence of system nonlinearities on linear FRF measurements.

Nonlinear distortions and multisine signals. II. Minimising the distortion

This paper examines the effects of nonlinear distortions on frequency response functions estimated using multisine test signals. The aim is to minimise the distortion introduced by the nonlinearity, for a given input power constraint. A number of different multisine signals are compared for this purpose, with zero, random and low crest factor harmonic phases. The results are compared with those of other authors in this field.

Identification of nonlinear cascade systems using paired multisine signals

The identification of nonlinear cascade models has been widely studied as they often reflect the physical structure of practical nonlinear systems. The problem when using such models is to establish their structure and then to identify their linear subsystems. Both can be based on measured Volterra kernels. By performing tests with a pair of input signals, specially designed in order to measure these kernels, enough information can be gathered to separate the linear systems. A brief introduction is given to the measurement of Volterra kernels using periodic multisine signals. A method using combined tests is then proposed to estimate the non-parametric and parametric models of the linear sub-systems. An example is given for a simulated system with a second order nonlinearity.