Practical choices in the FRF measurement in presence of nonlineardistortions

The frequency response function (FRF) of the best linear approximation to a nonlinear system is usually measured by averaging system responses to a normally distributed, filtered, and clipped random excitation (Gaussian noise). This signal is compared to the multisine signal with random phases. It is shown that a random phase multisine signal defined over an even-odd frequency grid is superior to the Gaussian signal in terms of the variance and the bias of the measured FRF of the approximated nonlinear system     

Identification of linear systems captured in a feedback loop

The identification of model parameters using measured input-output data from linear systems operating in a closed loop is discussed. A frequency-domain maximum likelihood estimator which takes into account the correlation between the input and output disturbances is presented. Its properties are analyzed and illustrated by simulation examples and real measurements     

Design of multisine excitations to characterize the nonlineardistortions during FRF-measurements

Multisine excitation signals are designed which will be used to detect and qualify the nonlinear distortions on frequency response function (FRF) measurements, and this without making additional experiments. The main idea in this method is to apply well chosen periodic excitations where not all harmonics are excited. The nonexcited frequency lines are used to detect, qualify and quantify the nonlinear distortions, while the FRF is measured at the same time at the excited harmonics. The selection of the multisine that will be used depends on the characteristics of the system that are studied. For that reason, not every multisine will produce in every case accurate, robust, and reliable results for every system. This paper presents some signals by which the following aims are accomplished: simplicity, robustness, and a reliable nonlinear characterization     

Measuring the parameters of linear systems

Translated from Izmeritel'naya Tekhnika, No. 5, pp. 9–10, May, 1992.     

Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

In this paper, monitoring of simple linear profiles is investigated in the presence of nonequality of variances or heteroscedasticity, ie, generalized autoregressive conditional heteroscedasticity. In this condition, using of the common methods regardless of the heteroscedasticity leads to the fault interpretations. We consider a simple linear profile and assume that there is a generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model within the profiles. Here, we particularly focus on Phase II monitoring of simple linear regression. We studied the generalized autoregressive conditional heteroscedasticity effect, briefly GARCH effect, on the average run length criterion. As the remedial measures, the weighted least squares method to estimate the regression parameters and the heteroscedasticity‐consistent approaches to estimate the covariance matrix of regression parameters, are used to extract the GARCH effect. Two control chart methods namely T² and exponentially weighted moving average 3 are discussed to monitor the simple linear profiles. Their performances are evaluated by using the average run length criterion. Finally, a real case from an industry field is studied.     

Monitoring simple linear profiles in the presence of within- and between-profile autocorrelation

The current study investigates the effect of within-profile and between-profile autocorrelations on the performance of four monitoring methods of simple linear profiles in Phase II. To this end, a general correlation model between error terms is considered such that the correlation structure of within-profiles errors and the error terms between consecutive profiles follow an autoregressive (AR) times series model of order one. Extensive simulations have been done to assess the effect of both autocorrelation types and the profile size on the estimations of the model parameters as well as the performance of control charts. The performance of the monitoring schemes is investigated and compared with respect to the average run length (ARL) metric. The simulation study results show that the autocorrelation within and between profiles has a negative impact on the monitoring technique's performance. It reduces the control chart's ability to detect process shifts compared to no or weak autocorrelation cases. Moreover, the performance of all the methods is improved by increasing the profile size. An illustrative example is also provided to demonstrate the use of the proposed methods for monitoring the stability of profiles in the chemical industry.     

Spontaneous emission of atomic systems in the presence of incident fields

We characterise the spontaneous emission time and direction from small numbers of dipole-coupled two-level atoms (2LAs) in the presence of incident fields. We show how to use adiabatic passage to admit population transfer between states in the one-quantum subspace for two and three 2LAs. Our method is a multi-atom generalisation of stimulated-Raman-adiabatic-passage (STIRAP) for a single multi-level atom. We use numerical results to justify an ansatz that enables us to give analytical expressions for the directional emission which depends on the incident fields. Our results admit a characterisation of the efficacy of population transfer in small numbers of dipole-coupled 2LAs, and are applicable to proof-of-principle experiments involving dipole-coupled 2LAs.     

Stability of circulatory elastic systems in the presence of magnetic damping

Summary The effect of a type of magnetic damping upon the stability of some circulatory elastic systems is examined. The results are compared with those obtained for internal and external viscous damping and the differences and similarities are discussed.

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Stabilität nicht drehungsfreier elastischer Systeme in Gegenwart magnetischer Dämpfung

Zusammenfassung Der Einfluß einer speziellen magnetischen Dämpfung auf die Stabilität einiger nicht drehungsfreier elastischer Systeme wird geprüft. Die Ergebnisse werden mit jenen für interne und externe viskose Dämpfung verglichen und die Unterschiede und ähnlichkeiten diskutiert.

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With 4 Figures

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This research was supported by the National Aeronautics and Space Administration under Grants NGR 14-007-011 and NGR 14-007-067.     

Integral parameters of linear measuring systems

Conclusion Relationships (7) and (11) make it possible to determine the integral parameters of a complex linear system according to the given parameters of its component transducers, and to estimate the accuracy of such systems. The results obtained can also be used to analyze transient processes in complex linear systems.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 31–32, January, 1976.     

Stochastic stability of linear viscoelastic systems

The stochastic almost-sure stability of a single degree-of-freedom linear viscoelastic system subjected to random fluctuation in the stiffness parameter is investigated. For small damping and weak random fluctuation, asymptotic expressions are derived for the Lyapunov exponent and the rotation number using the method of stochastic averaging. From the sign of the Lyapunov exponent, the condition for asymptotic stability with probability 1 of the trivial equilibrium state is obtained.     

Evolution of linear waves in a liquid in the presence of a curtain of bubbles

We investigate certain features of the evolution of waves in an acoustically compressible liquid in passage through a curtain of bubbles between two parallel planes. We consider the problem of reflection from a plane solid wall separated from the liquid by a curtain of bubbles. Investigations showed that in relation to the duration of the pulse it is possible to select a curtain with corresponding parameters to moderate the effect of the wave on the wall. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 987–992, November–December, 1998.     

Advances in the linear/nonlinear control of aeroelastic structural systems

Summary Active aeroelastic control is a recently emerging technology aimed at providing solutions to a large class of problems involving the aeronautical/aerospace flight vehicle structures that are prone to instability and catastrophic failures, and to oscillations that can yield structural failure by fatigue. In order to prevent such damaging phenomena to occur, the linear/nonlinear aeroelastic control technology should be applied. Its goals are among others: (i) to alleviate and even suppress the vibrations appearing in the subcritical flight speed range, (ii) to enlarge the flight envelope by increasing the flutter speed, and (iii) to enhance the post-flutter behavior by converting the unstable limit cycle oscillation to a stable one. A short review of the available control techniques and capabilities is presented first. Attention is focused on the open/closed-loop of 2D and 3D lifting surfaces as well as on panels exposed to supersonic flowfields. A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented. Emphasis is placed on theoretical and numerical results obtained with the various control strategies that are considered in a comparative way. Finally, conclusions and directions for further work are presented.This paper represents an updated version of the General Lecture presented at the 3rd European Conference on Structural Control, July 12–15, 2004, Vienna, Austria.