Multisine Excitation Research Articles

Time-Variant Frequency Response Function Measurements on Weakly Nonlinear, Arbitrarily Time-Varying Systems Excited by Periodic Inputs

In quite some applications, the linear dynamics of the system under test evolve over time in a smooth nonperiodic manner. The dynamic behavior of such systems is uniquely described by the time-variant frequency response function (TV-FRF). However, since most real-life systems behave nonlinearly to some extent, it is important to detect and quantify the deviation between the ideal linear time-variant (LTV) framework and the true non-LTV dynamics. Therefore, in this paper, a nonparametric estimation procedure is developed for detecting and quantifying the noise level and the level of the nonlinear distortions in TV-FRF measurements using random-phase multisine excitations. As a result, the users can decide whether or not the LTV framework is accurate enough to describe the true dynamics in their particular application. The proposed measurement procedure is illustrated on a time-variant electronic circuit.

Initial estimates for Wiener–Hammerstein models using phase-coupled multisines

Block-oriented models are often used to model nonlinear systems. These models consist of linear dynamic (L) and nonlinear static (N) sub-blocks. This paper addresses the generation of initial estimates for a Wiener–Hammerstein model (LNL cascade). While it is easy to measure the product of the two linear blocks using a Gaussian excitation and linear identification methods, it is difficult to split the global dynamics over the individual blocks. This paper first proposes a well-designed multisine excitation with pairwise coupled random phases. Next, a modified best linear approximation is estimated on a shifted frequency grid. It is shown that this procedure creates a shift of the input dynamics with a known frequency offset, while the output dynamics do not shift. The resulting transfer function, which has complex coefficients due to the frequency shift, is estimated with a modified frequency domain estimation method. The identified poles and zeros can be assigned to either the input or output dynamics. Once this is done, it is shown in the literature that the remaining initialization problem can be solved much easier than the original one. The method is illustrated on experimental data obtained from the Wiener–Hammerstein benchmark system.

Metrological Characterization of a Signal Generator for the Testing of Medium-Voltage Measurement Transducers

Nowadays, voltage transducers in medium-voltage (MV) distribution networks operate in nonsinusoidal conditions while their calibration is still based on simple sine-wave tests. A more significant characterization could be achieved using complex multitone signals. However, this requires an MV generator able to apply arbitrary voltage waveforms to the transducer under test. The authors have recently proposed a simple MV signal generator that can be effectively employed for this purpose. In this paper, the performance of this MV generator has been carefully analyzed. A characterization procedure based on multisine excitation has been proposed and tested. In particular, the main causes of uncertainty have been identified and their impact on the accuracy of the generated voltage evaluated. The analysis considers both linear and nonlinear effects, such as harmonic distortion and hysteresis.

Multi-frequency simultaneous measurement of bioimpedance spectroscopy based on a low crest factor multisine excitation

Bioimpedance spectroscopy (BIS) is becoming a powerful diagnostic tool for a wide variety of medical applications, and the multi-frequency simultaneous (MFS) measurement of BIS can greatly reduce measurement time and record the transient physiological status of a living body compared with traditional frequency-sweep measurement technology. This paper adopts the Van der Ouderaa’s multisine, which has 31 equidistant and flat amplitude spectra and a low crest factor of 1.405 as the broadband excitation, and realizes the MFS measurement of BIS by means of spectral analysis using the fast Fourier transform algorithm. The approach to implement the multisine based on a field-programmable gate array and a digital to analog converter is described in detail, and impedance measurement experiments are performed on three resistance-capitance three-element phantoms. Experimental results show a commendable accuracy with a mean relative error of 0.55% for the impedance amplitudes, and a mean absolute error of 0.20° for the impedance phases on the 31 frequencies ranging linearly from 32 to 992 kHz. This paper validates the feasibility of the MFS technology for BIS measurement based on the multisine excitation.

Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry

Continuous scan laser Doppler vibrometry (CSLDV) is a technique which has been described and explored in the literature for over two decades, but remains niche compared to SLDV inspection by a series of discrete-point measurements. This is in part because of the unavoidable phenomenon of laser speckle, which deteriorates signal quality when velocity data is captured from a moving spot measurement. Further, applicability of CSLDV has typically been limited to line scans and rectangular areas by the application of sine, step, or ramp functions to the scanning mirrors which control the location of the measurement laser spot. In this paper it is shown that arbitrary functions to scan any area can easily be derived from a basic calibration routine, equivalent to the calibration performed in conventional discrete-point laser vibrometry. This is extended by performing the same scan path upon a test surface from three independent locations of the laser head, and decomposing the three sets of one-dimensional deflection shapes into a single set of three-dimensional deflection shapes. The test was performed with multi-sine excitation, yielding 34 operating deflection shapes from each scan.

Modelling hydraulic pitch actuator for wind turbine simulation under healthy and faulty conditions

A detailed nonlinear model for a hydraulic pitch actuator under healthy and faulty situations is introduced in the FAST/AERODYN wind turbine simulator. Frequency response functions (FRF) are determined by using a random phase multi-sine excitation for different healthy and faulty operating conditions. The major changes observed in the FRF arise significantly above the actuator bandwidth. A linear model of the actuator thus appears to be sufficient to simulate the wind turbine in healthy conditions. However, when it comes to the study of fault diagnosis, it is advised to use a nonlinear model and to resort to active fault detection methods to probe the high frequency behaviour. Finally a user friendly graphical interface is presented for the wind turbine simulator.

Enhancing Vibration Damping of Smarts Structures by Energy Transfer between Modes

In a context of embedded structures, the next challenge is to develop an efficient, energetically autonomous vibration control technique. Synchronized Switch Damping techniques (SSD) have demonstrated interesting properties in vibration control with a low power consumption. The damping attenuation can be improved thanks to energy transfer between a voltage source and the SSD circuit. Harvesting energy on a second structure can provide this voltage source but drastically complex the overall system. We propose here a new technique to enhance the classic SSD circuit due to energy harvesting. Our original approach consists in transferring energy between modes of a same structure: energy is harvested on non-controlled mode to increase the attenuation of a targeted mode. In this paper, we present theoretical analysis and numerical simulations of our energy-transfer architecture applied to an academic case, a free-clamped beam. Our electrical architecture called Synchronized Switching Damping and Harvesting (SSDH) is composed of a harvesting circuit (Synchronized Switch Harvesting on Inductor SSHI), a dc-dc converter (Buck-Boost topology) and a vibration modal control circuit (similar to a Synchronized Switch on Voltage SSDV). In a multi-sine excitation, an increase of the attenuation damping of 3.8dB with our new technique compared to classic SSDI is achieved.

Experimental determination of frequency response function estimates for flexible joint industrial manipulators with serial kinematics

Two different approaches for the determination of frequency response functions (FRFs) are used for the non-parametric closed loop identification of a flexible joint industrial manipulator with serial kinematics. The two applied experiment designs are based on low power multisine and high power chirp excitations. The main challenge is to eliminate disturbances of the FRF estimates caused by the numerous nonlinearities of the robot. For the experiment design based on chirp excitations, a simple iterative procedure is proposed which allows exploiting the good crest factor of chirp signals in a closed loop setup. An interesting synergy of the two approaches, beyond validation purposes, is pointed out.

Measurement and characterization of glucose in NaCl aqueous solutions by electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) allows measuring the properties of the system as a function of the frequency as well as distinguishing between processes that could be involved: resistance, reactance, relaxation times, amplitudes, etc. Although it is possible to find related literature to in vitro and in vivo experiments to estimate glucose concentration, no clear information regarding the condition and precision of the measurements are easily available.This article first address the problem of the condition and precision of the measurements, as well as the effect of the glucose over the impedance spectra at some physiological (normal and pathological) levels. The significance of the measurements and the glucose effect over the impedance are assessment regarding the noise level of the system, the experimental error and the effect of using different sensors. Once the data measurements are analyzed the problem of the glucose estimation is addressed. A rational parametric model in the Laplace domain is proposed to track the glucose concentration.The electrochemical spectrum is measured employing odd random phase multisine excitation signals. This type of signals provides short acquisition time, broadband measurements and allows identifying the best linear approximation of the impedance as well as estimating the level of noise and non-linearities present in the system. All the experiments were repeated five times employing three different sensors from the same brand in order to estimate the significance of the experimental error, the effects of the sensors and the effect of the glucose over the impedance.

Online Measurement of Battery Impedance Using Motor Controller Excitation

This paper presents a fast cost-effective technique for the measurement of battery impedance online in an application such as an electric or hybrid vehicle. Impedance measurements on lithium-ion batteries between 1 Hz and 2 kHz give information about the electrochemical reactions within a cell, which relates to the state of charge (SOC), internal temperature, and state of health (SOH). We concentrate on the development of a measurement system for impedance that, for the first time, uses an excitation current generated by a motor controller. Using simple electronics to amplify and filter the voltage and current, we demonstrate accurate impedance measurements obtained with both multisine and noise excitation signals, achieving RMS magnitude measurement uncertainties between 1.9% and 5.8%, in comparison to a high-accuracy laboratory impedance analyzer. Achieving this requires calibration of the measurement circuits, including measurement of the inductance of the current sense resistor. A statistical correlation approach is used to extract the impedance information from the measured voltage and current signals in the presence of noise, allowing a wide range of excitation signals to be used. Finally, we also discuss the implementation challenges of an SOC estimation system based on impedance.

Analysis and Compensation of PEM Fuel Cell Instabilities in Low-Frequency EIS Measurements

This paper analyzes possible humidity-related instabilities of polymer electrolyte membrane (PEM) fuel cell (FC) operation that affect electrochemical impedance spectroscopy measurements. The compensation of ohmic resistance variations due to such instabilities, achieved using the well known multisine excitation technique with properly chosen high-frequency harmonic components, is proposed here as a new approach to improve low-frequency measurements. Additionally, this method allows a more accurate determination of equivalent circuit parameters identified from impedance spectra and their uncertainties taking into account correlation between impedances at different frequencies, and thus avoiding uncertainty overestimation of low-frequency parameters (such as transport and activation equivalent resistances) that is likely to occur with classic measurement techniques. The proposed method is experimentally validated on a single PEM FC.

Crest factor optimization of the multisine waveform for bioimpedance spectroscopy

The multisine excitation is widely used in impedance measurements to retain the advantages of the sine wave, while reducing the measurement time. Adding up sine waves increases the amplitude of the excitation signal, but, for the linearity assumption to be valid, the overall amplitude of the signal needs to be kept low. Thus, the crest factor (CF) of the excitation signal must be minimized. A novel empirical method for the minimization of the CF is described in this paper. As in the case of other known methods, the computed CF may be guaranteed to be only a local minimum. However, a systematic variation of initial parameters, which is possible due to the sparing algorithm, ensures a CF value very close or equal to the global minimum. The results of CF minimization and comparison with the results from other sources are provided. The direct CF optimization results (set of optimal phases) are not well suited for practical implementation. The influence of phase accuracy on the CF is discussed, and an algorithm for the recalculation of initial phases to the rougher set is described. It is shown that previously obtained optimization results (minimal CF) can be highly preserved, even in the case of rough phase resolutions. The CF of the multisine also depends on the frequency distribution and amplitudes of its components. The CF of multisines with several frequency distributions are compared.

Efficient Excitation Signals for the Fast Impedance Spectroscopy

This paper deals with finding the highly efficient multifrequency excitation waveforms for fast bioimpedance spectroscopy. However, the solutions described here could be useful also in other fields of impedance spectroscopy. Theoretically, the useful excitation power of optimized binary multifrequency signals (BMS) exceeds the power of comparable multisine waveforms. However, part of power of the BMS waveforms is spread between higher harmonics of the wanted frequency components. In practical use of voltage excitation, the higher harmonics complicate the signal processing and produce current spikes passing through the capacitive elements of the impedance to be measured. In the paper, we show that the excitation power of well-optimized multisine with decaying amplitudes comes close to the power of comparable binary waveform while reducing the problems caused by unwanted frequency components. This allows simpler signal processing. Besides, we also show that the overall efficiency of using of the multisine excitation in impedance measurement becomes even higher efficient than the BMS in practice, despite the fact that the power of binary waveforms is the highest. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.7115

Quantifying the Time-Variation in FRF Measurements Using Random Phase Multisines With Nonuniformly Spaced Harmonics

Recently methods have been developed to detect and quantify the influence of time-variation in frequency response function measurements using random excitations. These methods can also be applied to random phase multisine excitations, provided uniformly spaced excited harmonics. However, in quite a few applications, a nonuniform harmonic spacing is required, for example, a quasi-logarithmic spacing to cover a large frequency range, and a random spacing to detect and quantify nonlinear distortions. Therefore, in this paper, the results are extended to random phase multisines with nonuniformly spaced harmonics. An in-depth study of the noise sensitivity (bias and variance) of the proposed procedure is made.

Characterization of Intermodulation and Memory Effects Using Offset Multisine Excitation

This paper proposes a new class of multisine excitations that allows efficient characterization of nonlinear circuits. By offsetting the frequency of tones, one can distinguish between different intermodulation products in a multisine response. This property leads to many applications for nonlinear circuit characterization, such as in-band distortion measurements, memory effects characterization, and model performance assessment. Some applications are highlighted in this paper, focusing especially on the characterization of memory effects. The effectiveness of the approach is demonstrated with a series of measurement results.

Generating initial estimates for Wiener-Hammerstein systems using phase coupled multisines

Block oriented nonlinear models capture the dynamics of a nonlinear system with linear dynamic sub-systems (L), the nonlinear behavior is modelled using static nonlinear sub-blocks (N). In this paper we study the generation of initial estimates for the linear dynamic blocks of a Wiener-Hammerstein system that has a cascaded LNL structure. While it is very easy to identify the product of the transfer functions of the first and last dynamic block using linear system identification methods, it turns out to be very difficult to split the global dynamics over these individual blocks. In this paper a method is proposed that allows the poles of the best linear approximation to be assigned to the first or second linear block. Once this split is made, it is shown in the literature that the remaining initialization problem can be solved much easier than the original one. The first step of the method is the design of a special random phase multisine excitation, using pair-wise coupled random phases. Next, a modfied best linear approximation will be estimated on a shifted frequency grid. It will be shown that this procedure shifts the poles and zeros of the first linear sub-block with a known frequency offset, while those of the second sub-block are not changed. The shifted poles and zeros result in a transfer function with complex coefficients that can be identified using a modified frequency domain estimation method. This results in a simple initialization method, based on a linear system identification step.

Dynamic behavior of cracked rotor subjected to multisine excitation

Abstract It is widely known that a developing shaft crack manifests itself in the appearance of nonlinear effects resulting in higher harmonics in a vibration spectrum. However, such symptoms are characteristic not only for developing shaft cracks but also for other malfunctions such as a shaft bow, a coupling misalignment, etc. That is why novel shaft crack detection methods introduce a specially designed diagnostic force applied to the shaft in order to amplify the particular symptoms of the crack. Most often a simple harmonic force is used for such purposes, yet the results may not be reliable. The present paper analyzes the possible application of the multisine excitation technique for an early shaft crack detection problem. This technique was previously used for identification problems where the influence of nonlinear distortions on the linear system behavior was to be evaluated and measured. In the present paper the multisine technique is adopted for the detection of a shaft crack in a rotor. The possibility to evaluate the crack depth is also verified. The approach is illustrated with the numerical results of the flexible rotating shaft modeled with the rigid finite element method. In order to assess the effectiveness of the proposed method the numerical results obtained for the uncracked and cracked rotors are compared. The robustness of the method to additional disturbances is checked by introducing some noise to the system. The results demonstrate a potential of the presented method to detect the shaft cracks and to evaluate their severity. Possible problems of the practical implementation of the method are briefly discussed.

Comparison of IMD Symmetry and Asymmetry Model in Power Amplifier Based on Multisine Excitation

This paper proposes system level behavior model of a nonlinear power amplifier that exhibit the IMD asymmetry effect based on multisine excitation. For this work, a third order power series coefficients are originatively represented with both the system level circuit features such as a second output intercept point (OIP2), a third output intercept point (OIP3), amplifier gain and its excitation amplitudes. In addition, the memory effect like the asymmetry in lower and upper intermodulation products are distinguished through the analytic description and measurement. The main advantage of the proposed theory is able to analyze the composition of the nonlinear response in power amplifier. This paper also presents the measured results to validate the analytic expressions.

Optimisation of multisine waveform for bio-impedance spectroscopy

The multisine excitation is widely used in impedance measurements to retain the advantages of the sine wave, while reducing the measurement time. Adding up sine waves increases the amplitude of the excitation signal, but, for the linearity assumption to be valid, the overall amplitude of the signal needs to be kept low. Thus, the crest factor (CF) of the excitation signal must be minimized. A novel empirical method for minimization of the CF is presented in this paper. As in case of other known methods, the computed CF may be guaranteed to be only a local minimum. However, a systematic variation of initial parameters, which is possible due to the sparing algorithm, ensures the CF value, very close or equal to the global minimum. A brief analysis of the calculation errors and comparison with the results from other sources is provided. In the DSP applications, initial phases of the waveforms must match the grid of sample points if separate signal sources are used to generate the components. An equation for calculation of the indexes of the sample points corresponding to the optimal initial phases is provided, and the time discreteness caused relative error of CF is illustrated.

Extending Reading Range of Commercial RFID Readers

In this paper, multisine excitation signals are used to extend the reading range of commercial RF identification readers. To do so, a commercial reader is equipped with an external multisine front-end that implements previous mathematical proposals. A mathematical description is presented in order to show the ability of multisine signals to communicate data, with minimal changes in the downlink path, while no changes are required in the conventional tag architecture. Moreover, and most important, if a proper multisine design is performed, a conventional reader receiver is still able to demodulate and decode the backscattered multisine signal from the tag, without any hardware change. Thus, guidelines are presented for multisine design, including multisine nature, central tone positioning, tone separation, and bandwidth requirements. In order to evaluate the reading range improvement, when compared with the conventional single carrier approach with the same average power, two experiments are conducted: in the first one, an oscilloscope is used to measure the tag response and to decide whether the tag does or does not respond. In the second measurement scenario, the downlink path is implemented by the reader combined with the front-end and the uplink is implemented solely by the reader. In this case, the decision on successful tag response is taken when the reader reads the tag identification. The first measurement scenario has pointed out for a maximum reading range improvement of near 43% for an eight-tone multisine signal with 2-MHz tone separation. In the second scenario, a more realistic one, a reading range improvement of almost 25% has been obtained for a 8 + 1 tones multisine.