Multisine Excitation Research Articles

Fast Measurement of Quantization Distortions in DSP Algorithms

A measurement technique is proposed to characterize the nonidealities of digital signal processing algorithms which are induced by quantization effects, overflows (fixed point), or nonlinear distortions in one single experiment/simulation. The main idea is to apply specially designed multisine excitations in order to discriminate between the output of the ideal system and the contributions of the systems nonidealities. This approach allows the comparison and quantification of the quality of different implementation alternatives. Applications of this method include, but are not limited to, digital filters, fast Fourier transforms, and audio codecs.

Intermodulation Distortion of Third-Order Nonlinear Systems With Memory Under Multisine Excitations

This paper presents a methodology to compute the distortion output of a class of third-order nonlinear dynamic systems from only standard two-tone test results. Closed-form expressions are presented to compute the distortion output and metrics as adjacent channel power ratio and co-channel power ratio/noise power ratio for an arbitrary multisine with N tones. The impact of memory effects in a multisine excitation is also addressed, improving the design of RF components by a careful understanding of memory effects mechanism in real modulated signals. An experimental validation is presented to prove the proposed theory.

Optimized Excitation Signals for MIMO Frequency Response Function Measurements

Many different excitation signals can be chosen for the nonparametric frequency response function measurements of a linear multiple-input-multiple-output (MIMO) system. In the presence of output noise they will result in different signal-to-noise ratios (SNRs) of the frequency response function measurements. In this paper, these effects are analyzed and compared for three classes of multisine excitations: random multisines, approximately orthogonal random multisines, and orthogonal random multisines, taking also into account the crest-factor minimization. It is shown that the orthogonalization of the inputs yields an essential increase in the measured SNR

In-band distortion of multisines

Multisine signals are shown to be useful for estimating distortion of communication signals. In particular, a generalized approach for the evaluation of effective in-band distortion in a nonlinear amplifier using multisine excitation is presented. The output of the nonlinearity is represented as the sum of uncorrelated components by the transformation of a behavioral model. Simulated and measured results are presented for code-division multiple-access signals

Assessment of nonlinear distortions in modal testing and analysis of vibrating automotive structures

In this paper, new developments for the nonparametric processing of modal test data are presented. Classically, random noise signals are applied to deal with possible nonlinear distortions during frequency response function measurements of linear dynamic systems. However, the use of multisine excitation signals allows the engineer to control much more his experiments. First of all, the nonparametric estimation of multivariable frequency response functions can be more easily based on an “errors-in-variables” stochastic framework. In addition, the application of a well-chosen multisine excitation permits improvement of the data quality, as well as the detection, qualification and quantification of nonlinear distortions during FRF measurements. To make the presented techniques available for multi-input modal testing, attention is paid to the design of optimal multi-input excitations by maximizing the Fisher information matrix as well as minimizing the crest factor of the applied excitation.

Tracking of Cracks in Airplane Components Using Nonlinear Surface Wave Propagation Techniques

Ultrasonic surface waves provide a sensitive means to detect cracks in airplane structures. Until now several obstacles remained to use ultrasonic surface waves for on-line damage detection (i.e. in-flight). In this article a method will be proposed to detect a growing fatigue crack while the aircraft is operating. In contrast to classical ultrasonic measurement methods, that use a high voltage pulse, we applied an optimized multi-sine excitation signal with an amplitude of a few volts only (this agrees better with the applicable safety regulations for aircraft). Furthermore, an indicator quantifying the nonlinearity of the ultrasonic surface wave propagation is used. By using a nonlinearity index the influence of changing operation conditions that can be observed with most linear methods is eliminated. The proposed method is validated on a steel beam that is fatigue loaded with a force signal obtained from in-flight data.

Improvement of the impedance measurement reliability by some new experimental and data treatment procedures applied to the behavior of copper in neutral chloride solutions containing small heterocycle molecules

The electrochemical behavior of copper in chloride solutions containing 0.001 M concentrations of small five- and six-ring member heterocyclic molecules was investigated by means of impedance spectroscopy. The investigation was performed by a new technique based on a broadband multisine excitation. This method allows for a quantification and separation of the measurement and stohastic nonlinear noises and for an estimation of the bias non-linear contribution. It as well reduces the perturbation brought to studied system by the measurement process itself. The measurement data for some experimental conditions was quantified by fitting into a equivalent circuit corresponding to a physical model both of them developed earlier. In general, the experimental results obtained show that the number of atoms in the heterocyclic ring and the molecular conformation have a significant influence on the electrochemical response of copper in the investigated environments.

Designing multisine excitations for nonlinear model testing

This paper deals with the design of bandpass multisine excitations appropriate for microwave nonlinear model testing. A formal analysis showed that if the output power spectral density of a general nonlinear dynamic system is used as a metric for signal similarity, then it is possible to derive a set of statistical characteristics to be approximated. Using these nth-order extensions of the autocorrelation or the power spectral-density functions as the approximation goals, the multisine design problem is formulated as an optimization scheme where the various tone amplitudes and phases become the target design variables.

Instantaneous impedance measurements on aluminium using a Schroeder multisine excitation signal

Time-varying phenomena, such as crystallographic pitting corrosion, can be investigated by electrochemical impedance spectroscopy (EIS). For this purpose, a stepped sine excitation is most frequently used. However, when the frequency ranges from 25 Hz down to 15 mHz this experiment takes at least 30 min. In this work a periodic Schroeder multisine excitation signal is presented, by which the measurement time can be reduced to 2 min for the same frequency range. To evaluate the correctness of the EIS results obtained with the multisine, data was acquired for aluminum (99.5 wt.%) immersed in 0.5 M NaCl with oxygen bubbling by means of a stepped sine, next a multsine and finally a stepped sine excitation. From the spectra obtained with both stepped sines a new virtual spectrum is calculated as if all excited frequencies would have been recorded at the moment when the multisine was imposed to the system. A comparison of the multisine spectrum with this interpolated spectrum was then used for validation. The results show that the instantaneous behaviour of a time-varying system, observed during EIS is better approximated by the use of a multisine excitation signal. Moreover, the approximation further ameliorates when the immersion time evolves.

Measuring the Sensitivity of Microwave Components to Bias Variations

This paper presents a method to measure the sensitivity of microwave components to memory effects caused by the dc biasing circuit. This allows us to determine the required (impedance) properties of the dc biasing circuit to reduce slow dynamics under a certain level. The proposed measurement technique is based on the nonlinear vectorial network analyzer, which allows us to measure not only the absolute magnitude but also the absolute phase relations between the waves. Superimposing a multisine excitation signal on the dc bias allows us to measure the slow dynamics caused by the dc biasing circuit as a function of frequency and input power. Furthermore, it is verified whether or not the measured phenomena depend on the type of excitation signal.

Instantaneous impedance measurements on aluminium using a Schroeder multisine excitation signal

Time-varying phenomena, such as crystallographic pitting corrosion, can be investigated by electrochemical impedance spectroscopy (EIS). For this purpose, a stepped sine excitation is most frequently used. However, when the frequency ranges from 25 Hz down to 15 mHz this experiment takes at least 30 min. In this work a periodic Schroeder multisine excitation signal is presented, by which the measurement time can be reduced to 2 min for the same frequency range. To evaluate the correctness of the EIS results obtained with the multisine, data was acquired for aluminum (99.5 wt.%) immersed in 0.5 M NaCl with oxygen bubbling by means of a stepped sine, next a multsine and finally a stepped sine excitation. From the spectra obtained with both stepped sines a new virtual spectrum is calculated as if all excited frequencies would have been recorded at the moment when the multisine was imposed to the system. A comparison of the multisine spectrum with this interpolated spectrum was then used for validation. The results show that the instantaneous behaviour of a time-varying system, observed during EIS is better approximated by the use of a multisine excitation signal. Moreover, the approximation further ameliorates when the immersion time evolves.

Analysis of swept-sine runs during modal identification

Experimental modal analysis of large aerospace structures in Europe combine nowadays the benefits of the very reliable but time-consuming phase resonance method and the application of phase separation techniques evaluating frequency response functions (FRF). FRFs of a test structure can be determined by a variety of means. Applied excitation signal waveforms include harmonic signals like stepped-sine excitation, periodic signals like multi-sine excitation, transient signals like impulse and swept-sine excitation, and stochastic signals like random. The current article focuses on slow swept-sine excitation which is a good trade-off between magnitude of excitation level needed for large aircraft and testing time. However, recent ground vibration tests (GVTs) brought up that reliable modal data from swept-sine test runs depend on a proper data processing. The article elucidates the strategy of modal analysis based on swept-sine excitation. The standards for the application of slowly swept sinusoids defined by the international organisation for standardisation in ISO 7626 part 2 are critically reviewed. The theoretical background of swept-sine testing is expounded with particular emphasis to the transition through structural resonances. The effect of different standard procedures of data processing like tracking filter, fast Fourier transform (FFT), and data reduction via averaging are investigated with respect to their influence on the FRFs and modal parameters. Particular emphasis is given to FRF distortions evoked by unsuitable data processing. All data processing methods are investigated on a numerical example. Their practical usefulness is demonstrated on test data taken from a recent GVT on a large aircraft. The revision of ISO 7626 part 2 is suggested regarding the application of slow swept-sine excitation. Recommendations about the proper FRF estimation from slow swept-sine excitation are given in order to enable the optimisation on these applications for future modal survey tests of large aerospace structures.

Detection of nonlinear distortions with multisine excitations in the case of nonideal behavior of the input signal

A method for the detection, qualification, and quantification of nonlinear distortions on a frequency response function (FRF) measurement was described in previous papers by Schoukens et al.. The kernel idea of that method is to use well-chosen periodic excitations where only some of the considered frequency components are excited. The nonexcited frequency lines (detection lines) are used to detect, qualify, and quantify the nonlinear distortions. Due to the presence of a low-quality generator, a nonlinear actuator, or due to the interaction of the generator with the nonlinear system, unwanted excitation power can be present at the detection lines at the input of the system. In this case, the basic conditions necessary to apply the detection method are no longer valid. In this paper, a first-order compensation method is described that allows the detection, qualification, and quantification of nonlinear distortions on the FRF measurement with the original technique of previous papers by Schoukens et al., in the case that the desired input cannot be applied at the device under test. This first-order compensation method is illustrated on simulations and a real measurement example.

The use of multisine excitations to characterise damage in structures

In order to detect the presence of damage and imperfections in materials, a new and promising method for non-destructive material testing has been developed. The technique focuses on the non-linear distortions that are present in the results of a frequency response function (FRF) or transfer function measurement of the sample. The kernel idea in the described method is to use well-chosen periodic excitations where only some of the considered frequency components are excited. The non-excited frequency lines are used to detect, qualify (even or odd non-linear distortions) and quantify (What is the level of the non-linear distortions?) the non-linear distortions. Undamaged materials are often essentially linear in their response. However, the non-linear behaviour of the same material increases significantly when damage appears. The method is applied in the field of damage detection and health monitoring. The method is illustrated by experiments on uncracked and cracked artificial slate beams used in civil constructions and during mechanical cyclic fatigue loading. The developed technique demonstrated to be a very fast and efficient tool to assess global damage in a material.

Multisine load cycle design for fatigue testing

To experimentally quantify the fatigue life of critical airplane components (such as, for instance, the slat tracks), extensive tests must be performed on a test rig. In this paper, a method is proposed to design the load signal which has to be applied in order to exactly obtain a certain damage content. The method presented uses a (band-limited) perturbed multisine (MS) excitation signal. Therefore, the load can be easily controlled. In addition, because the designed multisine is periodic, the health of the structure can easily be monitored on-line. The proposed method will be validated both on simulations and on (low cycle) fatigue measurements of a steel beam.

IDENTIFICATION OF ROTOR-BEARING SYSTEMS IN THE FREQUENCY DOMAIN PART I: ESTIMATION OF FREQUENCY RESPONSE FUNCTIONS

This paper discusses the non-parametric identification if MIMO rotor-bearing systems in the frequency domain for real as well as for complex modal testing. The FRFs are estimated on the basis of the maximum likelihood estimator, considering noise on both inputs and outputs (error-in-variables model). It is demonstrated that multisine excitations with random phases yield improved FRF measurements as compared to random excitations. Moreover, quantitative uncertainties (covariances of the FRFs) are obtained allowing us to quantify the quality of the measurements. The experiments are performed on a rotor test rig and the evaluation is made for both real and complex modal analysis.

IDENTIFICATION OF ROTOR-BEARING SYSTEMS IN THE FREQUENCY DOMAIN PART II: ESTIMATION OF MODAL PARAMETERS

This paper discusses the parametric identification of multiple-input–multiple-output (MIMO) rotor-bearing systems in the frequency domain on the basis of the maximum likelihood estimator (MLE). An identification procedure, considering noise on both inputs and outputs (errors-in variables model), is developed for real as well as for complex modal testing. Quantitative measures for the uncertainties (covariances) of the estimated parameters were to be obtained. It is shown that the MLE solution of real and complex modal analysis is fully equivalent. It follows that, in case of complex modal testing, reduction of the system is not allowed in general when noise information is taken into account. A comparison between random and broadband periodic (multisine) excitations is made. Measurements on a rotor test rig demonstrated that multisines yield more accurate estimates of the modal parameters (as compared to random excitation).

Design of multisine excitations to characterize the nonlinear distortions 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.

Robust broadband periodic excitation design

This paper considers a rather practical problem arising when inexperienced users misuse the (otherwise well-designed) periodic broadband excitation signals during the measurement or signal processing phase of an identification process. Using a fractional period of the excitation signal instead of full periods may affect not only the precision because of the well-known leakage effect, but may cause a serious loss of information on the measured system as well. The power of the excitation signal in certain frequency bands may be much lower (30-40 db) than it would be expected, and thus the measurement in a noisy environment may give poor result. A solution is presented here to make periodic broadband (multisine) excitation signals more robust against such misuse. The suggested solution is analyzed, and the theoretical results are verified by practical examples.

Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach

This paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations. In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties. In the second part a parametric model for the RLDS is identified. Convergence in probability of this model to the RLDS is proven. A function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate.