Swept-sine Signal Research Articles

Parameter Identification of Switched Reluctance Motor SRM Using Exponential Swept-Sine Signal

Switched reluctance motors (SRMs) received major interest in several domains, e.g., in electric vehicles. This interest is due to the many advantages of SRMs, including operation at a wide range of speeds, high performances, low cost, robustness to run under degraded conditions, and controllability. One of the major aspects in the design and implementation of controllers for SRMs is the estimation of the motor parameters. An accurate estimate of these parameters is a challenge due to the highly nonlinear behavior of SRMs in addition to their magnetic saturated operating mode to maximize the energy transfer. This paper aims at estimating the parameters of SRM by developing a new SRM model using an analytical technique. The proposed technique is based on a parallel connection of several Hammerstein models that have polynomial nonlinearity. The model is driven by a swept-sine signal, and then finite element method analysis is performed to estimate the SRM parameters. The effectiveness of the proposed method is highlighted by numerical simulation. All these simulations were performed using MATLAB/SIMULINK.

Parameter Optimization for an Accurate Swept-Sine Identification Procedure of Nonlinear Systems

Modeling the nonlinearity of a system is of primary importance both for optimizing its design and for controlling the behavior of physical systems operating with a wide dynamic range of input values, for which the linearity hypothesis may not be sufficient. To become of practical use, the identification of nonlinear models must be accurate and computationally efficient. For these reasons, in recent years, among the numerous models of nonlinear systems that have been proposed in the technical literature, the Hammerstein model has been widely applied as a consequence of the proposal of a new pattern identification technique based on pulse compression, which makes the identification of the model very accurate in numerous applications for which it has been adopted. Hammerstein model identification of a nonlinear system requires characterization of the linear filters present on the different branches of the model. These linear filters, which constitute the parameters of the model to be identified, must be considered with respect to their trends over time or, equivalently, in their frequency trends, as amplitude and phase responses. The identification can be considered accurate if the trends obtained for each filter adequately characterize it for the entire frequency range to which that specific filter is subjected in the normal operation of the system to be identified. This work focuses on this aspect, i.e., on the adequacy of the frequency range for which the filter is identified and on how to obtain correct identification in the entire frequency range of interest. The identification procedure based on exponential swept-sine signals defines these filters in the time domain by making use of intermediate functions that are related to the impulse responses of the model filters through a linear transformation. In this paper, we analyze, in detail, the roles of the bandwidths of both the excitation signal and the matched filter, which are the basis of the procedure, we verify the assumptions made about the amplitudes of their frequency bands, and we propose criteria for defining the bandwidths in order to maximize accuracy in model identification. The experiment performed makes it possible to verify that the proposed procedure avoids possible limitations and significantly improves the quality of the identification results, both if the description is made in the time domain and in the frequency domain.

Multi-purpose controllable electrochemical impedance spectroscopy using bidirectional DC–DC converter

In this paper, we propose a multi-purpose controllable electrochemical impedance spectroscopy (MP-cEIS) device for online and offline battery monitoring and testing during charge and discharge processes. The proposed MP-cEIS device is based on the widely used synchronous buck converter, with a low-cost and simple input filter to provide the bidirectional operation. It also includes a closed-loop feedback system to control the injection of the EIS excitation signal. For the control system design, an average model of the proposed MP-cEIS is derived. Two methods, based on H∞ and quantitative feedback theory (QFT), are presented for the design of a robust controller, which guarantees the stability and tracking of the excitation signal despite model uncertainties. The excitation signal in the proposed MP-cEIS is programmable. The performance of the proposed MP-cEIS is evaluated experimentally, with multi-sine and swept-sine signals, and the results are shown.

A data-driven nonlinear state-space model of the unsteady lift force on a pitching wing

Accurate unsteady aerodynamic models are essential to estimate the forces on rapidly pitching wings and to develop model-based controllers. As system identification is arguably the most successful framework for model predictive control in general, in this paper we investigate whether system identification can be used to build data-driven models of pitching wings. The forces acting on the pitching wing can be considered a nonlinear dynamic function of the pitching angle and therefore require a nonlinear dynamic model. In this work, a nonlinear data-driven model is developed for a pitching wing. The proposed model structure is a polynomial nonlinear state-space model (PNLSS), which is an extension of the classical linear state-space model with nonlinear functions. The PNLSS model is trained on experimental data of a pitching wing. The experiments are performed using a dedicated wind tunnel setup. The pitch angle is considered as the input to the model, while the lift coefficient is considered as the output. Three models are trained on swept-sine signals at three offset angles with a fixed pitch amplitude and a range of reduced frequencies. The three training datasets are selected to cover the linear and nonlinear operating regimes of the pitching wing. The PNLSS models are validated on single-sine experimental data at the respective pitch offset angles. The PNLSS models are able to capture the nonlinear aerodynamic forces more accurately than a linear and semi-empirical models, especially at higher offset angles.

Parameter Identification of Switched Reluctance Motor Using Exponential Swept-Sine Signal

Switched reluctance motors (SRMs) present major interest in several domains, e.g., in electric vehicles, because of their wide range speed variation, high performances, low cost, and robustness to run under degraded conditions. This paper aims at developing a new analytical approach for modeling of SRM parameters. Specifically, an identification scheme is proposed to obtain estimates of SRM parameters. Since SRMs have a highly nonlinear behavior, their modeling proves to be challenging. Furthermore, to maximize the energy transfer, SRMs are always operated in magnetically saturated mode. Presently, we will show that SRMs can accurately be described by a generalized polynomial Hammerstein model. The latter is parallel connection of several Hammerstein models having polynomial nonlinearity. Based on this model structure, we design an identification method that consists in: (i) exciting the system with a swept-sine signal; (ii) estimating the model parameter by using finite element method analysis. The effectiveness of the proposed method is highlighted by numerical simulation.

Finite impedance boundary conditions determined in situ for modeling underwater acoustical measurement in laboratory tanks

In underwater acoustics, laboratory tank sound propagation models may be improved using in situ characterization of water tank boundaries. An underwater acoustic tank model is developed with finite impedance boundaries determined in situ from impulse response measurements calculated from the frequency deconvolution of swept-sine signals following techniques commonly used in room acoustics. Impulse responses were used to obtain the acoustic absorption of the acrylic tank walls through reverse Schroeder integration determining the reverberation time and solving the Eyring equation for absorptive effects. This approach improves modeling of sound propagation in water tanks and is validated with numerical test cases and measurements. An improved tank model considering measured finite impedance boundaries will further develop the ability for more realistic data simulation in water tanks which will be used to design machine learning refinement.

Swept-sine integration method for complex amplitude extraction of swept-sine signal

Swept-sine vibration test plays a significant role in product validations. As its basic step, the accuracy and efficiency of complex amplitude (which includes the amplitude and phase information of swept-sine signal) extraction have an important impact on the performance of swept-sine vibration test. In order to improve the efficiency while ensuring its accuracy, a swept-sine integration method is proposed. The proposed swept-sine integration method, which is inspired by tracking filter method and tracking integration method, utilizes a weighted integral process to extract the complex amplitude. A numeral example is presented to compare the performance of the proposed method with several other methods for complex amplitude extraction which are also reviewed in this paper. By comparing the results of the numerical example, some light is shed on the strength of the method proposed. Afterwards, the swept-sine integration method is applied in a real test, further validating the appliance value of this method.

Comparison of room acoustics parameters measured using different techniques

ISO Standard 3382 is used around the world to investigate the room acoustics parameters of performing arts spaces. The measured data serves as feedback for new projects; to evaluate the results with design intent, and benchmark exercises with well-known halls. It is not always practical for acoustical consultants to carry out tests using precision techniques that can include omnidirectional sources and other apparatuses that are difficult to transport from one place to another. To investigate the results obtained with different techniques, we measured the room acoustics parameters in six venues. These venues include a multipurpose theatre seating 1500, two small black-box type venues seating 150 each, one chamber music hall seating 200 and two large halls with no seats and capacity for 700 people. It is a broad sample, including halls of different volumes and shapes. At the precision technique sessions, it was used one omnidirectional source, number of samples according to ISO 3382, and swept sine signal. At the simplified technique sessions, we use balloon bursts and handclaps. The data analysis used the same software for both techniques. This article presents the results and the pros and cons of using the simplified technique.

On the practical application of the impulse response measurement method with swept-sine signals in building acoustics.

Impulse response (IR) measurement methods with deterministic signals have been used in various fields of acoustics for decades, yet there is still a hesitancy to apply them by some practitioners, especially in the building acoustics community. This hesitancy is also the topic of discussion in ASTM standards committees because IR methods are not allowed in ASTM standards. The criticism that prevents a more widespread adoption is that the description of IR methods in existing standards such as ISO 18233 is not sufficient to enable practitioners and equipment manufacturers to reliably implement them. Previous publications have described the theoretical background well, but they have not given sufficient guidance for the practical application with respect to the parameters of the measurement signal. To provide more guidance and show the practical advantages of IR measurement methods, this paper investigates the effects of the design parameters of swept-sine signals. Measurements in a reverberant chamber are used to highlight potential problems and appropriate solutions derived from a theoretical background. Suggestions for the design of measurement signals and for the post-processing of the measured data are provided to achieve optimal and reliable results. This contribution hopefully gives practitioners more confidence in applying the method in the future.

Estimating elasticity modulus of the piezo ceramic disc (PCD) using basic mathematical modelling

The objective of this paper is to determine a mathematical modelling of piezoceramic disc vibration using a single degree freedom mechanical model, with estimation of its elasticity modulus. The experimental vibration displacement values of piezo ceramic disc have been achieved utilizing the swept-sine signal excitation following the peak values in the signal response measured by the laser Doppler vibrometer. Consistency between the mathematical modelling and experimental values have been observed from 97 to 80% between excitation amplitudes of 0.5 and 3.5 V when the mathematical modeling of piezo ceramic disc is normally taken into consideration with a linear working range. The results obtained from experimental studies on resonance frequency are in a compliance with reference value declared by producer of the piezo ceramic disc.

Achieving realism and repeatability of an orchestra simulated within a concert hall

Virtual acoustic techniques can allow for direct comparison between concert halls, but care must be taken to ensure the virtual reconstruction connects back to the subtle perceptions of the real environment. To achieve better realism with repeatability between measured halls, a compact spherical loudspeaker array is being used to simulate an orchestra. This sound source is placed at twenty different source locations around the stage. For each instrument measurement position, a swept-sine signal is processed to radiate from the source with a particular instrument’s directivity, and the spatial room impulse response (RIR) is measured. This processing is accomplished through filters designed from an instrument directivity database measured with 32 microphones. For each instrument, a set of full-frequency filters, one for each loudspeaker driver, were designed from one-third octave band spherical harmonic weights. These processing techniques are directly analogous to higher order Ambisonics (HOA). In the audience, a 32-element spherical microphone array is used to capture the spatial RIR, and each measurement is convolved with single-instrument anechoic recordings and auralized using HOA. Separate auralizations of each instrument are combined together into a full-orchestral auralization. The measurement setup, filter design, and equalization techniques will be presented. [Work supported by NSF Award 1302741.]

The artificial neural network modelling of the piezoelectric actuator vibrations using laser displacement sensor

Abstract We report an improvement of the artificial neural network (ANN) modelling of a piezoelectric actuator vibration based on the experimental data. The controlled vibrations of an actuator were obtained by utilizing the swept-sine signal excitation. The peak value in the displacement signal response was measured by a laser displacement sensor. The piezoelectric actuator was modelled in both linear and nonlinear operating range. A consistency from 90.3 up to 98.9% of ANN modelled output values and experimental ones was reached. The obtained results clearly demonstrate exact linear relationship between the ANN model and experimental values.

Synchronized Swept-Sine: Theory, Application, and Implementation

Exponential, or sometimes called logarithmic, swept-sine signal is very often used to analyze nonlinear audio systems. In this paper, the theory of exponential swept-sine measurements of nonlinear systems is reexamined. The synchronization procedure necessary for a proper analysis of higher harmonics is detailed leading to an improvement of the formula for the exponential swept-sine signal generation. Moreover, an analytical expression of spectra of the swept-sine signal is derived and used in the deconvolution of the impulse response. A Matlab code for generation of the synchronized swept-sine, deconvolution, and separation of the impulse responses is given with discussion of some application issues and an illustrative example of harmonic analysis of current distortion of a woofer is provided.

Impulse Responses Measured with MLS or Swept-Sine Signals Applied to Architectural Acoustics: An In-depth Analysis of the Two Methods and Some Case Studies of Measurements Inside Theaters

The measurement of impulse responses inside of a room or a theatre is a critical task in architectural acoustics. The impulse responses are usually measured using either Exponential Sine Sweep (ESS) or Maximum Length Sequence (MLS) signals. The theory behind MLS generation and use is well developed and does not involve computational problems. When a non-linear system is measured, the distortion appears in the deconvolved impulse response as a series of peaks distributed over time, in deterministic positions. In case of presence of noise during the measurement, the phase of any spurious noise, even an impulsive one, is randomly distributed over the entire length of the recovered impulse response. The ESS signal shows some advantages over MLS, such as a better signal to noise ratio (SNR) and a robust non-linearity rejection. Typically, in the same conditions, the ESS has a dynamic range of about 15dB higher than MLS. Nonetheless, the generation of an ESS signal and the subsequent analysis of impulse responses involve some problems whose solutions are not yet common practice and short impulsive noises can contaminate the sampled data, causing bad effects on the deconvolved impulse response, in form of a frequency decreasing sweep. For the above mentioned reasons ESS is generally more suitable than MLS for use in architectural acoustics, but in some cases the use of MLS signal is still to be preferred. Differences and advantages between impulse response measurements obtained by means of MLS or ESS, are analyzed and discussed in this paper and an in-depth analysis of both measurement methods is presented. Some case studies of impulse response measurements performed inside historical Italian opera houses using both MLS and ESS, in non-ideal conditions (for example in presence of spurious noise), are presented and examined, highlighting differences, advantages and pitfalls of both measurement methods.

A digital measurement system based on laser displacement sensor for piezoelectric ceramic discs vibration characterization

This study describes the innovative design of a digital measurement system based on a laser displacement sensor (LDS) as a vibrometer which is capable to measure a dynamic displacement response dependence on a stimulated vibration. The frequency response of a piezoelectric ceramic disc is obtained by processing the input/output signals obtained from the function generator and digital oscilloscope (digitizer) cards driven by a personal computer. Resonant frequencies of vibration are achieved utilizing the swept-sine signal excitation following the peak values in the signal response measured by LDS. The analogue signal from LDS controller represents directly a mechanical vibration of a piezoceramic disc. The test measurement results indicate that the system can distinguish resonance frequencies of piezoelectric ceramic discs up to 40kHz with the resolution 1Hz. Piezoelectric coefficient d33 and its linearity along the excited voltage amplitudes have been calculated by the applied methods as a demonstration of a successful system concept. The results achieved are in compliance with the reference value declared by the manufacturer of the piezoceramic disc.

Modeling and Compensation for the Distortion of Parametric Loudspeakers Using a One-Dimension Volterra Filter

Recently, the general Volterra filter (VF) has been adopted for the modeling of parametric loudspeakers. However, the computation complexity of the VF is too high for real-time implementation. In this paper, a one-dimension Volterra filter (ODVF) with much lower complexity is introduced to model and compensate for the nonlinearity of parametric loudspeakers. A theoretical framework for ODVF model identification is established and a method of measuring the ODVF kernels using the exponential swept-sine signal is provided. The validity of modeling the nonlinearity of the parametric loudspeaker using the ODVF is verified theoretically and experimentally. Based on the established ODVF model, an inverse filter is designed to compensate for the 2nd harmonic distortion of the parametric loudspeakers. To further reduce the 3rd harmonic distortion, an improved compensation method is also proposed. Experimental results show that the performance of the ODVF-based compensation is comparable to that of the Volterra-filter based compensation.

Recent Topics in Acoustic Scattering Coefficient Determination for Wall Surfaces

Three recent topics in acoustic scattering coefficient determination for wall surfaces are briefly presented: 1) validation of the reverberation room method of ISO 17497-1, 2) a new method of measuring normal-incidence coefficients, and 3) alternative determination by numerical simulation. First, the ISO method is reconsidered regarding unclear requirements of two approaches with stepwise and continuous rotation. It is theoretically and experimentally verified that the stepwise approach has a minimum number of angular steps, whereas the continuous approach has a minimum revolution period if using MLS signals, however if using swept sine signals, in the same way as the stepwise approach. Furthermore, the minimum requirements increase as the sample's scattering coefficient is higher, and unexpectedly, as the room's absorption area is smaller. Second, a new laboratory method is introduced for measuring normal-incidence coefficients, which would be useful to evaluate suppression of flutter echoes. The measurement is done in a rectangular room where installing highly absorbent materials on all vertical walls, and a test sample on the floor. In the one-dimensional field, normal-incidence coefficients of the sample can be determined by measuring the change in reverberation time with and without it. Third, as the alternative to measurement, numerical determination of scattering coefficients is demonstrated and further practical applications are discussed.

Acoustical Measurements Using Perceptual Masking Effects or Musical Compositions

Abstract The swept sine technique has proven to lead to accurate estimations of the room impulse response, even in situations of low SNR, non-linearity and time-variance of the system under test. Regarding the distributive property of the convolution, the swept sine signal can be split into several segments, namely grains, and sent separately to the room. At the reception, the full frame is assembled from the grains by applying the overlap-add based procedure. Choosing appropriate windows, values to the truncation and the overlap of the captured grains, the degree of degradation on the final results, measured by the amount of produced noise, can be controlled. Therefore, each grain can be matched according to the tempered musical scale, which can be applied on musical compositions, or used in perceptual models, taking into account the human auditory masking effects, to compose a test signal frame for acoustical measurements. The possibility of polyphony musical compositions for use on acoustical measurements is assessed and discussed.

Investigation and Assessment of the Edge Grip of Snowboards with Laser Vibrometry – A Proposal of a Standardised Method

The edge grip of a snowboard defines its ability of holding the arc of a carving turn without intending to break out. In order to assess the vibrational movements of the edge under simulated loading conditions, two boards were put on the edge on a soft foam surface and loaded with 400N such that the boards bent under the added load and the edge was in full contact with the surface. The shovels of the boards were excited with a swept sine signal from 5-200Hz and the displacements measured with a laser vibrometer. The last edge point in contact with the surface proved to have the largest movement range. Maximal displacement was caused by the first torsional mode at 115-125Hz, followed by combined bending/torsional modes at lower frequencies (23-30Hz, 80-90Hz). One board exhibited a larger movement range in the first torsional mode compared to the other board, and the frequency peak of this mode was wider. The mobility index of this board, introduced in this study as the normalized area under the displacement curve of the last edge point, was 1.5 times higher than the index of the other board. The method used in this study offers an accurate quantification of the movement of the edge under standardized load conditions.

Impulse response measurement in public space using musical signal including swept-sine signals

In design of public spaces, e.g. railway stations, airport terminal buildings and underground shopping centers, careful attention should be paid from an acoustical viewpoint. It is not only for acoustical comfort but also for safety ensured by a public address system with high intelligibility. As a study for this aim, we have been investigating acoustical characteristics of various public spaces. In these studies, it is strongly desired to measure impulse responses in the spaces under live condition with occupants but the usual measurement method using Swept-Sine signals are not applicable because the signals sound very peculiar to the occupants. To mitigate such a problem, we are trying a method using test music signals in which Swept-Sine signals are inserted. In this paper, the availability of this measurement technique is outlined and some measurement results are introduced.