Identification of cascade of Hammerstein models for the description of non-linearities in vibrating devices

International audienceIn a number of vibration applications, systems under study are slightly nonlinear. It is thus of great importance to have a way to model and to measure these nonlinearities in the frequency range of use. Cascade of Hammerstein models conveniently allows one to describe a large class of nonlinearities. A simple method based on a phase property of exponential sine sweeps is proposed to identify the structural elements of such a model from only one measured response of the system. Mathematical foundations and practical implementation of the method are discussed. The method is afterwards validated on simulated and real systems. Vibrating devices such as acoustical transducers are well approximated by cascade of Hammerstein models. The harmonic distortion generated by those transducers can be predicted by the model over the entire audio frequency range for any desired input amplitude. Agreement with more time consuming classical distortion measurement methods was found to be good

Linear and Nonlinear Speaker Characterization

This project developed both linear and nonlinear characterization techniques for use with dynamic loudspeakers. These techniques were designed to provide insight into the effectiveness of specifications typically used to describe loudspeaker transfer characteristics. Provisions were made for non-idealities present in the measurement environment. Final results included one-dimensional plots of linear speaker response, and two-dimensional plots of nonlinear response. Suggestions were made for future experimentation and development

Loudspeaker Modelling with Recurrent Neural Networks

Digital twins of loudspeakers are a useful assets for fine-tuning purposes during the design and the manufacturing phase. They can serve as an alternative to real-time measurement for objective evaluation of adjustments made by digital signal processing. Binaural loudspeaker models could introduce a more repeatable framework for subjective listening and provide flexibility for remote work due to the reduced need for actual physical devices. Neural Networks are a well-proven tool for system identification of different audio hardware devices. This thesis project will focus on creating a digital twin of a multimedia stereo loudspeaker system by using stereo audio waveform as the input and a binaural recording of the system's playback as the target waveform for Recurrent Neural Network (RNN) training. The RNN architecture is inspired by the current state-of-the-art method for single channel audio effects modelling, and is adapted for the stereo waveform use case. Firstly, the RNN model is tested with different synthesized target data that simulates the real recorded data. This approach allows us to estimate the properties which are the most challenging for the RNN to learn. Secondly, the experiments are run with a real recorded, time-aligned dataset, and the RNN's performance is objectively evaluated by the Error-To-Signal Ratio (ESR). In the current state-of-the-art method on single channel audio modelling, the initial hidden state of the RNN is computed by using no-gradient startup inference to accumulate the hidden state over the first few hundred samples of the training sequence. The thesis project proposes a new method called Discontinuous Sequence Training (DISCO). The method prepares the training dataset according to the RNNs architecture’s hyper-parameter sequence length and the system's impulse response length, such that it allows for correct initialization of the initial hidden state without additional pre-training inference. DISCO reaches the training and inference precision of hidden state initialization in the current state-of-the-art method for black-box modelling with RNNs only by modifying the dataset

Numerical Simulation of a Tube-Delay Audio Effect

A virtual tube delay effect based on the real-time simulation of acoustic wave propagation in a garden hose is presented. The thesis describes the acoustic measurements conducted and the analysis of the sound propagation in long narrow tubes. \nDelay lines and digital filters were designed to simulate the propagation delay, losses, and reflections from the end of the tube. A stereo delay effect plugin in PURE DATA has been also implemented

Beiträge zu breitbandigen Freisprechsystemen und ihrer Evaluation

This work deals with the advancement of wideband hands-free systems (HFS’s) for mono- and stereophonic cases of application. Furthermore, innovative contributions to the corr. field of quality evaluation are made. The proposed HFS approaches are based on frequency-domain adaptive filtering for system identification, making use of Kalman theory and state-space modeling. Functional enhancement modules are developed in this work, which improve one or more of key quality aspects, aiming at not to harm others. In so doing, these modules can be combined in a flexible way, dependent on the needs at hand. The enhanced monophonic HFS is evaluated according to automotive ITU-T recommendations, to prove its customized efficacy. Furthermore, a novel methodology and techn. framework are introduced in this work to improve the prototyping and evaluation process of automotive HF and in-car-communication (ICC) systems. The monophonic HFS in several configurations hereby acts as device under test (DUT) and is thoroughly investigated, which will show the DUT’s satisfying performance, as well as the advantages of the proposed development process. As current methods for the evaluation of HFS’s in dynamic conditions oftentimes still lack flexibility, reproducibility, and accuracy, this work introduces “Car in a Box” (CiaB) as a novel, improved system for this demanding task. It is able to enhance the development process by performing high-resolution system identification of dynamic electro-acoustical systems. The extracted dyn. impulse response trajectories are then applicable to arbitrary input signals in a synthesis operation. A realistic dynamic automotive auralization of a car cabin interior is available for HFS evaluation. It is shown that this system improves evaluation flexibility at guaranteed reproducibility. In addition, the accuracy of evaluation methods can be increased by having access to exact, realistic imp. resp. trajectories acting as a so-called “ground truth” reference. If CiaB is included into an automotive evaluation setup, there is no need for an acoustical car interior prototype to be present at this stage of development. Hency, CiaB may ease the HFS development process. Dynamic acoustic replicas may be provided including an arbitrary number of acoustic car cabin interiors for multiple developers simultaneously. With CiaB, speech enh. system developers therefore have an evaluation environment at hand, which can adequately replace the real environment.Diese Arbeit beschäftigt sich mit der Weiterentwicklung breitbandiger Freisprechsysteme für mono-/stereophone Anwendungsfälle und liefert innovative Beiträge zu deren Qualitätsmessung. Die vorgestellten Verfahren basieren auf im Frequenzbereich adaptierenden Algorithmen zur Systemidentifikation gemäß Kalman-Theorie in einer Zustandsraumdarstellung. Es werden funktionale Erweiterungsmodule dahingehend entwickelt, dass mindestens eine Qualitätsanforderung verbessert wird, ohne andere eklatant zu verletzen. Diese nach Anforderung flexibel kombinierbaren algorithmischen Erweiterungen werden gemäß Empfehlungen der ITU-T (Rec. P.1110/P.1130) in vorwiegend automotiven Testszenarien getestet und somit deren zielgerichtete Wirksamkeit bestätigt. Es wird eine Methodensammlung und ein technisches System zur verbesserten Prototypentwicklung/Evaluation von automotiven Freisprech- und Innenraumkommunikationssystemen vorgestellt und beispielhaft mit dem monophonen Freisprechsystem in diversen Ausbaustufen zur Anwendung gebracht. Daraus entstehende Vorteile im Entwicklungs- und Testprozess von Sprachverbesserungssystem werden dargelegt und messtechnisch verifiziert. Bestehende Messverfahren zum Verhalten von Freisprechsystemen in zeitvarianten Umgebungen zeigten bisher oft nur ein unzureichendes Maß an Flexibilität, Reproduzierbarkeit und Genauigkeit. Daher wird hier das „Car in a Box“-Verfahren (CiaB) entwickelt und vorgestellt, mit dem zeitvariante elektro-akustische Systeme technisch identifiziert werden können. So gewonnene dynamische Impulsantworten können im Labor in einer Syntheseoperation auf beliebige Eingangsignale angewandt werden, um realistische Testsignale unter dyn. Bedingungen zu erzeugen. Bei diesem Vorgehen wird ein hohes Maß an Flexibilität bei garantierter Reproduzierbarkeit erlangt. Es wird gezeigt, dass die Genauigkeit von darauf basierenden Evaluationsverfahren zudem gesteigert werden kann, da mit dem Vorliegen von exakten, realen Impulsantworten zu jedem Zeitpunkt der Messung eine sogenannte „ground truth“ als Referenz zur Verfügung steht. Bei der Einbindung von CiaB in einen Messaufbau für automotive Freisprechsysteme ist es bedeutsam, dass zu diesem Zeitpunkt das eigentliche Fahrzeug nicht mehr benötigt wird. Es wird gezeigt, dass eine dyn. Fahrzeugakustikumgebung, wie sie im Entwicklungsprozess von automotiven Sprachverbesserungsalgorithmen benötigt wird, in beliebiger Anzahl vollständig und mind. gleichwertig durch CiaB ersetzt werden kann