This article addresses identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates nonlinear homogeneous order contributions from which Volterra kernels can be identified independently. The proposed separation method exploits phase relations between test signals rather than amplitude relations that are usually used. This method is compared with standard separation process. Its contribution to identification is illustrated on a simulated loudspeaker with nonlinear suspension.

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This work takes place in the context of the development of an active control of instruments with geometrical nonlinearities. The study focuses on Chinese opera gongs that display a characteristic pitch glide in normal playing conditions. In the case of the xiaoluo gong, the fundamental mode of the instrument presents a softening behaviour (frequency glides upward when the amplitude decreases). Controlling the pitch glide requires a nonlinear model of the structure, which can be partially identified with experimental techniques that rely on the formalism of nonlinear normal modes. The fundamental nonlinear mode has been previously experimentally identified as a softening Duffing oscillator. This paper aims at performing a simulation of the control of the oscillator’s pitch glide. For this purpose, the study focuses on a single-degree-offreedom nonlinear mode described by a softening Duffing equation. This Duffing oscillator energy proves to be ill-posed - in particular, the energy becomes negative for large amplitudes of vibration, which is physically inconsistent. Then, the first step of the present study consists in redefining a new energetically well-posed model. In a second part, guaranteed-passive simulations using port-Hamiltonian formalism confirm that the new system is physically and energetically correct compared to the Duffing model. Third, the model is used for control issues in order to modify the softening or hardening behaviour of the fundamental pitch glide. Results are presented and prove the method to be relevant. Perspectives for experimental applications are finally exposed in the last section of the paper.

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This paper proposes a new macroscopic physical model of ferromagnetic coils used in audio circuits. To account for realistic saturation and hysteretic phenomena, this model combines statistical physics results, measurement-driven refinements and portHamiltonian formulations that guarantee passivity, thermodynamic consistency and composability according to both electric and thermal ports. As an illustration, the model is used to simulate a passive high-pass filter. Different types of audio inputs are considered and simulations are compared to measurements.

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This paper addresses identification of nonlinear circuits for power-balanced virtual analog modeling and simulation. The proposed method combines a port-Hamiltonian system formulation with kernel-based methods to retrieve model laws from measurements. This combination allows for the estimated model to retain physical properties that are crucial for the accuracy of simulations, while representing a variety of nonlinear behaviors. As an illustration, the method is used to identify a nonlinear passive peaking EQ.

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Vactrols, which consist of a photoresistor and a light-emitting element that are optically coupled, are key components in optical dynamic compressors. Indeed, the photoresistor’s program-dependent dynamic characteristics make it advantageous for automatic gain control in audio applications. Vactrols are becoming more and more difficult to find, while the interest for optical compression in the audio community does not diminish. They are thus good candidates for virtual analog modeling. In this paper, a model of vactrols that is entirely physical, passive, with a program-dependent dynamic behavior, is proposed. The model is based on first principles that govern semi-conductors, as well as the port-Hamiltonian systems formalism, which allows the modeling of nonlinear, multiphysical behaviors. The proposed model is identified with a real vactrol, then connected to other components in order to simulate a simple optical compressor.

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