Robust and Real-Time Physical Modeling Sound Synthesis for Nonlinear Systems: String Vibration

Risse T, Bilbao S, Hélie T. Robust and Real-Time Physical Modeling Sound Synthesis for Nonlinear Systems: String Vibration. J Audio Eng Soc. 2026;74(7/8):485-496. doi:10.17743/jaes.2026.0271

@article{Risse2026_23386,
  author = {Risse, Thomas and Bilbao, Stefan and Hélie, Thomas},
  title = {{Robust and Real-Time Physical Modeling Sound Synthesis for Nonlinear Systems: String Vibration}},
  journal = {Journal of the Audio Engineering Society},
  volume = {74},
  number = {7/8},
  pages = {485--496},
  year = {2026},
  month = jul,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2026.0271},
  url = {https://doi.org/10.17743/jaes.2026.0271}
}

TY  - JOUR
TI  - Robust and Real-Time Physical Modeling Sound Synthesis for Nonlinear Systems: String Vibration
AU  - Risse, Thomas
AU  - Bilbao, Stefan
AU  - Hélie, Thomas
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 74
IS  - 7/8
SP  - 485
EP  - 496
PY  - 2026
DA  - 2026/07/08
DO  - 10.17743/jaes.2026.0271
UR  - https://doi.org/10.17743/jaes.2026.0271
PB  - Audio Engineering Society
LA  - en
AB  - The aim of physical modeling is to allow for realistic rendering of musical sound based purely on a mathematical description of a dynamical system. For expressive musical use, real-time performance is essential. But other major concerns are the requirement for numerical stability, perceptual fidelity, and robustness. Fulfilling these simultaneous requirements for strongly nonlinear systems is challenging. In the case of nonlinear string vibration, stability may be ensured by enforcing a numerical energy balance, and recently, efficient explicit methods have become available based on the use of scalar auxiliary variable techniques. However, convergence rates can be slow and seem to be system-dependent. Especially for musical use, numerical drift of the auxiliary variable over long time scales can result in dramatic unwanted effects, including pitch drifts after several impacts on the same resonator. In this paper, a novel method for mitigating this unwanted drift while preserving power balance is presented. A set of modified equations is proposed to control the drift artifact through an energy-balanced feedback-loop. Numerical experiments are run to check convergence on simulations with three different nonlinearities. A real-time implementation is provided as a Max/MSP external, enabling up to 60-note polyphony on a laptop.
ER  -