Håvard Arnestad

• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes & Kirkebø, Jan Egil (2023). Beampattern bounds for block errors in sonar arrays using interval arithmetic. OCEANS. ISSN 0197-7385. doi: 10.1109/OCEANSLimerick52467.2023.10244467.
• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2023). Worst-case analysis of array beampatterns using interval arithmetic. Journal of the Acoustical Society of America. ISSN 0001-4966. 153(6), p. 3312–3323. doi: 10.1121/10.0019715. Full text in Research Archive Show summary

  Over the past decade, interval arithmetic (IA) has been used to determine tolerance bounds of phased-array beampatterns. IA only requires that the errors of the array elements are bounded and can provide reliable beampattern bounds even when a statistical model is missing. However, previous research has not explored the use of IA to find the error realizations responsible for achieving specific bounds. In this study, the capabilities of IA are extended by introducing the concept of “backtracking,” which provides a direct way of addressing how specific bounds can be attained. Backtracking allows for the recovery of the specific error realization and corresponding beampattern, enabling the study and verification of which errors result in the worst-case array performance in terms of the peak sidelobe level (PSLL). Moreover, IA is made applicable to a wider range of arrays by adding support for arbitrary array geometries with directive elements and mutual coupling in addition to element amplitude, phase, and positioning errors. Last, a simple formula for approximate bounds of uniformly bounded errors is derived and numerically verified. This formula gives insights into how array size and apodization cannot reduce the worst-case PSLL beyond a certain limit.

• Viggen, Erlend Magnus & Arnestad, Håvard (2023). Modelling acoustic radiation from vibrating surfaces around coincidence: Radiation into fluids. Journal of Sound and Vibration. ISSN 0022-460X. 560. doi: 10.1016/j.jsv.2023.117787. Full text in Research Archive Show summary

  It is well-known that vibrating surfaces generate sound waves in adjacent fluids. According to the classical radiation model, the nature of these waves depends on whether the vibration’s phase speed cv is above (supersonic) or below (subsonic) the fluid sound speed cf. The transition between these two domains is known as coincidence. In the supersonic domain, the sound wave radiates into the fluid. In the subsonic domain, the classical model states that the wave becomes evanescent and clings to the surface. In the last 30 years, however, several articles on leaky guided waves have reported radiating waves in the subsonic domain, which is at odds with the classical model. In this article, we investigate an enhanced model for sound radiation near and below coincidence. Unlike the classical model, this model fully respects conservation of energy by balancing the radiated power with power lost from the guided wave underlying the vibration. The model takes into account that this power loss and the consequent attenuation of the surface vibration result in an inhomogeneous radiated sound wave — an effect that cannot be neglected near coincidence. We successfully validate the model against exact solutions for leaky A0 Lamb waves around coincidence. The model can also be used as a perturbation method to predict the attenuation of leaky A0 waves from the properties of free A0 waves, giving more accurate estimates than existing perturbation methods. We further investigate subsonic leaky A0 waves using the enhanced model. Thereby we, for example, explain the peculiar reappearance or persistence of the leaky A0 wave at lower frequencies, an effect brought to attention by previous theoretical studies.

• Gereb, Gabor & Arnestad, Håvard (2023). Interval computations in acoustics. In Viggen, Erlend Magnus (Eds.), Proceedings of the 46th Scandinavian Symposium on Physical Acoustics. Norsk Fysisk Selskap. ISSN 978-82-8123-023-1.
• Arnestad, Håvard; Austeng, Andreas; Näsholm, Sven Peter & Rindal, Ole Marius Hoel (2022). The Effect of Retrospective Transmit Focusing on Minimum Variance Beamforming. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. doi: 10.1109/IUS54386.2022.9958050. Show summary

  Minimum variance (MV) beamforming is a well-known adaptive beamforming approach. Retrospective transmit beamforming (RTB), on the other hand, is a technique implemented in some modern ultrasound scanners that strives to obtain two-way focus everywhere in the imaged region. However, it is not immediately clear how these methods should be combined in the image reconstruction pipeline. In this work, we suggest a general and efficient implementation for combining MV with RTB, and we study a few effects and synergetic benefits in comparison to multiple line acquisition processing and conventional delay-and-sum beamforming. Our finding is that RTB improves the resolution and robustness of MV beamforming outside the focal zone.

• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Sonar array beampattern bounds and an interval arithmetic toolbox. Proceedings of Meetings on Acoustics (POMA). ISSN 1939-800X. 47. doi: 10.1121/2.0001613. Show summary

  The framework of interval arithmetic (IA) and its extension to complex numbers has in the last decade been applied as a tool for finding robust tolerance bounds of antenna arrays. The IA framework complements statistical methods, as inclusive upper and lower bounds of the beampattern are obtained directly, only assuming error bounds on specifically chosen array parameters. Recently, beampattern synthesis for sonar arrays subject to amplitude excitation errors has been extended from linear arrays with omnidirectional elements to non-linear arrays with directive elements. In this work, we demonstrate that the analysis can be developed further to include both amplitude and phase errors. Moreover, we account for error bounds in element position and orientation, thus representing a more comprehensive method for evaluating the worst-case performance due to uncertainty bounds in a multitude of design parameters. For this purpose, we have created an open-source MATLAB toolbox to calculate beampattern bounds for an array with bounded error tolerances. The toolbox features an object oriented library of interval classes and an interactive graphical user interface with easily configurable settings, where results for different interval representations are shown along with their corresponding bounds. The beampattern bounds of a sonar array is illustrated through an example.

• Viggen, Erlend Magnus & Arnestad, Håvard (2022). Inhomogeneous P- and S-wavefields radiated into isotropic elastic solids. In Viggen, Erlend Magnus (Eds.), Proceedings of the 45th Scandinavian Symposium on Physical Acoustics. Norsk Fysisk Selskap. ISSN 978-82-8123-022-4. Full text in Research Archive Show summary

  A vibrating surface in contact with a solid material will generate P- and S-waves in the solid. When the surface vibration is spatially attenuated, we must take into account that the generated waves are always inhomogeneous. In an isotropic elastic solid, such inhomogeneous waves are attenuated perpendicularly to their direction of propagation. When the surface vibration's phase speed is lower than the P- and/or S-waves' speed of sound, the inhomogeneity affects the radiation of P- and S-waves in a major but relatively poorly understood way. For a better understanding, finding the total radiated intensity of the two inhomogeneous waves is key. Our work takes a step towards such an understanding by deriving analytical expressions for the velocity, strain, stress, and intensity fields of arbitrarily inhomogeneous P- and S-waves. Furthermore, we investigate whether the total radiated intensity can be found as the sum of the intensities of the individual P- and S-waves. We find that this is only possible when the surface vibration is unattenuated; for attenuated vibrations, the total radiated intensity should be calculated numerically.

• Arnestad, Håvard Kjellmo & Viggen, Erlend Magnus (2021). A fast semi-analytical method for propagating leaky Lamb wavefields. In Viggen, Erlend Magnus (Eds.), Proceedings of the 44th Scandinavian Symposium on Physical Acoustics. Norsk Fysisk Selskap. ISSN 978-82-8123-021-7. Full text in Research Archive Show summary

  A fast method is presented for calculating the wavefields from initialized leaky Lamb waves on plates immersed in sufficiently light fluids. The method works by precomputing the dispersion relation and attenuation, and propagating the wavefields in the frequency domain. An angular spectrum approach is used to include leakage into surrounding fluid. Compared to matching FEM simulations, the computations are performed in the order of seconds, rather than hours. The method also benefits from being much easier to set up correctly, but is on the other hand less general in that it cannot handle e.g. scattering from defects. The correspondence is shown to be good for the case of interest.

• Viggen, Erlend Magnus & Arnestad, Håvard Kjellmo (2021). Understanding sound radiation from surface vibrations moving at subsonic speeds. In Viggen, Erlend Magnus (Eds.), Proceedings of the 44th Scandinavian Symposium on Physical Acoustics. Norsk Fysisk Selskap. ISSN 978-82-8123-021-7. Full text in Research Archive

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• Arnestad, Håvard; Rindal, Ole Marius Hoel; Austeng, Andreas & Näsholm, Sven Peter (2024). Estimation of probability densities in ultrasound imaging.
• Han, Chaoran; Arnestad, Håvard; Austeng, Andreas & Näsholm, Sven Peter (2024). Spectral estimation inspired by a non-linear beamformer: Insights into null-subtraction imaging.
• Viggen, Erlend Magnus & Arnestad, Håvard (2023). Explaining the cutoff, reappearance, and persistence of subsonic leaky A0 Lamb waves.
• Näsholm, Sven Peter; Arnestad, Håvard; Austeng, Andreas & Rindal, Ole Marius Hoel (2023). Calculating the generalized contrast-to-noise ratio using kernel density estimation. Show summary

  The histogram-based generalized contrast-to-noise ratio (gCNR) evaluates how well image regions with different intensity can be distinguished. The gCNR is defined as ‘one minus the overlap region’ of normalized histograms from two regions. Histogram-based gCNR depends on user parameters like bin size and bin offset, but there are also approaches to robustify the histogram calculation. Kernel density estimation (KDE) is a well-established alternative to histograms to estimate probability density functions (PDFs), and is generally considered to be more robust. We suggest replacing histograms with KDE in gCNR calculations.

• Gereb, Gabor & Arnestad, Håvard (2023). Interval computations in acoustics.
• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2023). Bounding the beampattern of acoustic arrays using interval arithmetic.
• Viggen, Erlend Magnus & Arnestad, Håvard (2023). Why leaky flexural plate waves misbehave at low frequencies.
• Austeng, Andreas; Arnestad, Håvard; Bjåstad, Tore Grüner; Måsøy, Svein-Erik & Rindal, Ole Marius Hoel (2022). Issues with Histogram Matching for Fair Evaluation of Image Quality Metrics.
• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Bounding the beampattern of acoustic arrays using interval arithmetic.
• Arnestad, Håvard & Viggen, Erlend Magnus (2022). A Fast Simulation Method for Lamb Wave Propagation in Coupled Non-Parallel Plates.
• Arnestad, Håvard; Austeng, Andreas; Näsholm, Sven Peter & Rindal, Ole Marius Hoel (2022). The Effect of Retrospective Transmit Focusing on Minimum Variance Beamforming.
• Viggen, Erlend Magnus & Arnestad, Håvard (2022). An explanatory model for sound radiation from subsonic surface vibrations. Show summary

  Surface vibrations will generate pressure waves in an adjacent fluid. It is commonly held that these waves radiate away from the surface only if the vibration is supersonic, i.e., faster than the fluid's sound speed. However, multiple articles have shown mathematically that even subsonic vibrations can yield radiating waves. Even so, the physical understanding of this phenomenon has been insufficient. In our work, we derive and validate an explanatory physical model to provide such an understanding.

• Arnestad, Håvard; Gereb, Gabor; Birkenes Lønmo, Tor Inge; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Sonar array beampattern bounds: tolerance analysis using interval arithmetic. Show summary

  The framework of interval arithmetic (IA) and its extension to complex numbers has in the last decade been applied as a tool for finding robust tolerance bounds of antenna arrays. The IA framework complements statistical methods, as inclusive upper and lower bounds of the beampattern are obtained directly, only assuming error bounds on specifically chosen array parameters. Recently, beampattern synthesis for sonar arrays subject to amplitude excitation errors has been extended from linear arrays with omnidirectional elements to non-linear arrays with directive elements. In this work, we demonstrate that the analysis can be developed further to include both amplitude and phase errors. Moreover, we account for error bounds in element position and orientation, thus representing a more comprehensive method for evaluating the worst-case performance due to uncertainty bounds in a multitude of design parameters. For this purpose, we have created an open-source MATLAB toolbox to calculate beampattern bounds for an array with bounded error tolerances. The toolbox features an object oriented library of interval classes and an interactive graphical user interface with easily configurable settings, where results for different interval representations are shown along with their corresponding bounds. The beampattern bounds of a sonar array is illustrated through an example.

• Arnestad, Håvard & Viggen, Erlend Magnus (2022). A fast method for simulating Lamb wave propagation in coupled non-parallel plates.
• Viggen, Erlend Magnus & Arnestad, Håvard (2022). Intensity of inhomogeneous waves in simple solids.
• Arnestad, Håvard Kjellmo & Viggen, Erlend Magnus (2021). A fast semi-analytical method for propagating leaky Lamb wavefields. Show summary

  A fast method is presented for calculating the wavefields from initialized leaky Lamb waves on plates immersed in sufficiently light fluids. The method works by precomputing the dispersion relation and attenuation, and propagating the wavefields in the frequency domain. An angular spectrum approach is used to include leakage into surrounding fluid. Compared to matching FEM simulations, the computations are performed in the order of seconds, rather than hours. The method also benefits from being much easier to set up correctly, but is on the other hand less general in that it cannot handle e.g. scattering from defects. The correspondence is shown to be good for the case of interest.

• Viggen, Erlend Magnus & Arnestad, Håvard Kjellmo (2021). Understanding sound radiation from surface vibrations moving at subsonic speeds.

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