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The directional loudspeaker array has various applications due to its capability to direct sound generation towards the target listener and reduce noise pollution. Differential beamforming has recently been applied to the loudspeaker line array to produce a broadside frequency-invariant radiation pattern. However, the existing methods cannot achieve a compromise between robustness and broadband frequency-invariant beampattern preservation. This paper proposed a robust broadband differential beamforming design to allow the loudspeaker line array to radiate broadside frequency-invariant radiation patterns with robustness. Specifically, we propose a method to determine the ideal broadside differential beampattern by combining multiple criteria, namely null positions, maximizing the directivity factor, and achieving a desired beampattern with equal sidelobes. We derive the above ideal broadside differential beampattern into the target beampattern in the modal domain. We propose a robust modal matching method with Tikhonov regularization to optimize the loudspeaker weights in the modal domain. Simulations and experiments show improved frequency-invariant broadside beamforming over the 250–4k Hz frequency range compared with the existing modal matching and null-constrained methods.

Electrolytic aluminum operation accidents have caused great losses to countries and people. Therefore, taking two typical accidents of explosion and leakage in electrolytic aluminum production as the research object, the form of accident risk characterization was explored and a risk characterization visualization system was designed. Based on the methods of risk assessment and characterization, the likelihood and consequence of accidents were studied. The influencing factors of likelihood and a type of Euclidean distance formula were used to characterize the likelihood. The consequence portion was characterized by two components, with one being the failure degree determined by the accident and the other being the exposure degree of people and equipment. The intensity of event was used to characterize the failure degree and the spatial search model was used to characterize the exposure degree. Finally, the visual system of electrolytic aluminum operation accidents was established based on the risk characterization model.