TubeLab：具有硬频谱约束的管乐器管腔交互式逆向设计

中文摘要 AI 辅助

我们提出了 TubeLab，一个基于浏览器的声学模拟器和逆向设计工具，用于无音孔的管乐器管腔。正问题通过传递矩阵法求解。逆向设计——寻找一种管腔修正，使选定的共振频率向指定的音乐目标移动——被表述为一个 Tikhonov 正则化最小二乘问题，其雅可比矩阵通过每个模态的单次伴随反向传播计算。对于频率必须保持的模态，采用鞍点公式处理，该公式无论正则化强度如何都强制执行硬等式约束。共振频率与最先进的有限元计算结果在十一种几何形状和 132 个模态对上的一致性在 1.21 音分以内。针对 16 个数控加工迪吉里杜管的敲击声实验验证，涵盖六种不同的管腔设计，在 189 个匹配模态对上产生 9.6 音分的均方根偏差。相同标称管腔的复制样本彼此相差 4.5 音分均方根，因此约 36% 的残差方差是制造散布。

英文摘要

We present TubeLab, a browser-based acoustic simulator and inverse design tool for wind instrument bores without tone holes. The direct problem is solved by a Transfer Matrix Method. Inverse design - finding a bore correction that shifts selected resonance frequencies toward specified musical targets - is formulated as a Tikhonov-regularized least-squares problem whose Jacobian is computed by a single adjoint backward pass per mode. Modes whose frequencies must be preserved are handled by a saddle-point formulation that enforces hard equality constraints regardless of the regularization strength. Resonance frequencies agree with state-of-the-art finite-element calculations to within 1.21 cent over eleven geometries and 132 mode pairs. Experimental validation against tap-tone measurements of 16 numerical control-machined didgeridoos spanning six distinct bore designs yields 9.6 cent RMS deviation over 189 matched mode pairs. Replicate specimens of the same nominal bore disagree with each other by 4.5 cent RMS, so about 36% of the residual variance is fabrication scatter.

发表机构

• Istituto Nanoscienze –- CNR, S3（意大利国家研究委员会纳米科学研究所）

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