测量弓弦模型上的学习弓控：修正的最小弓压力定律、循环控制器与监督上限的域
Learned Bow Control on a Measured Bowed-String Model: a Revised Minimum-Bow-Force Law, a Recurrent Controller, and the Domain of a Supervision Ceiling
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中文总结 AI 辅助
本研究提出隐式求解Stribeck摩擦的有限差分弓弦模型，修正最小弓压力定律，并比较多种学习弓控器，发现门控循环网络优于前馈网络，且控制器性能受生成标签的查找规则上限约束。
中文摘要 AI 辅助
本文提出了一种具有隐式求解Stribeck摩擦的有限差分弓弦模型，并配有状态诊断、四根弦上的Schelleng弓压力极限以及学习型弓控器的比较。隐式求解是必要的，且定量上如此：滞后的接触力无法在离散网格上捕捉弦，因此在任何弓压力下都不会形成粘滞阶段。采用已发表测量而非拟合的摩擦、阻抗和品质因数，四根弦的粘滞分数均为89.1%，而理想值为90%。Schelleng最大弓压力在每根弦上均得以恢复。最小值则不然：它遵循$Z v_b \eta^{-1}$而非预测的$Z^2 v_b \eta^{-2}$，将两个平方依赖均降为一次幂。在匹配容量下，六个控制器在四根弦和每种二十个随机种子上进行测试，门控循环网络在大多数情况下优于前馈网络，尤其是在中程扰动下。前馈网络仅从模型自身可玩性图置于Helmholtz区域之外的起始点完成更多行程。一个最小门控变体失败，因为仅从输入计算的门控无法清除锁存状态。训练损失既不选择容量也不选择上下文长度，且没有学习型控制器优于生成其标签的查找规则。该界限有一个域。将控制器得分对规则得分进行回归，斜率为0.32，低于1超过十个标准误差，因此控制器在规则失效处超越规则，并在规则有效处受其约束。在刚性手指止动下，被控对象可证明是不变的，因此音高间的迁移损失仅属于控制器，并可追溯到单一特征。一个无粘滞测试的状态分类器将小幅周期滑移标记为Helmholtz运动，而谐波性度量将弓从未握住的弦评为高于Helmholtz运动。
英文摘要
A finite-difference bowed-string model with implicitly resolved Stribeck friction is presented, with a regime diagnostic. Without implicit resolution no stick phase forms at any bow force. With friction, impedance and quality factor from published measurement rather than fitted, all four strings return a stick fraction of 89.1% against an ideal 90%. Schelleng's maximum bow force is recovered on every string. His minimum, $F_{\min} \propto Z^2 v_b β^{-2}$, is replaced by a law, $F_{\min} = C Z v_b / β$ with a dimensionless $C = 1.112 \pm 0.017$ that reproduces on sixty-four held-out operating points. Six controllers at matched capacity, on four strings at twenty seeds, place a gated recurrent network ahead of a feedforward one, its margin over the mean of the other five largest when the commanded bow speed is overridden at mid-stroke. The feedforward network completes more strokes, mostly from a cold start no player would use. A minimal gated variant fails because gates computed from the input alone cannot clear a latched state. Training loss selects neither the capacity nor the context length. No learned controller improves on the lookup rule that generated its labels where that rule is correct. Of the rule's 1089 cells, 57 are playable on a properly settled plant and unplayable by its labels, and the controller commands them where the lookup will not. The controller's score regresses on the rule's with a slope of 0.32, more than ten standard errors below unity, so it overtakes the rule where the rule fails and is bounded by it where it holds. Under a rigid finger stop the plant is provably invariant, so transfer loss between pitches is the controller's alone, traced to one feature. A regime classifier without a stick test mistakes small-amplitude periodic slipping for Helmholtz motion, and a harmonicity measure rates a string the bow never grips above it.
发表机构
- Columbia University（哥伦比亚大学）
- Recognition Technologies, Inc.（识别技术公司）
机构由 AI 辅助整理，请以论文原文为准。
