国分町の某所で某先生と飲んでいた時に、うれしいメールが参りました。Enhancing â‑a probability-of-detection models for the analysis of ultrasonic non-destructive testing signals: The impact of sample size, flaw size distribution, and nonlinear regression（超音波探傷信号の分析のための高度化â‑aモデル：サンプルサイズ、きず分布、非線形回帰の影響）とのタイトルでNuclear Engineering and Design誌1に投稿していた論文の受理通知です。
この論文、タイトルの通り非破壊検査信号の分析に関するものなので、素直に考えると非破壊検査に関する論文誌に投稿する、べきものではあります。が、原子力においても今後このような非破壊検査に関する確率論的な評価・分析を、ということで、あえて原子力工学の論文誌に出してみました。実は当初別の原子力工学論文誌に投稿したのですが、そちらはout of scopeということで拒絶されてしまいました。気を取り直して投稿したNuclear Engineering and Design誌では掲載に至りましたが、やはり原子力分野ではなかなかこういった考え方は受け入れられづらい、ということなのかもしれません。
何はともあれ論文の概要は以下。
Title: Enhancing â‑a probability-of-detection models for the analysis of ultrasonic non-destructive testing signals: The impact of sample size, flaw size distribution, and nonlinear regression
Abstract: Quantitative assessment of non-destructive testing (NDT) capability often relies on probability of detection (POD) curves obtained by the â‑a method that is commonly used in the recent POD analyses. However, practical guidance regarding the required number of flaws and their optimal size distribution remains limited. This study addresses this issue by exploring the influence of sample size and flaw size distribution on â‑a POD estimation through Monte Carlo simulations. A known, nonlinear, saturating relationship between flaw size and signal amplitude obtained by numerical simulations of angle-beam ultrasonic inspection is adopted as a reference, and synthetic datasets are generated under various sampling conditions. The analysis shows that in the conventional â‑a method, which performs a linear regression after variable transformation, POD estimates can become strongly biased and highly scattered when sampled flaws are not concentrated near the true (and unknown) flaw size of interest. In contrast, regression models applied without variable transformation, particularly a sigmoid model designed to reflect the saturation behavior of NDT signals, produce more stable estimates of flaw sizes of interest. These include a50 and a90, which are flaw sizes corresponding to 50% and 90% probabilities of detection, respectively. Furthermore, they exhibit substantially reduced dependence on the chosen flaw size range. These findings indicate that using regression functions consistent with the underlying signal physics can relax stringent requirements on flaw size distribution and enable reliable â‑a POD studies with a comparatively small number of flawed specimens. They also underscore the importance of physics‑based modeling and suggest that concepts developed in model‑assisted POD (MAPOD) can be effectively leveraged even when simulation data are not directly used to construct POD curves.