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<p>To achieve precise numerical quantitative identification of tooth root crack lengths, a novel framework based on the coordinated fusion of mechanism modeling and data-driven methods is proposed. It overcomes the limitations of traditional methods, which typically transform quantitative problems into classification tasks and fail to effectively identify unknown crack length. Firstly, a condition domain invariance feature (CDIF) modeling method is designed by combining the Spearman correlation coefficient, a strong monotonicity constraint, and a dynamic model to obtain CDIF indicators. Subsequently, the subtraction average-based optimizer-variational mode decomposition (SABO-VMD) algorithm is improved to a multi-feature sensitive mode selection version (MFSMSV) through the incorporation of the CDIF indicators. Next, an incomplete data reconstruction method is established based on the CDIF model. A multi-layer Feature-wise Linear Modulation (MFiLM) adjustment mechanism is then constructed to guide the Transformer in extracting the crucial crack-related features, thereby further improving the feature extractor of MDN (MFiLM-TransMDN). Finally, tooth root cracks are quantitatively identified using the output layer of MFiLM-TransMDN. The proposed method is verified on the experimental datasets containing various crack lengths. An average identification error of only 0.0569&#xa0;mm is achieved. A maximum reduction of 0.6163&#xa0;mm is demonstrated compared to others. Especially in the scenario of unknown crack length, it still maintains high accuracy with an average error of 0.0205&#xa0;mm. These results indicate that the proposed framework can not only accurately identify known cracks, but also exhibits good generalization ability and adaptability to unknown crack lengths. This framework effectively quantifies diagnostic uncertainty, thereby enhancing the reliability and engineering applicability of the model.</p>

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A hybrid mechanism-data driven method for quantitative identification of unknown tooth root crack lengths

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Na Yang,
  • Jie Liu,
  • Hui Ma,
  • Wei-qiang Zhao

摘要

To achieve precise numerical quantitative identification of tooth root crack lengths, a novel framework based on the coordinated fusion of mechanism modeling and data-driven methods is proposed. It overcomes the limitations of traditional methods, which typically transform quantitative problems into classification tasks and fail to effectively identify unknown crack length. Firstly, a condition domain invariance feature (CDIF) modeling method is designed by combining the Spearman correlation coefficient, a strong monotonicity constraint, and a dynamic model to obtain CDIF indicators. Subsequently, the subtraction average-based optimizer-variational mode decomposition (SABO-VMD) algorithm is improved to a multi-feature sensitive mode selection version (MFSMSV) through the incorporation of the CDIF indicators. Next, an incomplete data reconstruction method is established based on the CDIF model. A multi-layer Feature-wise Linear Modulation (MFiLM) adjustment mechanism is then constructed to guide the Transformer in extracting the crucial crack-related features, thereby further improving the feature extractor of MDN (MFiLM-TransMDN). Finally, tooth root cracks are quantitatively identified using the output layer of MFiLM-TransMDN. The proposed method is verified on the experimental datasets containing various crack lengths. An average identification error of only 0.0569 mm is achieved. A maximum reduction of 0.6163 mm is demonstrated compared to others. Especially in the scenario of unknown crack length, it still maintains high accuracy with an average error of 0.0205 mm. These results indicate that the proposed framework can not only accurately identify known cracks, but also exhibits good generalization ability and adaptability to unknown crack lengths. This framework effectively quantifies diagnostic uncertainty, thereby enhancing the reliability and engineering applicability of the model.