Open Access

ARTICLE

Structure-Informed Machine Learning for Multi-Property Prediction of NBT-Based Lead-Free Piezoceramics

Yalong Liang¹, Xiaohui Yuan¹, Yuning Han², Pei Li^3,*

1 School of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, China
2 School of Materials Science and Engineering, Henan University of Science and Technology, Luoyang, China
3 Centre for Industrial Mechanics, Institute of Mechanical and Electrical Engineering, University of Southern Denmark, Sønderborg, Denmark

* Corresponding Author: Pei Li. Email:

Computers, Materials & Continua 2026, 89(2), 16 https://doi.org/10.32604/cmc.2026.086403

Received 29 May 2026; Accepted 05 August 2026; Issue published 15 September 2026

Abstract

NBT-based lead-free piezoceramics are promising alternatives to Pb-containing materials, yet their functional properties arise from complex and coupled composition–processing–structure–property relationships. Here, we develop a structure-informed machine learning framework to predict and interpret the piezoelectric coefficient d₃₃, depolarization temperature T_d, and relative dielectric permittivity ε_r. A database of 214 records from 34 publications was compiled, including 204 records for model development and 10 records for independent literature validation. The correlation analysis involved 38 variables, including 35 candidate input descriptors and three target properties. After Pearson correlation-based redundancy filtering, 30 nonredundant input descriptors were retained for model development. To incorporate physically meaningful structural information, structural feature variables were introduced to describe phase-boundary characteristics, local lattice distortion, and effective phase state, thereby improving the interpretability of composition/processing–property relationships. ExtraTreesRegressor (ETR), deep neural networks (DNNs), and residual network (ResNet)-style multilayer perceptrons (MLPs) were evaluated using random five-fold cross-validation, while Bayesian neural networks (BNNs) were used for uncertainty quantification and SHAP analysis was used to identify influential descriptors. Under random five-fold cross-validation, the best-performing models achieved R² values of 0.79, 0.89, and 0.90 for d₃₃, T_d, and ε_r, respectively, suggesting that structural descriptors provide informative physical features for property prediction. SHAP results further highlighted the important role of processing-related descriptors, particularly calcination parameters, in tuning dielectric responses. This framework provides a physically interpretable and uncertainty-aware strategy for candidate screening and optimization of high-performance NBT-based lead-free piezoceramics.

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Keywords

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Supplementary Material

Supplementary Material File

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