TDR-Transformer: A transformer neural network model to determine soil relative permittivity variations along a time domain reflectometry sensor waveguide

文献类型： 外文期刊

第一作者： Wang, Zhuangji

作者： Wang, Zhuangji;Timlin, Dennis;Fleisher, David;Sun, Wenguang;Beegum, Sahila;Reddy, Vangimalla R.;Wang, Zhuangji;Tully, Katherine;Gong, Xiaofei;Kojima, Yuki;Hua, Shan;Sun, Wenguang;Beegum, Sahila;Horton, Robert

作者机构：

关键词： Time Domain Reflectometry (TDR); TDR waveform interpretation; Nonuniform relative permittivity (epsilon r ); Transformer neural network; Machine learning

期刊名称：COMPUTERS AND ELECTRONICS IN AGRICULTURE （ 影响因子：8.9； 五年影响因子：9.3 ）

ISSN： 0168-1699

年卷期： 2025 年 237 卷

页码：

收录情况： SCI

摘要： Interpreting soil relative permittivity (er) variations along a time domain reflectometry (TDR) waveguide provides an opportunity to determine soil water content at multiple depths using a vertically installed TDR sensor. Compared to placing sensors at different depths, vertical sensor installation reduces measurement efforts and enhances data-use-efficiency. Revealing er variations includes two aspects: identifying er change positions and determining er values. Traditional inverse analyses are not widely applied due to their high computational demands. Machine learning-based methods, e.g., TDR-CNN, provide a forward computational workflow to track er change positions and reduce computational load, but errors in er values are relatively large. In this study, TDRTransformer is developed as a new waveform interpretation model to improve er estimation accuracy. Modified from the standard transformer architecture, an encoder with convolutional neural layers is used to extract waveform geometric features, and a decoder generates a sequence of er values to represent er variations. Attention is a mechanism that can dynamically extract and process the relevant information within the data, which processes and integrates the waveform geometric information in the encoder, ensures the causality (timeorder) of the waveform data in the decoder, and transfers information from the encoder to the decoder. TDRTransformer was trained and tested using simulated waveforms where er changes along the waveguides, but soil electrical conductivity (EC) was assumed to be small and stable. The RMSE for er values was within 0.5-1.6 % and the RMSE of er change positions was within 5-8 %. A soil infiltration experiment and a precipitationevaporation experiment illustrated applications of TDR-Transformer to observed waveforms. Consequently, TDR-Transformer is a promising artificial intelligence model to interpret TDR waveforms in soils with nonuniform er, and fine-tuning TDR-Transformer is recommended for specific commercial TDR sensor designs.

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