Sensitivity matrix update method for electrical resistance tomography based on error-constrained cross fusion residual attention network

Abstract Electrical resistance tomography (ERT) is an imaging technique of conductivity distribution. The image reconstruction algorithm based on the empty field sensitivity matrix is widely used because it provides an approximate solution to the complex ERT inverse problems. However, due to the soft field effect, the sensitivity matrix changes with the media distribution, leading to significant errors in image reconstruction. To address this issue, an error-constrained deep learning scheme for bubble flow, namely cross fusion residual attention network (CFRA-Net) is designed to update the sensitivity matrix during gas–liquid–solid fluidized bed operation. CFRA-Net employs a multi-head self-attention mechanism to enhance bubble features in boundary measurements, a multilevel cross fusion (CF) module to fuse empty field strength and boundary measurement information, and a novel serial-channel residual spatial attention block to boost the feature extraction capability of the model. A weighted loss function is designed to give more weight to the gas phase distribution region. Additionally, this paper establishes a dataset for gas–liquid–solid three-phase flow, considering background field conductivity variations. Validation and reliability of the proposed method are assessed through ablation, comparison, and noise experiments. The experimental results demonstrate that CFRA-Net achieves rapid updates of the sensitivity matrix, high imaging accuracy, and robust noise immunity.