Density Prediction Model for Spectral Data Based on Residual Convolutional Neural Network

Ruiting Li; Faqian Liu; Duo Chen; Hui Li; Jianfei Li; Wenhao Zhang; Jiasheng Ni; Jiancai¹ Leng; Zhenzhen² Zhang

doi:10.3788/LOP251106

Laser & Optoelectronics Progress, Volume. 62, Issue 13, 1306010(2025)

Density Prediction Model for Spectral Data Based on Residual Convolutional Neural Network

Ruiting Li¹, Faqian Liu¹, Duo Chen^1,2、*, Hui Li^2、**, Jianfei Li¹, Wenhao Zhang^1,2, Jiasheng Ni^1,2、***, Jiancai¹ Leng¹, and Zhenzhen² Zhang²

Author Affiliations

¹International School for Optoelectronic Engineering, Qilu University of Technology (Shandong Academy of Science), Jinan 250353, Shandong , China

²Laser Institute,Shandong Academy of Science, Jining 272073, Shandong , China

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Fig. 1. Experimental system architecture and training process based on residual CNN model

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Fig. 2. Density and temperature changes of lead-acid battery during charging and discharging

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Fig. 3. Different density sulfuric acid solutions and physical FP and FBG sensors. (a) Sulfuric acid solution; (b) physical sensor

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Fig. 4. Schematic diagram of the residual convolutional neural network model for analyzing sensor spectral data

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Fig. 5. Training loss curves and corresponding accuracy curves of the model. (a) Loss curves; (b) accuracy curves

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Fig. 6. Histogram of statistical squared errors for spectral data prediction results

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Fig. 7. Comparison of predicted and real values of spectra

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Table 1. Hierarchical structure of residual convolutional neural network

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Table 1. Hierarchical structure of residual convolutional neural network

Layer type	Parameter configuration	Output dimension	Mathematical operation
Input layer		（B， 1， 2034）	Raw spectral intensity vector
Conv layer 1	Conv1D（1→64， kernel is 7， stride is 2， pad is 3）	（B， 64， 1017）	$O = R e L U [B N (W x + b)]$
MaxPool	MaxPool1D（kernel is 3， stride is 2， pad is 1）	（B， 64， 509）	Downsampling with max operation
ResBlock×4	Each block contains sub-layers	（B， 64， 509）	See Table 2 for internal structure
Flatten layer	Flatten（start_dim is 1）	（B， 32576）	Spatial dimension vectorization

Table 2. Internal structure of the residual block

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Table 2. Internal structure of the residual block

Sublayer	Parameter configuration	Dimension
Conv layer A	Conv1D（64→64， kernel is 3， pad is 1）	（B， 64， 509）
BN A	BN（64）	（B， 64， 509）
ReLU A	ReLU	（B， 64， 509）
Conv layer B	Conv1D（64→64， kernel is 3， pad is 1）	（B， 64， 509）
BN B	BN（64）	（B， 64， 509）

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Ruiting Li, Faqian Liu, Duo Chen, Hui Li, Jianfei Li, Wenhao Zhang, Jiasheng Ni, Jiancai¹ Leng, Zhenzhen² Zhang. Density Prediction Model for Spectral Data Based on Residual Convolutional Neural Network[J]. Laser & Optoelectronics Progress, 2025, 62(13): 1306010

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