In recent years, frequent outbreaks of brown tide in the offshore waters of the Bohai Sea, primarily caused by the overgrowth of Aureococcus anophagefferens, the causative species of brown tide, have significantly disrupted the marine ecosystem and caused severe economic losses. Therefore, developing effective methods to detect and predict Aureococcus anophagefferens cell density is essential for brown tide monitoring and control. Fluorescence spectroscopy, a widely used method for detecting algal cell density, offers advantages such as non-destructive testing, high sensitivity, low interference, and simple preprocessing. Specifically, LED-induced fluorescence technology facilitates the rapid acquisition of one-dimensional fluorescence spectra; however, the spectral intensity data points from a single sample are far fewer than those from three-dimensional fluorescence spectra. Recurrence plots can expand spectral data dimensions through phase space reconstruction, increasing the data volume of individual samples. However, the original recurrence plot algorithm is susceptible to the influence of human bias. In fluorescence analysis, nonlinear models are often used to mitigate the inner filter effects. Among these, the broad learning system (BLS) is advantageous due to its simple structure, low computational requirements, and small sample size demands. Nevertheless, the original BLS struggles with direct two-dimensional data input. To address these issues, we propose using unthresholded recurrence plots and an improved two-dimensional BLS (2D-BLS) to predict brown tidal algal cell density.

We focus on Aureococcus anophagefferens as the causative species of brown tides and propose an improved 2D-BLS for predicting brown tide cell density, incorporating unthresholded recurrence plots. LED-induced fluorescence spectroscopy is employed for rapid one-dimensional spectral data collection, and the unthresholded recurrence plot is used to enrich the data volume set by expanding the dimensionality of the spectral data. The Jaccard similarity coefficient is applied to optimize the phase space reconstruction parameters, selecting delay times and embedding dimensions that maximize differences in spectral transformations across varying cell density. The one-dimensional spectral data is transformed using unthresholded recurrence plots, and the corresponding normalized cell density data forms the dataset. Comparisons between traditional recurrence and unthresholded recurrence plots validate the effectiveness of this approach. In addition, a 2D-BLS is introduced, utilizing left and right projection matrices to overcome the original BLS’s inability to handle two-dimensional matrix inputs. The original regularization method is replaced with elastic net regression, yielding the 2D-ENBLS model for predicting brown tide cell density.

Compared to traditional recurrence plots, the unthresholded recurrence plots eliminate the need for subjective threshold selection while preserving the richness of spectral data, thus amplifying the differences between spectral information at various cell density (Fig. 5). A comparison of the weight distributions among Elastic Net, Lasso, and Ridge regression methods shows that the improved 2D-BLS with Elastic Net regression balances the sparsity and stability requirements (Fig. 8). The prediction performance of the 2D-BLS is compared to that of the convolutional neural network-based cascade broad learning system (CNN-BLS). The 2D-BLS model demonstrates improved evaluation metrics, with training and testing times reduced to approximately one-eighteenth and one-fourth of those for the CNN-BLS model, respectively, highlighting the greater efficiency of the 2D-BLS (Table 1). Ablation experiments are conducted to compare the predictive performance of the 2D-ENBLS, the original 2D-BLS, and the Ridge regression-based 2D-L2BLS models. Results show that 2D-ENBLS outperforms other models in terms of R2, RMSE, and MAE, while achieving faster training and testing times of 0.016753 seconds and 0.001553 seconds, respectively (Table 2). Scatter plots of measured versus predicted cell density of Aureococcus anophagefferens across the three models indicate that 2D-ENBLS has the smallest deviation between predicted and actual values. This confirms that the 2D-ENBLS model not only overcomes the limitation of previous models in processing two-dimensional data directly but also significantly enhances performance, validating its overall superiority (Fig. 10).

By addressing the limitations of traditional methods in microalgae cell density prediction, the 2D-ENBLS model introduces an unthresholded recurrence plot to enrich one-dimensional spectral data while avoiding subjective threshold selection. The 2D-BLS, enhanced by left and right projection matrices, enables direct two-dimensional data processing, overcoming the original BLS’s limitations. Replacing the original regularization method with elastic net regression ensures both sparsity and stability. The experimental results indicate that the proposed model achieves average R², RMSE, and MAE values of 0.9994, 0.00594, and 0.00355, respectively, on both the training and test sets. These metrics surpass those of other models and deliver the best performance in terms of time efficiency. This demonstrates that the model not only preserves the richness of the data features but also provides highly accurate and rapid predictions of brown tide algae cell density, offering valuable insights for research involving other one-dimensional spectral data mining and prediction challenges.