Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) is widely used for analyzing complex mixed solutions, like glutamic acid fermentation broth and whole blood samples. However, baseline drift problems considerably impede its accuracy in quantitative analysis. These drifts may stem from molecular absorption overlaps, particle scattering, or instrumental errors, posing significant challenges in isolating true spectral signals. Existing baseline correction algorithms, such as asymmetric least squares (AsLS) and its enhanced version, fractional differential asymmetric least squares (FdAsLS), adopt uniform parameters throughout the entire spectrum. Although effective in simpler contexts, this “one-size-fits-all” approach fails to consider the diverse local characteristics of different spectral regions. Consequently, these methods often perform inadequately in dealing with complex spectra where baseline drift varies across bands. To surmount these limitations, we propose a piecewise fractional differential asymmetric least squares (PFdAsLS) algorithm, which incorporates a segmentation strategy. By partitioning the spectrum into segments based on local features and customizing correction parameters for each area, the algorithm improves the flexibility and accuracy of baseline correction. This segmentation strategy, in conjunction with fractional differentiation, empowers PFdAsLS to overcome the deficiencies of traditional methods and adapt to the intricacies of real-world spectral data, furnishing a more reliable and precise solution for spectral analysis.

The PFdAsLS algorithm introduces a segmentation-based baseline correction framework, permitting spectral signals to be divided into multiple sub-regions according to their local characteristics. Each region is then assigned specific fractional differential orders and regularization parameters to suit its unique features. The segmentation strategy applies small regularization parameters and lower fractional orders to regions with sharp signal variations, strengthening the algorithm’s capacity to capture local features. Conversely, for smooth background regions, larger regularization parameters and higher fractional orders are used to maintain baseline smoothness. This adaptability ensures that baseline correction is neither underfitted nor overfitted, even in highly heterogeneous spectra. Fractional differentiation plays a complementary role by providing a flexible means to control smoothness levels across the spectrum. When combined with the segmentation strategy, it boosts the ability of PFdAsLS to fit baselines. To evaluate the algorithm, experiments are conducted on both simulated and real datasets. In the simulated dataset, the spectral baseline is constructed using a three-segment function combined with peak signals and random noise to simulate real-world complexity. The root mean square error (RMSE) is employed as the primary metric to assess baseline correction performance. For real spectral data, ATR-FTIR is employed to collect data for two datasets: γ-PGA fermentation broth, aiming at glucose and sodium glutamate concentrations, and whole blood samples, targeting blood glucose concentration. Model prediction error (RMSEP) is utilized to evaluate the performance of baseline correction and its effect on quantitative analysis. The effectiveness of PFdAsLS is then compared with traditional AsLS and FdAsLS methods, enabling a comprehensive evaluation of its advantages.

In the simulated experiments, the baseline correction results demonstrate the evident advantages of PFdAsLS over traditional methods. The RMSE of FdAsLS is 3.739, while PFdAsLS reduces it to 1.381 via the segmentation strategy, achieving a 63.07% improvement. This significant reduction reflects the influence of the segmentation strategy, which enables the algorithm to adaptively handle local baseline variations. The segmented parameter configuration is especially effective in regions with sharp signal changes, substantially enhancing overall baseline fitting accuracy. For the γ-PGA fermentation broth dataset, the baseline correction results reveal that FdAsLS achieves RMSEP values of 2.356 for glucose and 0.873 for sodium glutamate. When PFdAsLS is applied, these values are further decreased to 2.086 and 0.792, corresponding to improvements of 12.94% and 9.28%, respectively. The segmentation strategy successfully tailors the baseline correction to each spectral region, significantly enhancing model accuracy. Additionally, PFdAsLS effectively eliminates negative absorption peaks, such as water-related peaks, which are retained in spectra corrected by FdAsLS. This reduction in interference further contributes to improved model prediction performance, as shown in the spectral and baseline fitting results. For the whole blood dataset, FdAsLS attains an RMSEP of 1.418 for blood glucose concentration. PFdAsLS further reduces the RMSEP to 1.175, signifying an improvement of 17.14%. The segmentation-based approach allows PFdAsLS to account for varying baseline characteristics across spectral regions, leading to more precise corrections. Furthermore, PFdAsLS effectively removes water-related interference peaks, which are a major source of error in blood spectra, thereby enhancing spectral quality and improving quantitative model accuracy. Overall, these results emphasize the superiority of PFdAsLS in handling complex spectral data. Its segmentation strategy, combined with fractional differentiation, enables precise baseline correction across diverse regions of the spectrum, resulting in enhanced signal quality and improved quantitative analysis performance.

Compared with traditional methods, PFdAsLS overcomes the limitations of applying uniform global parameters by employing a segmentation strategy. This enables it to adapt flexibly to the characteristics of different spectral regions. Combined with the flexibility of fractional differentiation, the algorithm significantly improves the precision and robustness of baseline correction, effectively resolving the baseline drift issues in spectra of complex mixed solutions obtained by ATR-FTIR.