In the biopharmaceutical industry, the production of monoclonal antibodies (mAbs) relies heavily on the optimization and real-time monitoring of cell culture processes. This study assesses the effectiveness of online machine learning (OML) models for the real-time monitoring of nutrient and metabolite concentrations, such as glucose, lactate, and ammonium, during the cell cultivation process using Raman spectroscopy as input data. The research addresses the challenge of limited data inherent in cell culture processes, particularly when transferring learned information to new bioreactor runs with different cell lines and media compositions. Traditional pretrained machine learning models often fail to generalize their learned information in such context. Our research demonstrates that OML models can dynamically adapt to the evolving conditions of cell culture processes, providing accurate and timely updates on critical nutrient and metabolite concentrations. We conducted a series of experiments comparing the performance of OML models against pretrained models in monitoring cell culture processes. The findings indicate that OML models exhibit superior performance in capturing the dynamic changes of nutrient and metabolite concentrations during cell cultivation. In contrast, pretrained models exhibit substantial performance degradation when applied to a completely new bioreactor run, highlighting the limitations of static learning approaches in handling the complex, dynamic nature of cell cultures. This study emphasizes the potential of OML in enhancing the robustness and efficiency of real-time process monitoring in mAb production, paving the way for more adaptive and resilient biomanufacturing processes.