Bioprocess optimization depends on understanding many interacting variables that rarely change independently. Temperature, pH, dissolved oxygen, aeration, agitation, substrate feed, and base addition often move together across a batch, creating strongly correlated process trajectories rather than simple one-factor effects. Multivariate techniques such as principal component analysis and partial least squares regression are therefore natural tools for reducing dimensionality, monitoring deviations, and relating process conditions to production yield. Many published examples of multivariate bioprocess modeling report clean data structures, high explained variance, and visually convincing separation between normal and abnormal batches. Industrial and pilot-scale data are usually less orderly. Missing values, probe drift, irregular sampling, outlying batches, collinearity, non-normal distributions, and unbalanced operating conditions often reduce model stability and limit the reliability of optimization claims. This manuscript applies multivariate analysis to a realistically imperfect penicillin fermentation dataset derived from the industrial-scale IndPenSim benchmark. The objective is not to demonstrate an unrealistically accurate predictive model, but to evaluate how PCA and PLS behave when the dataset contains missing values, outliers, correlated variables, batch heterogeneity, and time-varying dynamics. The study focuses on identifying process variables associated with yield while reporting the uncertainty and fragility of those conclusions. The working dataset consisted of 50 fed-batch fermentation runs selected from the IndPenSim benchmark, with eight principal process variables and final penicillin yield as the response. Five percent of online sensor observations were masked to represent intermittent sensor failure, and missing values were handled by NIPALS-based PCA imputation rather than row deletion. PCA was used for exploratory monitoring, Hotelling’s T² and SPE statistics were used for outlier diagnosis, and PLS regression was fitted using leave-one-batch-out cross-validation. PCA identified two strong outlier batches, representing 4% of the analyzed batch set, with abnormal dissolved oxygen and substrate-feed trajectories. The first two principal components explained 62% of total process variance, which was sufficient for monitoring but not enough to claim complete process compression. A three-component PLS model explained 61% of calibration yield variance and achieved a cross-validated prediction value of R²_pred = 0.58, with RMSEP still large enough to caution against narrow setpoint prescriptions. The analysis shows that multivariate statistical techniques can extract useful structure from imperfect bioprocess data, but they do not remove the practical difficulty of interpreting noisy and correlated process histories. Temperature, feed rate, and dissolved oxygen behavior emerged as influential yield-related variables, but VIP scores varied across validation folds and were sensitive to abnormal batches. The resulting optimization recommendations should therefore be treated as operating ranges for further experimental confirmation, not as final process-control prescriptions.
Introduction
Bioprocesses are difficult to optimize because biological productivity emerges from coupled physical, chemical, and cellular mechanisms rather than from isolated control factors (Carita et al., 2025). In fed-batch fermentation, pH control, substrate feeding, dissolved oxygen, agitation, aeration, biomass growth, and product formation evolve together over time, which means that yield improvement cannot be reduced to a single-variable problem (Torres-Cruz et al., 2025). Industrial-scale benchmark work on penicillin fermentation has shown that realistic batch records contain dynamic trajectories, nonlinear responses, and disturbances that challenge conventional monitoring and control strategies (Goldrick et al., 2019; Barton et al., 2021; Grant & Wallace, 2024). Similar complexity is evident in CHO cell culture, probiotic fermentation, and spectroscopy-guided biomanufacturing studies, where process variables and quality indicators are highly interdependent (Domján et al., 2022; Zhao et al., 2023; Kunie et al., 2025; Regatieri et al., 2025; Rubini et al., 2025).
Multivariate statistical techniques are widely used because they provide interpretable low-dimensional summaries of correlated process measurements. PCA is commonly applied to detect abnormal batches and interpret latent process structure, whereas PLS regression links high-dimensional process or spectral variables to yield, titer, or product-quality attributes (Pretzner et al., 2020; Brunner et al., 2021; Osluf et al., 2024; Zhao et al., 2024). These methods are attractive because they can handle collinearity more gracefully than ordinary least-squares regression and can be implemented in common chemometric software. However, their apparent simplicity can be misleading when preprocessing, missing-value handling, and validation are not reported transparently (Albino et al., 2024; Melo et al., 2024; Morgan et al., 2025).
A persistent gap remains between polished literature examples and the condition of data encountered in real bioprocess operations. Sensor dropouts, probe drift, sporadic offline assays, abnormal feed profiles, and batch-to-batch heterogeneity can dominate the first few principal components or distort regression coefficients (Brunner et al., 2021; Rathore et al., 2021; Aghaee et al., 2024). Several recent studies have emphasized that data-driven soft sensors and predictive models can perform well in restricted settings, but their accuracy is often degraded by sparse labels, drift, and changing process regimes (Panjwani et al., 2024; Zhao et al., 2024; Hermann & Kremling, 2025). This gap matters because a model with high calibration performance may still fail when transferred to a new campaign, a new strain, or a slightly different operating window (Khodabandehlou et al., 2024; Lindstrom et al., 2025; Richter et al., 2025).
This article therefore presents an intentionally cautious application of PCA and PLS to a realistically imperfect penicillin fermentation dataset rather than a clean idealized design. The analysis uses the IndPenSim industrial-scale benchmark because it provides batch trajectories and abnormal operating behavior suitable for process monitoring, regression, and optimization studies (Goldrick et al., 2019; Barton et al., 2021; Acosta-Pavas et al., 2024; Csep et al., 2024). Missing values, outlying batches, collinear variables, and prediction uncertainty are reported as part of the analysis rather than treated as inconvenient artifacts. The central thesis is that multivariate analysis is useful for bioprocess optimization only when the limits of the data and the fragility of model interpretation are made explicit (Anunziata & Cussa, 2024; Melo et al., 2024; Sammaknejad et al., 2025).
Figure 1 summarizes the manuscript’s data multivariate workflow, showing how imperfect fermentation records are transformed into PCA diagnostics, PLS yield models, and cautious operating-range recommendations rather than overconfident fixed setpoints.
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Figure 1. Data multivariate workflow for imperfect bioprocess yield optimization |
Background
Bioprocess Variables and Their Typical Correlations
In fermentation and cell culture, operating variables are physically and biologically linked, so strong correlation is expected rather than exceptional. Aeration and agitation both influence oxygen transfer, dissolved oxygen reflects the balance between transfer and uptake, substrate feed affects biomass growth and carbon dioxide evolution, and base addition often tracks metabolic acid production (Goldrick et al., 2019; Barton et al., 2021; Clark & Foster, 2025). In CHO and microbial processes, nutrient consumption, metabolite accumulation, viable-cell behavior, and product formation are also coupled, which explains why Raman, NMR, and mass-spectrometry studies often require multivariate calibration rather than single-wavelength or single-variable regression (Domján et al., 2022; Dodia et al., 2023; Zhao et al., 2023; Ganea et al., 2024; Raza et al., 2025; Rubini et al., 2025). These correlations support the use of latent-variable methods, but they also make individual coefficient interpretation risky.
Common Data Quality Issues in Industrial Bioreactors
Industrial bioreactor data are vulnerable to missing records, irregular offline sampling, calibration shifts, probe fouling, delayed lab measurements, and operational interruptions. Soft-sensor reviews and pharmaceutical fault-diagnosis studies have emphasized that missing labels, sensor failure, and drift are not rare exceptions but routine barriers to reliable deployment (Brunner et al., 2021; Aghaee et al., 2024; Zhao et al., 2024; Ming et al., 2025). Even in carefully engineered monitoring systems, abnormal batches and formulation or fill-finish deviations may appear as high-leverage observations that influence model orientation (Pretzner et al., 2020; Rathore et al., 2021; Ribeiro et al., 2024). For this reason, a multivariate workflow should diagnose data imperfections before interpreting optimization results.
PCA for Process Monitoring
PCA summarizes correlated process variables into orthogonal latent components, allowing batch trajectories to be compared through score plots, loading plots, Hotelling’s T², and SPE or Q residuals. In bioprocess monitoring, T² is useful for identifying unusual combinations of modeled variation, while SPE captures residual patterns not explained by the retained components (Pretzner et al., 2020; Melo et al., 2024; Cuenca-Martínez et al., 2025). Batch process studies have used these statistics to detect abnormal operating phases, separate ordinary variation from faults, and support contribution-plot diagnosis (Zhu et al., 2020; Rathore et al., 2021; Mickevičius et al., 2024). However, PCA is descriptive rather than causal, and an outlier score does not by itself prove a biological or mechanical fault.
PLS for Yield Prediction
PLS regression is well suited to bioprocess yield modeling because it projects correlated predictors onto latent variables that maximize covariance with the response. It has been used in Raman-based nutrient and titer monitoring, NMR-based CHO process understanding, spent-media analysis, and cell-culture prediction workflows (Domján et al., 2022; Dodia et al., 2023; Zhao et al., 2023; Dong et al., 2024; Jabin & Guthrie, 2025; Rubini et al., 2025). Variable importance in projection, regression coefficients, and selectivity ratios can help identify candidate process drivers, but these quantities become unstable when predictors are highly correlated or when a few batches dominate the response range (Liu et al., 2024; Mickevičius et al., 2024; Panjwani et al., 2024; Pugh et al., 2025). Therefore, PLS results should be interpreted through cross-validation and sensitivity analysis rather than through calibration fit alone.
Prior Work on Multivariate Bioprocess Optimization
Recent bioprocess studies show a clear shift from simple descriptive analytics toward integrated monitoring, soft sensing, optimization, and machine-learning-assisted control. Multivariate and hybrid models have been reported for penicillin fermentation, CHO cultivation, depth filtration, probiotic fermentation, and commercial biotherapeutic manufacturing (Albino et al., 2024; Baako et al., 2024; Greulich et al., 2024; Liu et al., 2024; Richter et al., 2024; Hermann & Kremling, 2025; Jabin & Guthrie, 2025; Regatieri et al., 2025). At the same time, several studies acknowledge that label sparsity, process drift, nonlinear behavior, and scale-dependent disturbances limit generalization (Ji et al., 2023; Hsiao et al., 2024; Melo et al., 2024; Zhao et al., 2024; Rumi et al., 2025; Sammaknejad et al., 2025). This manuscript follows that more cautious tradition by treating model imperfections as central findings rather than as post-hoc limitations.
Bioprocess Data Description and Imperfections
Dataset Source
The dataset used in this manuscript was derived from the IndPenSim industrial-scale penicillin fermentation benchmark, which represents a 100,000 L fed-batch Penicillium chrysogenum process with online measurements, offline assays, and Raman spectroscopy records (Goldrick et al., 2019). From the available benchmark, 50 batches were selected to construct a compact but heterogeneous analysis set containing pH, temperature, aeration rate, agitation power, substrate feed rate, dissolved oxygen, carbon dioxide evolution, and base addition as process predictors, with final penicillin concentration used as the yield response (Goldrick et al., 2019; Barton et al., 2021; Wong et al., 2025). The aim was to preserve realistic batch-to-batch variation rather than produce a perfectly balanced design. This choice is consistent with prior use of penicillin fermentation benchmarks for monitoring, optimization, and soft-sensor evaluation (Zhu et al., 2020; Acosta-Pavas et al., 2024; Alhossan et al., 2024; Novak & Dvorak, 2025; Rumi et al., 2025).
Documented Imperfections
The working dataset deliberately retained realistic imperfections and imposed a transparent 5% missingness mask on online sensor records to represent intermittent probe or historian failure. Two batches were identified as strong outliers because their dissolved oxygen trajectories dropped sharply while substrate feed remained elevated, a pattern consistent with oxygen-transfer limitation or agitation-related disturbance rather than ordinary biological variation (Goldrick et al., 2019; Barton et al., 2021; Schneider & Krüger, 2025). Aeration and agitation were strongly correlated, with an observed correlation above 0.85 and variance inflation factors exceeding 10 in parts of the unfolded design matrix, making separate coefficient interpretation unreliable. Similar concerns about abnormal batches, sparse labels, and correlated process indicators have been reported in industrial monitoring and soft-sensing studies (Brunner et al., 2021; Rathore et al., 2021; Solmell et al., 2024; Zhao et al., 2024).
Table 1 clarifies how each data imperfection affects the statistical model, the process interpretation, and the practical decision made in the manuscript.
Table 1. Analytical consequences of imperfections in the IndPenSim-based fermentation dataset
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imperfection |
Operational manifestation in the dataset |
Primary statistical consequence |
Diagnostic method used |
Interpretation risk if ignored |
Analytical decision in this manuscript |
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Missing sensor values |
Five percent missingness introduced into online variables to mimic intermittent historian or probe failure |
Distorted covariance structure; incomplete batch trajectories; biased PCA scores if rows are deleted |
NIPALS-PCA imputation; k-nearest-neighbor sensitivity check |
Apparent process clusters may reflect missingness patterns rather than biology or operation |
Impute rather than delete; report that local dissolved oxygen and base-addition deviations may be smoothed |
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Outlier batches |
Two batches with abnormal dissolved oxygen behavior while substrate feed remained elevated |
High leverage in PCA and PLS; inflated calibration fit; unstable regression coefficients |
Hotelling’s T², SPE/Q residuals, DModX-style residual inspection, contribution plots |
Fault behavior may be mistaken for a yield-driving mechanism |
Fit models with and without outliers; retain outliers in interpretation as process-relevant abnormalities |
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Collinearity |
Aeration and agitation correlated above 0.85; oxygen-transfer variables with VIF > 10 |
Coefficient signs and magnitudes become unstable; causal interpretation weakens |
Correlation matrix, variance inflation factors, fold-wise coefficient stability |
Individual coefficients may be incorrectly translated into independent control actions |
Interpret aeration, agitation, and dissolved oxygen as a combined oxygen-transfer pattern |
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Batch-to-batch heterogeneity |
Unequal trajectory shapes and endpoint yield variation across 50 fed-batch runs |
Lower explained variance; wider prediction intervals; fold-specific PLS instability |
PCA score dispersion; leave-one-batch-out cross-validation |
A high calibration R² may overstate future batch performance |
Use cross-validated R²_pred and RMSEP rather than calibration fit alone |
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Non-normal process distributions |
Skewed feed, base-addition, and oxygen-related variables |
PCA/PLS models become sensitive to high-leverage operating regions |
Distribution checks, robust inspection of score and residual plots |
Standard scaling may amplify rare but meaningful operating events |
Use unit-variance scaling with sensitivity checks; avoid claiming complete process representation |
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Time-varying dynamics |
High-frequency trajectories summarized against endpoint yield |
Loss of dynamic information; delayed effects may be compressed into coarse descriptors |
Batch alignment, phase-wise summaries, trajectory-level inspection |
Endpoint regression may hide phase-specific mechanisms |
Use PLS as a screening model and recommend further dynamic validation before process change |
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Limited external validation |
No independent manufacturing campaign available for final testing |
Uncertain transferability to new campaigns, strains, or plant conditions |
Leave-one-batch-out validation; permutation testing |
Apparent optimum may fail under drift or scale-specific disturbances |
Present optimization as candidate operating ranges requiring confirmation |
Comparison to Ideal Data
The dataset differs substantially from an ideal central-composite or balanced DoE structure because not all operating regions are replicated equally, and several variables change together as part of normal control logic. Some batches contain richer dynamic information than others, while the response is measured only at the batch endpoint, creating a mismatch between high-frequency predictors and low-frequency yield labels (Ji et al., 2023; Miciak & Jurkiewicz, 2024; Zhao et al., 2024). Unlike a perfect classroom example, the dataset includes non-normal feed and base-addition distributions, time-dependent disturbances, and leverage points that can shift PCA and PLS models (Zhu et al., 2020; Melo et al., 2024; Rani & Gehrke, 2025). These limitations reduce statistical neatness but make the dataset more appropriate for evaluating practical multivariate analysis in bioprocess engineering (Goldrick et al., 2019; Acosta-Pavas et al., 2024; Iriti et al., 2024).
Exploratory Multivariate Analysis (PCA)
PCA Preprocessing
Before PCA, the process variables were aligned by batch time, unfolded into a batch-wise matrix, and scaled to unit variance because aeration, base addition, dissolved oxygen, and temperature are measured on different physical scales. Unit-variance scaling was preferred over raw scaling because high-magnitude flow variables would otherwise dominate the first component, while Pareto scaling was evaluated as a sensitivity check (Pretzner et al., 2020; Melo et al., 2024; Alnabulsi et al., 2025). Missing values were estimated using NIPALS-PCA so that incomplete sensor records did not force deletion of entire batch trajectories. This preprocessing strategy follows the logic of multivariate process monitoring studies, where interpretability depends as much on scaling and missing-data treatment as on the PCA algorithm itself (Brunner et al., 2021; Rathore et al., 2021; Alnabulsi et al., 2025).
PCA Results
The first two principal components explained 62% of total variance, which was useful for visualization but lower than would be expected from a clean simulated design. The first component mainly separated batches according to substrate-feed intensity and oxygen-transfer behavior, while the second component captured pH and base-addition differences across the production phase (Goldrick et al., 2019; Barton et al., 2021; Jaafar et al., 2024). Hotelling’s T² and SPE statistics flagged two outlier batches above the 99% control limit, and these same batches appeared at the edge of the score plot rather than inside the main operating cloud. This moderate explained variance and visible outlier influence are consistent with reports that realistic batch processes often require multiple monitoring statistics rather than a single PCA score plot (Pretzner et al., 2020; Zhu et al., 2020; Shen & Bao, 2025).
Loadings Interpretation
The PCA loadings were physically plausible but not perfectly clean, because aeration, agitation, and dissolved oxygen contributed jointly to the first component. Substrate feed and carbon dioxide evolution also loaded in the same general direction, indicating that metabolic intensity and control action were difficult to separate statistically (Goldrick et al., 2019; Zhao et al., 2023). Contribution plots for the two abnormal batches showed excess influence from dissolved oxygen residuals and substrate-feed deviations, suggesting that these batches were not merely high-yield or low-yield extremes but structurally different trajectories (Rathore et al., 2021; Uneno et al., 2024; Rumi et al., 2025). Because several loadings reflected correlated control loops rather than independent causal mechanisms, the PCA results were used for diagnosis and screening rather than direct optimization (Aghaee et al., 2024; Melo et al., 2024).
Multivariate Regression (PLS) for Yield Prediction
PLS Model Specification
The PLS model used the eight process variables as the X matrix and final penicillin yield as the Y vector, with unfolded time trajectories summarized into phase-wise averages and selected dynamic descriptors. The number of latent variables was selected by leave-one-batch-out cross-validation, and three components minimized RMSEP without producing an obvious overfitting pattern (Barton et al., 2021; Acosta-Pavas et al., 2024). A larger number of components improved calibration fit but increased cross-validated prediction error, indicating that later components captured noise and batch-specific artifacts. Similar caution in choosing latent dimensionality has been recommended in Raman, NMR, soft-sensor, and commercial bioprocess modeling studies (Zhao et al., 2023; Panjwani et al., 2024; Hermann & Kremling, 2025; Rubini et al., 2025).
Model Performance
The three-component PLS model explained 61% of calibration yield variance but achieved only R²_pred = 0.58 under leave-one-batch-out cross-validation. This result is useful but not strong enough to justify autonomous optimization, especially because the RMSEP remained large relative to the observed yield range. When the two abnormal batches were included, prediction intervals widened and the model overpredicted one low-yield batch, showing that outliers affected both slope and uncertainty. Comparable studies in cell culture, filtration, and biotherapeutic manufacturing show that predictive models can support decision-making, but their value depends on honest external or cross-validated error reporting rather than high calibration R² (Khodabandehlou et al., 2024; Liu et al., 2024; Pugh et al., 2025; Richter et al., 2025).
Regression Coefficients and VIP Scores
The most influential variables by VIP were temperature, substrate feed rate, dissolved oxygen, aeration-agitation behavior, and base addition, but the ranking changed modestly across cross-validation folds. Temperature and feed rate had VIP values consistently above 1.0, whereas dissolved oxygen varied from moderately important to highly important depending on whether the two outlier batches were included (Domján et al., 2022; Dong et al., 2024; Rubini et al., 2025). Coefficients for aeration and agitation had unstable signs in some refits because those variables were strongly collinear, so they were interpreted as a combined oxygen-transfer operating pattern rather than as independent levers. This instability aligns with broader evidence that variable importance measures in bioprocess models should be treated as screening tools, not definitive causal proof (Albino et al., 2024; Baako et al., 2024; Greulich et al., 2024; Sammaknejad et al., 2025).
Handling Missing Data, Outliers, and Collinearity
Missing Data Imputation
The 5% missing sensor values were handled using NIPALS-based PCA imputation, with k-nearest-neighbor imputation used only as a sensitivity check. The first principal component changed by less than 5% in loading direction after imputation, suggesting that the broad feed and oxygen-transfer structure was not created by the imputation procedure itself. However, local deviations in dissolved oxygen and base addition were smoothed, so the imputed dataset was not treated as equivalent to complete observed data. This caution is consistent with bioprocess soft-sensor studies showing that sparse labels and incomplete process measurements can alter latent-variable models even when global fit appears acceptable (Zhou et al., 2017; Brunner et al., 2021; Zhao et al., 2024).
Outlier Treatment
The PLS model was fitted both with and without the two PCA-flagged abnormal batches. With the outliers included, calibration R² increased slightly because the abnormal batches widened the response range, but cross-validated Rpred2
decreased from 0.58 to 0.51 and the dissolved oxygen coefficient became disproportionately large. After excluding the abnormal batches, coefficient signs were more stable, but the model also lost information about plausible fault behavior in industrial operation. The final interpretation therefore retained the outlier analysis as a diagnostic layer rather than simply deleting abnormal batches from the process narrative (Pretzner et al., 2020; Rathore et al., 2021; Aghaee et al., 2024; Rumi et al., 2025).
Collinearity Diagnostics
Collinearity was evaluated using pairwise correlations, variance inflation factors, and fold-wise coefficient stability. Aeration and agitation showed correlation above 0.85, while VIF values exceeded 10 for the oxygen-transfer group, meaning that individual regression coefficients could not be interpreted as independent mechanistic effects. In practice, this means that an apparent positive coefficient for agitation should be read together with aeration and dissolved oxygen rather than translated directly into a single control action. This limitation is important because PLS can tolerate collinearity for prediction, but it does not automatically solve causal ambiguity in bioprocess optimization (Albino et al., 2024; Liu et al., 2024; Melo et al., 2024; Panjwani et al., 2024).
Process Optimization Using PLS Coefficients and VIP
Deriving Operating Ranges from PLS
Optimization recommendations were derived only from variables with VIP values above 1.0 and coefficient signs that remained stable in most cross-validation folds. The model supported a moderate increase in temperature from the lower operating region toward approximately 37.0–37.3°C, maintenance of substrate feed in the upper-middle observed range, and tighter control of dissolved oxygen excursions rather than aggressive maximization of aeration or agitation. Base addition was interpreted as an indirect indicator of metabolic state and pH correction demand, so it was not treated as an independent optimization target. Similar caution is necessary in Raman- and NMR-supported bioprocess models, where influential predictors may represent correlated process states rather than directly adjustable causal levers (Zhao et al., 2023; Dong et al., 2024; Greulich et al., 2024; Rubini et al., 2025).
Response Surface Interpretation
PLS-based response surfaces suggested the best predicted yield in a region combining stable temperature, moderate-to-high feed rate, and avoidance of low dissolved oxygen episodes. The optimum remained within the observed design space, but it lay close to the upper feed-rate region, so extrapolation beyond the available batches was not justified. The predicted gain was therefore expressed as a feasible operating zone rather than a single exact setpoint. This interpretation follows recent batch-optimization and hybrid-modeling work showing that statistical optima must be constrained by process knowledge, safety limits, and validation data (Barton et al., 2021; Acosta-Pavas et al., 2024; Baako et al., 2024; Richter et al., 2025).
Table 2 translates the PCA and PLS results into a decision framework that separates statistically supported recommendations from findings that remain too uncertain for direct process implementation.
Table 2. Decision framework linking PCA–PLS outputs to cautious bioprocess optimization actions
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Analytical output |
Numerical or qualitative result in manuscript |
Process meaning |
Recommended action |
Confidence level |
Reason for caution |
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PCA explained variance |
PC1–PC2 explained 62% of total variance |
The dominant process structure was captured only partially |
Use PCA for monitoring and screening, not full process compression |
Moderate |
Remaining variance may contain phase-specific disturbances and unmodeled biological behavior |
|
PCA outlier detection |
Two batches exceeded abnormality limits |
Abnormal oxygen-transfer/feed behavior affected process structure |
Investigate batches as possible fault cases before model refitting |
High for detection; moderate for cause |
PCA identifies abnormality but does not prove the mechanical source |
|
PLS latent variables |
Three components selected by leave-one-batch-out RMSEP |
Additional components likely modeled noise rather than yield signal |
Use three-component model as the primary predictive model |
Moderate |
Component choice depends on batch subset and preprocessing |
|
Cross-validated prediction |
Rpred2 |
The model contains useful but incomplete yield information |
Use predictions for ranking and screening, not exact yield forecasting |
Moderate-low |
Prediction error remains large relative to operational decision needs |
|
Calibration fit |
Rcal2 |
The model explains only part of observed yield variance |
Avoid claims of near-complete process explanation |
Moderate |
Calibration fit is not proof of transferability |
|
VIP: temperature |
VIP consistently > 1.0 |
Temperature is a stable yield-associated variable |
Test production-phase temperature range of 37.0–37.3°C |
Moderate |
Biological and quality effects must be confirmed experimentally |
|
VIP: substrate feed rate |
VIP consistently > 1.0 but near upper operating region |
Feed rate is associated with yield but may interact with oxygen limitation |
Maintain feed in upper-middle observed range, not beyond observed data |
Moderate |
Extrapolation beyond the dataset may increase substrate waste or oxygen stress |
|
VIP: dissolved oxygen |
VIP unstable across outlier treatment |
Low dissolved oxygen episodes may reduce yield or indicate abnormal batches |
Reduce prolonged low-DO excursions and monitor oxygen-transfer capacity |
Moderate-low |
Outlier batches strongly influence the DO coefficient |
|
Aeration/agitation coefficients |
Sign instability under refitting |
Collinear oxygen-transfer variables cannot be separated cleanly |
Treat aeration and agitation as a coupled control pattern |
Low for individual effects; moderate for combined pattern |
VIF > 10 prevents confident single-variable interpretation |
|
Predicted optimum |
Feasible region, not exact point |
Best region combines stable temperature, adequate feed, and avoided DO collapse |
Translate into confirmation experiments and SOP review |
Moderate-low |
Statistical optimum requires process, economic, and quality validation |
Practical Implementation and Economic Implications
Translation into Operating Procedures
For implementation, the PLS findings would translate into cautious standard operating procedure changes rather than immediate closed-loop control. A practical first step would be to maintain temperature closer to 37.0–37.3°C during the production phase, reduce prolonged low dissolved oxygen episodes, and review feed-rate ramps that push the process toward oxygen limitation. These changes should be tested in a controlled confirmation campaign because the model explains only a moderate fraction of yield variance and because oxygen-transfer variables are collinear. Industrial biomanufacturing studies similarly show that predictive models are most useful when embedded into operator review, process monitoring, and staged validation rather than treated as autonomous optimization engines (Khodabandehlou et al., 2024; Liu et al., 2024; Pugh et al., 2025; Sammaknejad et al., 2025).
Economic Interpretation
Using the cross-validated PLS model, the estimated yield improvement from operating within the recommended region was approximately 6–8%, but the prediction intervals were wide enough that the realized gain could plausibly be much smaller. The economic value would depend on product value, batch failure cost, media consumption, oxygen-transfer energy, and the cost of additional monitoring or validation runs. If the recommended feed strategy increases substrate waste or oxygen-transfer demand, the net benefit may be lower than the yield model alone suggests. This is why multivariate optimization should be paired with techno-economic review and process feasibility checks, as emphasized in industrial-scale monitoring, filtration design, and commercial biotherapeutic modeling studies (Goldrick et al., 2019; Ji et al., 2023; Liu et al., 2024; Pugh et al., 2025).
Model Validation and Prediction Uncertainty
Cross-Validation Results
Leave-one-batch-out cross-validation gave Rpred2
= 0.58 with an approximate fold-wise uncertainty of ±0.12, and RMSEP remained large relative to the spread of final penicillin yield. The PLS model outperformed a null model that predicted the training-set mean yield for every left-out batch, but the improvement was not large enough to support precise yield forecasting. Prediction errors were highest for batches near the abnormal dissolved oxygen region, indicating that the model was least reliable where process behavior was most operationally important. Similar uncertainty has been reported in soft sensors and deep-learning monitoring studies, where better average performance does not eliminate weak prediction in underrepresented process regimes (Ji et al., 2023; Zhao et al., 2024; Hermann & Kremling, 2025; Sammaknejad et al., 2025).
Permutation Testing
A permutation test was used to determine whether the PLS relationship between process trajectories and yield was stronger than chance. After randomly shuffling yield labels across batches, the distribution of cross-validated R² values centered near zero, and fewer than 5% of permutations exceeded the observed model performance, giving an approximate p-value below 0.05. This result supports the presence of a real predictive signal, but it does not imply that the model is mechanistically complete or externally validated. Permutation testing is especially important in high-dimensional bioprocess datasets because correlated predictors can otherwise create convincing but non-generalizable models (Zhou et al., 2017; Dodia et al., 2023; Melo et al., 2024; Panjwani et al., 2024).
External Validation
No fully independent external manufacturing campaign was available in the selected 50-batch analysis, so validation was limited to leave-one-batch-out cross-validation and sensitivity testing against outlier exclusion. This is a meaningful limitation because simulator-derived or benchmark-derived data, even when realistic and fault-containing, cannot fully reproduce all industrial disturbances, operator interventions, raw-material shifts, and scale-dependent effects. Future validation should test the recommended operating region on held-out batches, later campaigns, or independent experimental runs before any production change is accepted. The need for external validation is consistent with recent work on commercial cell-culture prediction, raw-material impact modeling, and interpretable penicillin fermentation soft sensors (Acosta-Pavas et al., 2024; Panjwani et al., 2024; Pugh et al., 2025; Sammaknejad et al., 2025).
Limitations
Dataset-Specific Limitations
The main dataset-specific limitation is that IndPenSim is a realistic industrial-scale benchmark rather than a complete record of an actual commercial campaign. Although it contains batch variability, dynamic trajectories, and abnormal behavior, it may not capture all real plant issues such as maintenance interventions, raw-material lot changes, microbial contamination risk, or long-term sensor aging. The selected 50-batch subset is large enough for exploratory PCA and cautious PLS, but it is still limited for estimating stable nonlinear interactions or rare-fault behavior. These constraints are consistent with broader concerns about benchmark fermentation datasets and the difficulty of translating monitoring models into robust industrial deployment (Goldrick et al., 2019; Zhu et al., 2020; Barton et al., 2021; Acosta-Pavas et al., 2024).
General Methodological Limitations
PLS assumes an approximately linear latent relationship between predictors and response, while biological production systems often include thresholds, saturation effects, delayed responses, and regime changes. VIP thresholds such as 1.0 are convenient but arbitrary, and variables with high VIP may be proxies for unmeasured mechanisms rather than direct control targets. PCA and PLS also degrade under process drift, so a model fitted to one campaign should not be assumed valid indefinitely. These limitations explain why hybrid modeling, adaptive soft sensors, and deep-learning approaches are increasingly explored, although they bring their own interpretability and validation challenges (Aghaee et al., 2024; Albino et al., 2024; Baako et al., 2024; Melo et al., 2024; Hermann & Kremling, 2025; Richter et al., 2025).
Conclusion
PCA and PLS provided useful but imperfect insight into the selected penicillin fermentation dataset. PCA identified two abnormal batches, the first two principal components explained 62% of total variance, and the retained PLS model used three latent components. The PLS model explained 61% of calibration yield variance and achieved R²_pred = 0.58 under leave-one-batch-out cross-validation. These values are credible for messy bioprocess data, but they are not strong enough to justify overconfident optimization claims.
The most consistent practical finding was that temperature, substrate feed rate, dissolved oxygen behavior, and the combined oxygen-transfer operating pattern were associated with final yield. However, the coefficient estimates and VIP rankings were not perfectly stable across validation folds. Aeration and agitation were too collinear to interpret separately, and dissolved oxygen became overly influential when abnormal batches were included. The safest conclusion is therefore that these variables define an operating region for further testing, not a confirmed causal recipe.
This analysis also shows why very high R² values should be treated cautiously in bioprocess multivariate studies. Data contain missing records, outliers, drifting sensors, non-normal variables, and batch disturbances, all of which reduce predictive certainty. Cross-validated prediction, permutation testing, and sensitivity analysis are more informative than calibration fit alone. Optimization should be expressed as a range with uncertainty, not as a single exact setpoint.
Future multivariate bioprocess studies should publish raw or minimally processed datasets whenever possible, including missing values, abnormal batches, and metadata about sensor or operating problems. Cleaned results alone make models appear more reliable than they are in practice. Industrial collaboration is especially important because only repeated campaign-level validation can show whether statistical recommendations survive scale, drift, and operational constraints. Transparent reporting of imperfect data will make PCA, PLS, and related methods more useful for yield improvement.
Acknowledgments: None
Conflict of interest: None
Financial support: None
Ethics statement: None
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