The ultimate guide to functional data analysis for scientists and engineers
Applying functional data analysis
How does functional data analysis (FDA) work in practice?
Once you’ve prepared your data and explored its main patterns with functional principal component analysis (FPCA), the next question is simple: what can you do with these insights? FDA becomes valuable when it helps you solve scientific or engineering problems. It gives you a structured way to see what influences your curves, how they behave under new conditions, or how closely they match desired profiles. This page presents the main practical uses of FDA and helps you identify the approach best suited to your data and processes.
Functional data analysis in action: Three key applications
Real-world applications of FDA typically fall into three categories:
- Understanding the drivers of curve variation.
- Utilizing functional regression.
- Comparing curves to targets or standards.
These types of scenarios illustrate where FDA can create value in your work.
1. Understanding the drivers of curve variation
Determining why a curve has a specific shape is critical to understanding a process. Understanding which experimental factors shift a peak, change a slope, alter timing, or affect other profile aspects is essential for diagnosing variation.
This scenario is common when working with:
- Spectra or chromatograms
- Stress-strain curves
- Temperature profiles
- Time sensor measurements
How FDA helps you investigate curve variation
FPCA identifies the dominant modes of variation in your data, such as shifts, stretches, amplitude changes, or complex patterns.
Modeling the FPC scores against your experimental factors allows you to answer questions such as:
- Which factor shifts the peak position?
- Which factors affect the specific region of interest?
- Which factor settings produce ideal output shapes?
Incorporating design of experiments to explore curve variation
To understand which experimental factors influence the entire curve, FDA can be combined with design of experiments. This structured approach lets you identify how factors influence the shape profile. Combining FDA with DOE provides a structured method to confirm effects, estimate interactions, and select factor settings that steer the curve as desired.
Using FPC scores as responses in a DOE analysis allows you to:
- Understand a factor's impact on a curve shape.
- Determine how interactions affect profile regions.
- Optimize factor settings to obtain an ideal curve.
Functional DOE is useful when curve shapes are important to understand and optimize.
2. Utilizing functional regression
Creating a regression model to help understand a function's shape is a very valuable feature of FDA. Many industrial processes use controllers like PIDs (proportional-integral-derivative) and PLCs (programmable logic controllers) with set points and ramp rates that change during operation. The shape of controller curves often affects responses of interest. Capturing these curves with FDA provides a richer understanding of their impact on processes. The same idea applies when your response is a curve and you need to understand how different settings change its shape.
Some examples of where factor shape can influence a response:
- Optimizing the heating profile to improve yield.
- Adjusting pH profile to reduce impurities.
- Modeling a reaction temperature trace for new factor settings.
- Predicting a stress strain curve for a new formulation.
FDA lets you combine FPC scores with regression or machine learning models, providing predictive power from the entire shape variation. It yields a more complete, shape-aware prediction that reflects your system's true behavior.
Using curves as predictors and responses
Functional regression provides the modeling framework that makes these curve-based predictions possible. It extends standard regression in two directions:
- Functional responses (predicting entire curves).
- Functional predictors (using curves to predict a tabular outcome).
It enables you to:
- Build models where dynamic signals are inputs.
- Predict full curves for new process settings or formulations.
- Understand which regions of a curve are most influential in predicting an outcome.
- Translate functional inputs such as spectra or sensor traces into predictions.
Functional regression is a powerful tool when the system’s shape is more informative than any single measurement.
3. Comparing curves to targets or standards
In processes where outcomes follow a desired pattern instead of a single value, determining whether a curve meets specifications is critical. FDA improves your ability to detect shape deviations.
For example, the ability to spot deviations is essential when:
- Dissolution profiles must follow an API release trajectory.
- Spectral signatures indicate impurities levels.
- Process monitoring curves must fall within expected boundaries.
- Energy consumption curves must remain within limits.
FDA helps you quantify similarity to a target curve, evaluate whether a profile is acceptable, and identify deviations. This shape-based evaluation allows for detection of anomalies and more reliable quality control.
How FDA helps detect deviations and evaluate similarity
FPCA provides a natural way to characterize normal or desired shapes.
By modeling the variation in a set of “good” curves, you can:
- Define an acceptable region of variation utilizing FPCs.
- Set specification limits for the FPC scores or an integrated error from target.
- Flag anomalies that exhibit out-of-spec shapes.
This shape monitoring is valuable in quality environments where profile changes indicate process drift.
Functional anomaly detection
Significant deviations from the mean shape indicate functional anomalies. FPCA allows the detection of differences in shape, timing, or amplitude that can be difficult to detect with traditional quality monitoring.
It helps you:
- Detect early signs of equipment degradation or process drift.
- Identify faulty batches based on shape differences rather than endpoint failures.
- Monitor systems where unusual curvature or timing patterns signal problems.
- Catch anomalies that would be invisible using traditional SPC charts.
By evaluating the curve as a whole, functional anomaly detection improves reliability and enables earlier intervention.
How JMP Pro streamlines your FDA workflow
Functional data workflows often require stitching together multiple tools and writing custom code to handle preprocessing, smoothing, FPCA, modeling, visualization, and optimization.
JMP Pro brings these steps together in one place so you can:
- Clean, align, and smooth your curves with guided tools.
- Perform FPCA and immediately explore how factors affect each component.
- Use FPC scores in standard regression, classification, or optimization models.
- Visualize shape changes in a Profiler that shows how factors shift entire curves.
- Integrate FDA with DOE for better interpretability and process understanding.
- Monitor processes and detect anomalies using shape-based methods.
JMP Pro unifies the functional data analysis workflow in a point-and-click environment, allowing you to focus on interpreting results instead of assembling tools and code.
Applying functional data analysis in industry
Across industries, FDA is giving teams visibility into patterns they couldn’t detect before. The stories below illustrate how Functional Data Explorer in JMP Pro helped uncover critical behavior in print-head testing, transform noisy biologics development profiles, and reveal shape-based correlations linked to yield.
Xaar
Fujifilm Diosynth Biotechnologies
Lynred
