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Automated feature-region selection for soft-sensor development from spectral-like measurements

Sebastián Espinel-Ríos, Wenchao Duan

arXiv:2609.27082v1eess.SP

TL;DR

High-dimensional, redundant measurements complicate soft-sensor development, motivating automated selection of informative contiguous regions. The framework combines channel-level target correlation and measurement quality to identify compact regions; selected glucose models reduced test RMSE by 88.3–94.6% versus full-feature benchmarks.

  • Problem

    In limited experimental datasets, high input dimensionality and feature redundancy can increase data requirements and overfitting risk.

    Source: §1 · p. 4

  • Method

    The framework combines channel-level target correlation and measurement quality to select compact feature regions for soft-sensor development.

    Source: §1 · p. 4

  • Results

    Using 11–42 of 400 channels, selected models reduced held-out test RMSE by 88.3–94.6% versus corresponding full-feature GPR benchmarks.

    Source: §5 · p. 20

  • Takeaways & Limitations

    The framework was demonstrated for glucose soft sensing across four investigated concentration ranges.

    Source: §5 · p. 20

    The glucose measurements in PBS provide a controlled proof of concept; deployment readiness requires future implementation and robustness checks.

    Source: §5 · p. 20

Abstract

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Sustainable production increasingly relies on process analytical chemistry and process analytical technology to support monitoring, control, and automation. Techniques used in these contexts, including Raman spectroscopy, infrared spectroscopy, and electrochemical voltammetry, generate high-dimensional signals ordered along physical measurement axes, referred to here as spectral-like measurements. These signals can contain redundant, weakly informative, and noisy regions, complicating the development of data-driven soft sensors to map them to process variables. Selecting informative regions is nontrivial, as visually prominent regions are not necessarily the most predictive, while synergistic effects among regions cannot be readily inferred. Here, we introduce an automated feature-region selection framework that identifies a parsimonious set of contiguous regions while preserving channel ordering. The framework combines channel-level target correlation and a signal-to-noise indicator into a latent information fingerprint. Variable-width candidate intervals are derived from peaks in this fingerprint, and their combinations are ranked using held-out validation data. Final selection favours models using fewer channels among candidates with comparable predictive performance. The framework is demonstrated using cyclic voltammetric measurements of glucose acquired with a gold electrode sensor across four progressively broader nominal concentration ranges up to 350 g/L. Gaussian process regression is used within the framework to accommodate possible nonlinear relationships, account for observation noise, and quantify epistemic uncertainty. The selected models retained only 11-42 of the original 400 channels and reduced held-out test root mean squared error by 88.3-94.6% relative to full-feature Gaussian process regression benchmarks.

Highlights

The framework automatically selects contiguous regions from spectral-like measurements for soft-sensor development. In glucose voltammetry, selected Gaussian-process models used far fewer channels and reduced held-out test error versus full-feature benchmarks.

Highlights

  • A latent fingerprint combines channel-level target correlation with a signal-to-noise indicator.Source: Highlights · p. 2
  • Candidate intervals are derived from fingerprint peaks and evaluated in combination.Source: Highlights · p. 2
  • Selected models reduced held-out test RMSE by 88.3–94.6% versus full-feature models.The models used 11–42 of the original 400 voltammetric channels.Source: Highlights · p. 2

1. Introduction

The introduction motivates selecting informative, contiguous regions from high-dimensional measurements for soft sensors, then outlines a framework and a glucose voltammetry demonstration. It also notes that comparing regression architectures systematically is outside the study’s scope.

1. Introduction

  • In limited experimental datasets, high dimensionality and feature redundancy can increase data requirements and overfitting risk, while measurement noise complicates soft-sensor development.Source: §1 · p. 4
  • The framework targets compact, informative regions in ordered measurements and evaluates candidate interval combinations with models.Manual region selection can require application-specific knowledge and may miss informative regions not evident by visual inspection.Source: §1 · pp. 4–5
  • Final interval combinations are evaluated on held-out validation data, with selection favouring fewer channels among candidates with comparable performance.Source: §1 · p. 5
  • Its information fingerprint combines channel-level target correlation and replicate-based measurement quality; peaks yield variable-width contiguous intervals before regression fitting.The intervals preserve local ordering, and the framework’s interval generation is independent of the downstream regression architecture.Source: §1 · pp. 4–5
  • A systematic comparison across regression models is beyond the study’s scope, which focuses on automated identification and selection of informative contiguous regions.Source: §1 · p. 5
  • The demonstration uses glucose cyclic voltammetry across four progressively broader nominal concentration windows: 0–75, 0–150, 0–250, and 0–350 g/L.Gaussian process regression is used to accommodate nonlinear relationships, quantify uncertainty in predictions, and incorporate observation noise.Source: §1 · p. 5

2. Problem definition

The problem definition formalizes soft-sensor prediction from ordered spectral-like measurements and frames the task as selecting non-overlapping contiguous regions for a reduced input matrix.

2. Problem definition

  • The input matrix represents high-dimensional spectral-like measurements, whose channels are ordered along a physical measurement axis.The corresponding target matrix contains variables to be inferred.Source: §2 · p. 6
  • Because the full feature matrix may contain redundant, weakly informative, or noisy regions, the objective is to construct parsimonious soft sensors from automatically selected contiguous intervals.Source: §2 · p. 6
  • Selected intervals are sets of contiguous, ordered feature indices, constrained to be non-overlapping; their features form the reduced matrix Xsel.Source: §2 · pp. 6–7
  • The selection task is to construct interval set E for a downstream model that improves or retains full-feature predictive performance on ordered measurements.The formulation focuses on single-output regression conditioned on the selected-feature vector.Source: §2 · p. 7

3. Automated workflow for soft-sensor development

This section describes an automated workflow for selecting contiguous, informative feature regions and fitting parsimonious Gaussian-process soft sensors. It also explains how the models return posterior predictions and quantify epistemic uncertainty.

3. Automated workflow for soft-sensor development

  • A 60%/20%/20% training, validation, and test split groups replicates by target level to prevent leakage across subsets.The test set is reserved for evaluating performance on unseen target-variable levels.Source: §3 · p. 7, §3.3 · p. 10

3.1. Point-wise scoring

  • Squared Spearman correlation scores monotonic target relevance, while a replicate-based signal-to-noise indicator contributes to each channel’s information fingerprint.The squared correlation weights positive and negative monotonic relationships equally, but does not capture general non-monotonic relationships.Source: §3.1 · pp. 7–8

3.2. Candidate interval generation from the information fingerprint

  • Prominent fingerprint peaks generate variable-width intervals, which are filtered and combined into contiguous candidate feature regions.Intervals are scored by average point-wise information, and combinations are evaluated up to a user-defined maximum cardinality.Source: §3.2 · pp. 8–9

3.3. Ranking of soft-sensor candidates and final model selection

  • Candidates are ranked by validation RMSE; among those within a relative tolerance of the minimum, the fewest-channel model is selected and refitted on training plus validation data.The held-out test set remains unused during selection.Source: §3.3 · pp. 9–10

3.4. Gaussian-process-based soft sensors

  • Gaussian-process regression treats targets as noisy observations and uses an RBF kernel with feature-specific length scales fitted by maximizing Gaussian log marginal likelihood.The GP defines a probability distribution over the modeled function.Source: §3.4 · pp. 10–11
  • Posterior variance quantifies epistemic uncertainty in the function conditional on fitted GP parameters and training observations, with predictions excluding observation noise.Source: §3.4 · p. 11
  • GPR models used BoTorch SingleTaskGP with GPyTorch, fitting parameters via ExactMarginalLogLikelihood and fit_gpytorch_mll.Source: §3.4 · p. 11
  • The default SingleTaskGP standardizes target observations during fitting and returns posterior quantities on the original target scale, without transforming input features.Source: §3.4 · p. 11

4. Case study: glucose soft sensing from voltammetric measurements

The case study applies automated feature-region selection to glucose cyclic voltammetry measured with an Au electrode across progressively broader concentration ranges. It evaluates compact region-based GPR models against full-feature GPR on held-out data, with selected regions and their combinations varying by range.

4.2. Automated soft-sensor development for the 0–75 g/L range

  • Validation-based ranking selected oxidation at 0.53–0.72 V and reduction at 0.45–0.69 V; together, these regions contain 42 of the original 400, as summarized in Table 2.The selected reduction region had the lowest average fingerprint score among retained candidates; validation-based model selection identifies combinations with joint predictive value.Source: §4.2 · p. 15
  • On held-out test concentration levels, the selected feature-region model achieved R2 0.990 and RMSE 1.84 g/L, reducing test RMSE by 88.3% versus the full-feature GPR benchmark’s 15.70 g/L.Source: §4.2 · p. 15

4.3. Automated soft-sensor development for the 0–150 g/L range

  • Validation-based ranking selected a single oxidation region spanning 0.60 to 0.71 V; it contains 12 of 400 measurement channels, a 97.0% input-dimension reduction.This region had the highest average fingerprint score among retained candidates but did not coincide with the dominant current-magnitude peaks in the original voltammograms.Source: §4.3 · p. 18
  • On held-out test concentration levels, the selected feature-region model achieved R2 0.989 and RMSE 2.38 g/L, versus the full-feature GPR’s test R2 −1.899 and RMSE 38.94 g/L, reducing test RMSE by 93.9%.Predictive relevance is not determined solely by the magnitude of the raw current response.Source: §4.3 · p. 18

4.4. Automated soft-sensor development for the 0–250 g/L range

  • Validation-based ranking selected oxidation at approximately 0.66–0.74 V and reduction at approximately 0.08–0.11 V; together, they retained 11 of 400 channels, reducing input dimensionality by 97.3%.The oxidation region overlapped with the region selected for 0–150 g/L, while the reduction region provided complementary predictive information.Source: §4.4 · pp. 18–19
  • On held-out test concentration levels, the selected feature-region model achieved R2 0.996 and RMSE 4.09 g/L, versus full-feature GPR’s R2 −0.442 and RMSE 75.64 g/L, reducing test RMSE by 94.6%.Source: §4.4 · p. 19

4.5. Automated soft-sensor development for the 0–350 g/L range

  • Validation-based ranking selected three regions—oxidation at approximately 0.66–0.74 V and 0.27–0.36 V, and reduction at 0.35–0.41 V—containing 22 of 400 channels, a 94.5% reduction.Candidate locations closely corresponded to those for 0–250 g/L, while selected reduction regions varied between concentration ranges.Source: §4.5 · p. 19
  • On held-out test concentration levels, the selected feature-region model achieved R2 0.992 and RMSE 9.98 g/L, versus full-feature GPR’s test R2 0.187 and RMSE 101.66 g/L, reducing test RMSE 90.2%.Source: §4.5 · p. 19

5. Conclusions

The framework selects compact contiguous regions from spectral-like measurements and evaluates their combinations for soft-sensor development. In glucose voltammetry, selected models reduced held-out test error relative to full-feature benchmarks, while deployment in process matrices remains future work.

5. Conclusions

  • The framework combines channel-level target correlation and replicate-based signal quality, derives contiguous candidate intervals, and ranks combinations by predictive performance and parsimony.Source: §5 · p. 20
  • Candidate-interval generation is independent of the regression architecture; GPR was used here to represent nonlinear relationships, account for observation noise, and estimate posterior uncertainty.GPR was considered suitable for small to medium-sized experimental datasets.Source: §5 · p. 20
  • Selected models retained 11–42 of 400 channels and reduced held-out test RMSE by 88.3–94.6% versus corresponding full-feature GPR benchmarks.Source: §5 · p. 20
  • Full-feature models’ near-perfect training and validation fits followed by poorer test performance were consistent with overfitting in the 400-channel representation.Feature-region selection retained strong calibration performance while improving prediction at held-out concentration levels.Source: §5 · p. 20
  • The glucose-in-PBS measurements provide a controlled proof of concept; deployment-ready sensing requires implementation and robustness checks with process-broth and other process-specific matrices.Source: §5 · p. 20

CRediT authorship contribution statement

Sebastián Espinel-Ríos and Wenchao Duan contributed to the paper across conceptualization, research, analysis, validation, and writing.

CRediT authorship contribution statement

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