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Property Estimation in Geotechnical Databases Using Labeled Random Finite Sets

Changbeom Shim, Youngho Kim, Craig Butterworth

arXiv:2410.22659v1eess.SPcs.CEcs.LG

TL;DR

Geotechnical property estimation must contend with imperfect, noisy, and incomplete data, including measurements indirectly related to a particular site. This paper applies LRFS and GLMB filtering to estimate clay properties from such measurements. In Norway and Taiwan cases, the estimates generally follow ground-truth patterns, filter noise, and recover missing points.

  • Problem

    Geotechnical databases contain imperfect data, and site-investigation measurements can be multivariate, uncertain, sparse, incomplete, and potentially corrupted.

    Source: §I · p. 1, §II · p. 2

  • Method

    The paper represents geotechnical properties as labeled finite-set states and uses Bayesian GLMB filtering to estimate properties from noisy and incomplete BID measurements.

    Source: §I · p. 1, A. Labeled RFSs · p. 2, B. GLMB filtering · p. 2

  • Results

    In Norway and Taiwan cases, estimates generally follow ground-truth patterns, recover missing values, and filter noise, though Taipei estimates are less accurate with fewer observations.

    Source: A. Case study 1: Onsøy site, Norway · p. 4, B. Case study 2: Taipei site, Taiwan · p. 4, §V · p. 5

  • Takeaways & Limitations

    The experiments show GLMB filtering can estimate clay properties from MUSIC-X measurements in the studied Norway and Taiwan cases without geotechnical knowledge.

    Source: §V · p. 5

    The work is a feasibility study without in-depth mathematical discussion or proofs of the connection between LRFS methods and geotechnical databases.

    Source: §V · p. 5

Abstract

from arXiv · show

The sufficiency of accurate data is a core element in data-centric geotechnics. However, geotechnical datasets are essentially uncertain, whereupon engineers have difficulty with obtaining precise information for making decisions. This challenge is more apparent when the performance of data-driven technologies solely relies on imperfect databases or even when it is sometimes difficult to investigate sites physically. This paper introduces geotechnical property estimation from noisy and incomplete data within the labeled random finite set (LRFS) framework. We leverage the ability of the generalized labeled multi-Bernoulli (GLMB) filter, a fundamental solution for multi-object estimation, to deal with measurement uncertainties from a Bayesian perspective. In particular, this work focuses on the similarity between LRFSs and big indirect data (BID) in geotechnics as those characteristics resemble each other, which enables GLMB filtering to be exploited potentially for data-centric geotechnical engineering. Experiments for numerical study are conducted to evaluate the proposed method using a public clay database.

I. INTRODUCTION

Data-centric geotechnics depends on real-world databases, but those datasets are often imperfect and indirectly related to any one site or project. This work proposes using LRFS and GLMB filtering for geotechnical property estimation, drawing on their relevance to uncertain data and multi-object tracking.

  • Geotechnical databases support data centricity, yet big indirect data (BID) are indirectly related to a specific site or project and typical datasets are imperfect.Source: §I · p. 1
  • Prior geotechnical work combines data-driven methods with domain knowledge and applies Bayesian approaches to several site-specific and soil-property problems.Examples include slope stability, landslide susceptibility, site retrieval, and soil-property prediction.Source: §I · p. 1
  • Labeled random finite set (LRFS) methods address multi-object tracking, where object counts are unknown and measurements are uncertain; GLMB and labeled multi-Bernoulli filters are widely studied.Source: §I · p. 1
  • The paper treats each geotechnical data property as an object in an LRFS and uses the GLMB filter for BID-based estimation, presenting this as the first geotechnical property-estimation work exploiting GLMB filtering.Experiments use a real geotechnical database.Source: §I · p. 1

II. GEOTECHNICAL DATABASES

Geotechnical databases aggregate generic information from multiple sites or countries rather than data tied directly to one project. Their site-investigation data can be MUSIC-X, motivating methods that handle uncertainty, sparsity, incompleteness, and potential corruption.

  • The CLAY/10/7490 database contains 7,490 records from 30 countries and includes 10 clay properties.The database is part of the 304dB resources provided by the ISSMGE committee.Source: §II · p. 2
  • The ten listed properties span consistency and plasticity indices, stress and strength ratios, sensitivity, pore pressure, and cone-resistance measures.They are denoted Y1 through Y10, including liquid limit (LL), plasticity index (PI), and undrained strength ratio.Source: §II · p. 2
  • The passage defines v as vertical effective stress, Pa as atmospheric pressure at 101.3 kPa, σ′p as preconsolidation stress, su as undrained shear strength, qt as corrected cone tip resistance, and u2 as pore pressure behind the cone.Source: §II · p. 2
  • Site-investigation data are described as MUSIC-X: multivariate, uncertain and unique, sparse, incomplete, and potentially corrupted across spatio-temporal dimensions.The paper argues that methods suited to these database characteristics are needed for decisions based on accurate site-specific data.Source: §II · p. 2

III. GENERALIZED LABELED MULTI-BERNOULLI FILTERS

The section establishes notation for finite-set and function operations and explains how time-step subscripts may be abbreviated when unambiguous.

  • The Kronecker delta δY[X] is one when X equals Y, while the indicator 1Y(X) is one when X is a subset of Y; otherwise each is zero.Source: §III · p. 2
  • F(X) denotes the class of finite subsets of X, and hX denotes the product of h(x) over x in X, with h∅ equal to one.Source: §III · p. 2
  • When unambiguous, the current step k may be omitted and the previous and next steps may be written as − and + instead of k−1 and k+1.Source: §III · p. 2

A. Labeled RFSs

The paper represents multiple geotechnical properties as a labeled finite-set-valued random variable for Bayesian estimation, using labels to identify properties and distinguish newly measured ones.

A. Labeled RFSs

  • A multi-property state x=(x, ℓ) pairs a value from state space X with a discrete label from label space L.Source: A. Labeled RFSs · p. 2
  • A label ℓ=(k, i) identifies an entry by its starting step k and identifier i, while B denotes labels for properties newly measured at k.Source: A. Labeled RFSs · p. 2
  • The property set X belongs to the finite subsets of X×L, and L(X) denotes its distinct labels.Source: A. Labeled RFSs · p. 2

B. GLMB filtering

The paper represents multiple properties with a GLMB filtering density and describes its forward recursion under Bayesian filtering. It presents LRFS filtering as a feasible approach for handling big indirect data (BID).

B. GLMB filtering

  • The multi-property LRFS is distributed in GLMB form, with its information included in the GLMB filtering density.The density uses a finite space C, non-negative weights w(I,c), and probability densities p(c)(x, ℓ).Source: B. GLMB filtering · p. 2
  • The next-step GLMB filtering density follows the Bayes recursion, with the joint prediction-and-update form generally used.The recursion involves birth density B and new measurements Z+.Source: B. GLMB filtering · p. 2
  • The authors frame LRFS filtering as a feasibility study for BID, noting a potential connection to set-theoretic relational databases.They do not claim to identify the best solution for the estimation problem.Source: B. GLMB filtering · p. 2

IV. NUMERICAL STUDY

The numerical study tests GLMB filtering on a public clay database, treating retained measurements as noisy, incomplete observations and database values as ground truths.

IV. NUMERICAL STUDY

  • The study evaluates LL, PI, and water content at sites in Norway and Taiwan using the CLAY/10/7490 database.The authors state that their focus is estimating clay properties from MUSIC-X sensor data, not analyzing a specific database.Source: §IV · p. 3
  • The experiments remove some database values and add noise to the remaining data to form incomplete noisy observations.Measured database values serve as ground truths because actual physical values are difficult to obtain.Source: §IV · p. 3
  • The filtering setup uses a general linear Gaussian model.Source: §IV · p. 3

A. Case study 1: Onsøy site, Norway

At Onsøy, GLMB filtering estimates clay properties from noisy, incomplete observations across 36 depths. The reported estimates generally follow ground-truth patterns and recover missing values.

A. Case study 1: Onsøy site, Norway

  • The Onsøy study covers 36 depths from 1.03 m to 16.28 m.Source: A. Case study 1: Onsøy site, Norway · p. 3
  • The observation setup uses detection probability PD = 0.5, observation-noise standard deviation σm = 10%, and process-noise standard deviation σp = 0.3 % per interval squared.Initial values are assumed roughly known, and the sampling interval is matched to the ground truth for simplicity.Source: A. Case study 1: Onsøy site, Norway · p. 3
  • The estimates generally follow Onsøy ground-truth patterns and recover missing values despite noisy, incomplete readings.LL estimates generally follow the ground truth; PI estimates improve on observations but are less accurate than LL, while water-content estimates capture its trend.Source: Figure 1 · p. 3, A. Case study 1: Onsøy site, Norway · p. 4

B. Case study 2: Taipei site, Taiwan

At Taipei, GLMB filtering estimates are less accurate for LL and PI than at Onsøy, which the authors attribute mainly to fewer observations. Water-content performance is similar across sites.

B. Case study 2: Taipei site, Taiwan

V. CONCLUSION

The paper applies Bayesian LRFS estimation with a GLMB filter to clay properties, treating multiple properties as multi-object states and deriving estimates by maximum a posteriori. Experiments on CLAY/10/7490 cover Norway and Taiwan; the work is a feasibility study without mathematical discussion or proofs.

V. CONCLUSION

  • In Norway and Taiwan, clay property estimates are obtained from MUSIC-X measurements without geotechnical knowledge.The paper identifies site retrieval as a prospective application in academia and industry.Source: §V · p. 5
  • GLMB filtering generates clay-property distributions by treating multiple properties as multi-object states, with final estimates obtained by maximum a posteriori.Evaluation uses the real geotechnical database CLAY/10/7490.Source: §V · p. 5
  • The study is a feasibility study without mathematical discussion or proofs of the theoretical connection between LRFS methods and geotechnical databases.Future directions include scalable methods and visual analytics for high-dimensional geotechnical data.Source: §V · p. 5

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