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Multi-kernel optimized relevance vector machine for probabilistic prediction of concrete dam displacement

  • Siyu Chen
  • Chongshi GuEmail author
  • Chaoning LinEmail author
  • Kang Zhang
  • Yantao Zhu
Original Article

Abstract

The observation data of dam displacement can reflect the dam’s actual service behavior intuitively. Therefore, the establishment of a precise data-driven model to realize accurate and reliable safety monitoring of dam deformation is necessary. This study proposes a novel probabilistic prediction approach for concrete dam displacement based on optimized relevance vector machine (ORVM). A practical optimization framework for parameters estimation using the parallel Jaya algorithm (PJA) is developed, and various simple kernel/multi-kernel functions of relevance vector machine (RVM) are tested to obtain the optimal selection. The proposed model is tested on radial displacement measurements of a concrete arch dam to mine the effect of hydrostatic, seasonal and irreversible time components on dam deformation. Four algorithms, including support vector regression (SVR), radial basis function neural network (RBF-NN), extreme learning machine (ELM) and the HST-based multiple linear regression (HST-MLR), are used for comparison with the ORVM model. The simulation results demonstrate that the proposed multi-kernel ORVM model has the best performance for predicting the displacement out of range of the used measurements dataset. Meanwhile, the ORVM model has the advantages of probabilistic output and can provide reasonable confidence interval (CI) for dam safety monitoring. This study lays the foundation for the application of RVM in the field of dam health monitoring.

Keywords

Optimized relevance vector machine Multi-kernel Jaya optimization algorithm Dam health monitoring Prediction model 

Abbreviations

RVM

Relevance vector machine

ORVM

Optimized relevance vector machine

CI

Confidence interval

HST

Hydrostatic-season-time

HTT

Hydrostatic-temperature-time

MLR

Multiple linear regression

PLSR

Partial least squares regression

SR

Stepwise regression

PJA

Parallel Jaya algorithm

ANN

Artificial neural network

MLP

Multilayer perceptron

SLFNs

Single hidden layer feedforward neural networks

ANFIS

Adaptive neural fuzzy inference system

MARS

Multivariate adaptive regression splines

GPR

Gaussian process regression

RBF-NN

Radial basis function neural network

ELM

Extreme learning machine

SVM

Support vector machine

SVR

Support vector regression

MLR-HST

HST-based multiple linear regression

SumGP

Multi-kernel Gaussian kernel + polynomial kernel

SumGL

Multi-kernel Gaussian kernel + Laplace kernel

SumLP

Multi-kernel Laplace kernel + polynomial kernel

G-ORVM

Gaussian kernel-based optimized relevance vector machine

GP-ORVM

SumGP kernel-based optimized relevance vector machine

R2

Coefficient of determination

RMSE

Root mean square error

MAE

Mean absolute error

ME

Maximum absolute error

AWCI

Average width of confidence interval

AVCI

Average variance of confidence interval

Notes

Acknowledgements

The authors are grateful to the financial sponsorship from National Natural Science Foundation of China (Grant Nos. 51739003, 51779086), National Key R&D Program of China (2018YFC0407104, 2016YFC0401601), Special Project Funded of National Key Laboratory (20165042112) and Key R&D Program of Guangxi (AB17195074).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai UniversityNanjingChina
  2. 2.College of Water Conservancy and Hydropower EngineeringHohai UniversityNanjingChina
  3. 3.National Engineering Research Center of Water Resources Efficient Utilization and Engineering SafetyHohai UniversityNanjingChina

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