Multi-response approach to improving identifiability in model calibration

Zhen Jiang*, Paul D. Arendt, Daniel Apley, Wei Chen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


In physics-based engineering modeling, two primary sources of model uncertainty that account for the differences between computer models and physical experiments are parameter uncertainty and model discrepancy. One of the main challenges in model updating results from the difficulty in distinguishing between the effects of calibration parameters versus model discrepancy. In this chapter, this identifiability problem is illustrated with several examples that explain the mechanisms behind it and that attempt to shed light on when a system may or may not be identifiable. For situations in which identifiability cannot be achieved using only a single response, an approach is developed to improve identifiability by using multiple responses that share a mutual dependence on the calibration parameters. Furthermore, prior to conducting physical experiments but after conducting computer simulations, in order to address the issue of how to select the most appropriate set of responses to measure experimentally to best enhance identifiability, a preposterior analysis approach is presented to predict the degree of identifiability that will result from using different sets of responses to measure experimentally. To handle the computational challenges of the preposterior analysis, we also present a surrogate preposterior analysis based on the Fisher information of the calibration parameters.

Original languageEnglish (US)
Title of host publicationHandbook of Uncertainty Quantification
PublisherSpringer International Publishing
Number of pages59
ISBN (Electronic)9783319123851
ISBN (Print)9783319123844
StatePublished - Jun 16 2017


  • (Non)identifiability
  • Bias correction
  • Calibration
  • Calibration parameters
  • Discrepancy function
  • Experimental uncertainty
  • Fixed-0 preposterior analysis
  • Gaussian process
  • Hyperparameters
  • Identifiability
  • Model discrepancy
  • Model uncertainty quantification
  • Modular bayesian approach
  • Multi-response gaussian process
  • Multi-response modular bayesian approach
  • Non-informative prior
  • Non-spatial covariance
  • Observed fisher information
  • Parameter uncertainty
  • Preposterior analysis
  • Preposterior covariance
  • Simply supported beam
  • Spatial correlation
  • Surrogate preposterior analysis

ASJC Scopus subject areas

  • Mathematics(all)

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