Multivariable Linear Filter Theory Applied to Space Vehicle Guidance

Smith, Gerald L.

doi:10.1137/0302003

Cited by 27 publications

(29 citation statements)

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“…This assumption allows us to solve ( 9 ) using standard differential equation techniques, then derive statistical distributions for the resulting solution and any quantities of interest related to it. Such an equation is frequently called a random differential equation, to distinguish from stochastic differential equations which require more sophisticated solution strategies such as the Itô formalism (see discussion in [ 48 ], section 4.7). See Fig 4 for an illustration.…”

Section: Tumor Growth and Response To Therapymentioning

confidence: 99%

Physiological random processes in precision cancer therapy

et al. 2018

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Many different physiological processes affect the growth of malignant lesions and their response to therapy. Each of these processes is spatially and genetically heterogeneous; dynamically evolving in time; controlled by many other physiological processes, and intrinsically random and unpredictable. The objective of this paper is to show that all of these properties of cancer physiology can be treated in a unified, mathematically rigorous way via the theory of random processes. We treat each physiological process as a random function of position and time within a tumor, defining the joint statistics of such functions via the infinite-dimensional characteristic functional. The theory is illustrated by analyzing several models of drug delivery and response of a tumor to therapy. To apply the methodology to precision cancer therapy, we use maximum-likelihood estimation with Emission Computed Tomography (ECT) data to estimate unknown patient-specific physiological parameters, ultimately demonstrating how to predict the probability of tumor control for an individual patient undergoing a proposed therapeutic regimen.

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Section: Tumor Growth and Response To Therapymentioning

confidence: 99%

Physiological random processes in precision cancer therapy

et al. 2018

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“…A random variable vector ( q ) containing both crack depth and crack location is treated as with prior PDF ( P 0 ). Based on the Bayes’ theorem of inverse problem (Cui et al, 2014; Liu, 2001; Smith, 2014), the posterior PDF ( P ), given the measurement data ( v obs ), is defined by…”

Section: Bayesian Inferencementioning

confidence: 99%

“…Second, the Bayesian approach is employed for the damage parameter estimations. Instead of using probabilistic optimization method (Lam et al, 2007; Ng et al, 2009), the Markov Chain Monte Carlo (MCMC) techniques (Metropolis et al, 1953) are applied along with the random walk metropolis algorithm (Hastings, 1970; Metropolis et al, 1953; Smith, 2014) to conduct notch damage uncertainty quantification. MCMC methods provide a flexible and powerful approach for sampling from the posterior distributions (Liu, 2001) and have been applied to inverse problems in various fields as reviewed by Cui et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Beam damage uncertainty quantification using guided Lamb wave responses

Wang

2017

Journal of Intelligent Material Systems and Structures

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In this article, a Bayesian inference approach is applied to conduct uncertainty quantification on notch damage in a beam structure using guided Lamb wave responses. The proposed methodology not only determines the notch damage characteristics but also quantifies associated uncertainties of these inferred values. The correlation between crack location and extent is investigated as well, because such information is essential for decision-making in the structural health monitoring applications. First, a spectral finite element model is used to characterize Lamb wave propagation responses in a beam under lead-zirconate-titanate actuation and sensing. Very few elements are required to accurately capture the wave propagation. The lead-zirconate-titanate sensor can pick up the reflected wave responses from both boundaries and damages. Total 18 simulation cases were generated by varying notch damage extent, damage location, and noise level. Second, the Markov Chain Monte Carlo techniques are employed to estimate the notch damage location and extent from guided Lamb wave responses, in which the random walk metropolis algorithm is used. Finally, both crack size/location and associated uncertainties are characterized. In summary, the proposed probabilistic damage detection is successfully demonstrated in beam structures using guided wave responses, which can be extended to other structural health monitoring applications.

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“…Sensitivity analysis assesses how sensitive the model output is to different values of the model inputs (Saltelli et al, 2008). Uncertainty quantification involves identifying the sources of uncertainty in the model, quantifying the uncertainty of the sources using probability distributions, and then propagating the uncertainty through the model to determine the impact on the output (Smith, 2013). Applicability analysis involves a systematic evaluation of the relevance of the validation evidence to support using the computational model for the specific proposed application of the model, or COU.…”

Section: Introductionmentioning

confidence: 99%

Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine

et al. 2019

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Physiological closed-loop controlled medical devices automatically adjust therapy delivered to a patient to adjust a measured physiological variable. In critical care scenarios, these types of devices could automate, for example, fluid resuscitation, drug delivery, mechanical ventilation, and/or anesthesia and sedation. Evidence from simulations using computational models of physiological systems can play a crucial role in the development of physiological closed-loop controlled devices; but the utility of this evidence will depend on the credibility of the computational model used. Computational models of physiological systems can be complex with numerous nonlinearities, time-varying properties, and unknown parameters, which leads to challenges in model assessment. Given the wide range of potential uses of computational patient models in the design and evaluation of physiological closed-loop controlled systems, and the varying risks associated with the diverse uses, the specific model as well as the necessary evidence to make a model credible for a use case may vary. In this review, we examine the various uses of computational patient models in the design and evaluation of critical care physiological closed-loop controlled systems (e.g., hemodynamic stability, mechanical ventilation, anesthetic delivery) as well as the types of evidence (e.g., verification, validation, and uncertainty quantification activities) presented to support the model for that use. We then examine and discuss how a credibility assessment framework (American Society of Mechanical Engineers Verification and Validation Subcommittee, V&V 40 Verification and Validation in Computational Modeling of Medical Devices) for medical devices can be applied to computational patient models used to test physiological closed-loop controlled systems.

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Multivariable Linear Filter Theory Applied to Space Vehicle Guidance

Cited by 27 publications

References 0 publications

Physiological random processes in precision cancer therapy

Physiological random processes in precision cancer therapy

Beam damage uncertainty quantification using guided Lamb wave responses

Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine

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