Juan Chiachío

Approximate Bayesian computation by subset simulation

A new approximate Bayesian computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of subset simulation for efficient rare-event simulation, first developed in S. K. Au and J. L. Beck [Probabilistic Engrg. Mech., 16 (2001), pp. 263-277]. It has been named ABC-SubSim. The idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space. The efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real-world applications of ABC. We show that the proposed algorithm outperforms other recent sequential ABC algorithms in terms of computational efficiency while achieving the same, or better, measure of accuracy in the posterior distribution. We also show that ABC-SubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a by-product.

Condition-based prediction of time-dependent reliability in composites

This paper presents a reliability-based prediction methodology to obtain the remaining useful life of composite materials subjected to fatigue degradation. Degradation phenomena such as stiffness reduction and increase in matrix micro-cracks density are sequentially estimated through a Bayesian filtering framework that incorporates information from both multi-scale damage models and damage measurements, that are sequentially collected along the process. A set of damage states are further propagated forward in time by simulating the damage progression using the models in the absence of new damage measurements to estimate the time-dependent reliability of the composite material. As a key contribution, the estimation of the remaining useful life is obtained as a probability from the prediction of the time-dependent reliability, whose validity is formally proven using the axioms of Probability Logic. A case study is presented using multi-scale fatigue damage data from a cross-ply carbon-epoxy laminate.

Logical inference for inverse problems

Estimating a deterministic single value for model parameters when reconstructing the system response has a limited meaning if one considers that the model used to predict its behaviour is just an idealization of reality, and furthermore, the existence of measurements errors. To provide a reliable answer, probabilistic instead of deterministic values should be provided, which carry information about the degree of uncertainty or plausibility of those model parameters providing one or more observations of the system response. This is widely-known as the Bayesian inverse problem, which has been covered in the literature from different perspectives, depending on the interpretation or the meaning assigned to the probability. In this paper, we revise two main approaches: the one that uses probability as logic, and an alternative one that interprets it as information content. The contribution of this paper is to provide an unifying formulation from which both approaches stem as interpretations, and which is more general in the sense of requiring fewer axioms, at the time the formulation and computation is simplified by dropping some constants. An extension to the problem of model class selection is derived, which is particularly simple under the proposed framework. A numerical example is finally given to illustrate the utility and effectiveness of the method.

A new algorithm for prognostics using subset simulation

This work presents an efficient computational framework for prognostics by combining the particle filter-based prognostics principles with the technique of Subset Simulation, first developed in S.K. Au and J.L. Beck [Probabilistic Engrg. Mech., 16 (2001), pp. 263-277], which has been named PFP-SubSim. The idea behind PFP-SubSim algorithm is to split the multi-step-ahead predicted trajectories into multiple branches of selected samples at various stages of the process, which correspond to increasingly closer approximations of the critical threshold. Following theoretical development, discussion and an illustrative example to demonstrate its efficacy, we report on experience using the algorithm for making predictions for the end-of-life and remaining useful life in the challenging application of fatigue damage propagation of carbon-fibre composite coupons using structural health monitoring data. Results show that PFP-SubSim algorithm outperforms the traditional particle filter-based prognostics approach in terms of computational efficiency, while achieving the same, or better, measure of accuracy in the prognostics estimates. It is also shown that PFP-SubSim algorithm gets its highest efficiency when dealing with rare-event simulation.

An energy-based prognostic framework to predict evolution of damage in composite materials

This chapter describes damage prognosis techniques in the context of structural health monitoring for aerospace materials, and illustrates the efficacy of the proposed methods using fatigue data from a graphite–epoxy composite coupon. Prognostics is a core element in health management sciences which aims to predict remaining useful lifetime of the systems or components through estimation of their future health state based on partial knowledge about the current health state and future system usage. The methods shown in this chapter use a physics-based modeling approach whereby the time-dependent behavior of the damaged material is idealized via mathematical equations that rely on physical principles. Rigorous mathematical tools are used to estimate the uncertainty associated with the prediction process. Information stemming from these predictions is usable in an operational context for informed decisions about safety and maintenance, among others.

An information theoretic approach for knowledge representation using Petri nets

A new hybrid approach for Petri nets (PNs) is proposed in this paper by combining the PNs principles with the foundations of information theory for knowledge representation. The resulting PNs have been named Plausible Petri nets (PPNs) mainly because they can handle the evolution of a discrete event system together with uncertain (plausible) information about the system using states ofinformation. This paper overviews the main concepts of classical PNs and presents a method to allow uncertain information exchange about a state variable within the system dynamics. The resulting methodology is exemplified using an idealized expert system, which illustrates some of the challenges faced in real-world applications of PPNs.

A new paradigm for uncertain knowledge representation by Plausible Petri nets

This paper presents a new model for Petri nets (PNs) which combines PN principles with the foundations of information theory for uncertain knowledge representation. The resulting framework has been named Plausible Petri nets (PPNs). The main feature of PPNs resides in their efficiency to jointly consider the evolution of a discrete event system together with uncertain information about the system state using states of information. The paper overviews relevant concepts of information theory and uncertainty representation, and presents an algebraic method to formally consider the evolution of uncertain state variables within the PN dynamics. To illustrate some of the real-world challenges relating to uncertainty that can be handled using a PPN, an example of an expert system is provided, demonstrating how condition monitoring data and expert opinion can be modelled.

A STOCHASTIC MODEL FOR TISSUE CONSISTENCE EVOLUTION BASED ON THE INVERSE PROBLEM

An inverse-stochastic framework is proposed to reproduce the pattern evolution and predict the mechanical properties of a tissue-engineered culture from ultrasonic measurements in an in-vitro culture. A Markovian type of evolution is expected in tissue cultures for mechanical properties such us bulk modulus (K) or attenuation coefficient (AC), under the hypothesis that the future of the process depends only upon its present state, and not upon past states. Additionally a spread in the evolution histories for different repetitions of the same process is expected, consequently stochastic models such us Markov chains [Gallager, 1996] seems to be more suitable. The method proposed is predictive in nature and can be applicable to any measurable biomechanical process, under the assumption that the process shows Markovian evolution.

Model-based damage evaluation of layered CFRP structures

An ultrasonic evaluation technique for damage identification of layered CFRP structures is presented. This approach relies on a model-based estimation procedure that combines experimental data and simulation of ultrasonic damage-propagation interactions. The CFPR structure, a [0/90]4s lay-up, has been tested in an immersion through transmission experiment, where a scan has been performed on a damaged specimen. Most ultrasonic techniques in industrial practice consider only a few features of the received signals, namely, time of flight, amplitude, attenuation, frequency contents, and so forth. In this case, once signals are captured, an algorithm is used to reconstruct the complete signal waveform and extract the unknown damage parameters by means of modeling procedures. A linear version of the data processing has been performed, where only Young modulus has been monitored and, in a second nonlinear version, the first order nonlinear coefficient β was incorporated to test the possibility of detection of ea...

A MULTISCALE MECHANICAL MODEL FOR THE CERVICAL TISSUE

A multi-scale constitutive model for the nonpregnant cervical tissue is presented. The mechanical response of the cervix is described by a model which takes into account material properties at different structural hierarchies of tissue through a multi-scale coupling scheme. The model introduces the deformation mechanisms of collagen fibrils at the nanoscale into a macroscopic description of the mechanical behavior of tissue continuum. The composition of soft tissues like cervical tissue consists of a distribution of cells embedded in an extracellular matrix (ECM). The microstructure of cervical ECM is composed of dense, hydrated and highly cross-linked collagen network embedded in a viscous proteoglycan ground substance. The mechanical behavior of cervix can be largely due to different constituents of its extracellular matrix, and the collagen fibers are the major responsible for its mechanical strength [M. House, 2009]. So the proposed model considers the stroma as the maximum responsible for the mechanical strength of the cervix.