Sparse bayesian polynomial chaos approximations of elasto-plastic material models

In this paper we studied the uncertainty quantification in a functional approximation form of elastoplastic models parameterised by material uncertainties. The problem of estimating the polynomial chaos coefficients is recast in a linear regression form by taking into consideration the possible sparsity of the solution. Departing from the classical optimisation point of view, we take a slightly different path by solving the problem in a Bayesian manner with the help of new spectral based sparse Kalman filter algorithms

Uncertainty quantification of leakages in a multistage simulation and comparison with experiments

The present paper presents a numerical study of the impact of tip gap uncertainties in a multistage turbine. It is well known that the rotor gap can change the gas turbine efficiency but the impact of the random variation of the clearance height has not been investigated before. In this paper the radial seals clearance of a datum shroud geometry, representative of steam turbine industrial practice, was systematically varied and numerically tested. By using a Non-Intrusive Uncertainty Quantification simulation based on a Sparse Arbitrary Moment Based Approach, it is possible to predict the radial distribution of uncertainty in stagnation pressure and yaw angle at the exit of the turbine blades. This work shows that the impact of gap uncertainties propagates radially from the tip towards the hub of the turbine and the complete span is affected by a variation of the rotor tip gap. This amplification of the uncertainty is mainly due to the low aspect ratio of the turbine and a similar behavior is expected in high pressure turbines

Parameter Estimation via Conditional Expectation --- A Bayesian Inversion

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes's theory is the proper mathematical background for this identification process. The possibility of being able to compute a conditional expectation turns out to be crucial for this purpose. We show how this theoretical background can be used in an actual numerical procedure, and shortly discuss various numerical approximations

Bayesian parameter identification in plasticity

To evaluate the cyclic behaviour under different loading conditions using the kinematic and isotropic hardening theory of steel a Chaboche visco-plastic material model is employed. The parameters of a constitutive model are usually identified by minimization of the distance between model response and experimental data. However, measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article the Choboche model is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behaviour as experimental data. Then the model parameters are identified by applying a variaty of Bayes’s theorem. Identified parameters are compared with the true parameters in the simulation and the efficiency of the identification method is discussed

Histamine index and clinical expression of rheumatoid arthritis activity

Background/Aim: Many arguments prove the pathophysiologic role of histamine in the process of remodeling and joint destruction in rheumatoid arthritis. The aim of our study was to find out if there was a relation between histamine concentration in synovial fluid and blood with clinical expression of disease activity. Methods: Histamine concentration in synovial fluid and blood was determinated in 19 patients with rheumatoid arthritis. Histamine concentration measurement was based on the Shore's fluorometric method. Histamine index (HI) was evaluated as a ratio between histamine concentration in synovial fluid and blood. Disease activity score, DAS 28 (3), with three variables (erythrocyte sedimentation rate, the number of swelled joints and the number of tender joints) was also evaluated. Results: Our results showed that there was no significant difference in concentration of histamine in synovial fluid and blood related to disease activity. However, there was a significiant difference in the histamine index which was increased proportionally with disease activity. Conclusion: Our study indicates that histamine index could be useful in estimation of rheumatoid arthritis activity

1D analytic and numerical analysis of multilayer laminates and thin film heat transfer gauges

The impulse response method is widely used for heat transfer analysis in turbomachinery applications. Traditionally, the 1D method assumes a linear time invariant, isotropic, semi-infinite block and does not accurately model the behaviour of laminated materials. This paper evaluates the error introduced by the single layer assumption and outlines the required modifications for multilayer analysis. The analytic solution for an N layer, semi-infinite laminate is presented. Adapted multilayer basis functions are derived for the impulse response method and used to evaluate the impact of uniform, isotropic assumptions. A numerical solution to the laminate problem is also presented. A penta-diagonal inversion algorithm, for a modified Crank-Nicolson scheme, is evaluated for fast stable implementation of multilayer simulation. The scheme shows comparable performance to the impulse response, whilst removing the requirement for linear time invariance. The methods are demonstrated in the case of analysing a thin film gauge, used in laboratory analysis of heat transfer in a turbine nozzle guide vane. Thin film gauge manufacturing techniques have advanced significantly in recent years. Advanced multilayer constructions are now used however, post-processing commonly relies on outdated single layer methods. This paper provides a universal methodology, required to analyse modern-day multilayer heat transfer measurements

Plasticity described by uncertain parameters - a variational inequality approach -

In this paper we consider the mixed variational formulation of the quasi-static stochastic plasticity with combined isotropic and kinematic hardening. By applying standard results in convex analysis we show that criteria for the existence, uniqueness, and convergence can be easily derived. In addition, we demonstrate the mathematical similarity with the corresponding deterministic formulation which further may be extended to a stochastic variational inequality of the first kind. The aim of this work is to consider the numerical approximation of variational inequalities by a “white noise analysis”. By introducing the random fields/processes used to model the displacements, stress and plastic strain and by approximating them by a combination of Karhunen-Lo`eve and polynomial chaos expansion, we are able to establish stochastic Galerkin and collocation methods. In the first approach, this is followed by a stochastic closest point projection algorithm in order to numerically solve the problem, giving an intrusive method relying on the introduction of the polynomial chaos algebra. As it does not rely on sampling, the method is shown to be very robust and accurate. However, the same procedure may be applied in another way, i.e. by calculating the residuum via high-dimensional integration methods (the second approach) giving a non-intrusive Galerkin techniques based on random sampling—Monte Carlo and related techniques—or deterministic sampling such as collocation methods. The third approach we present is in pure stochastic collocation manner. By highlighting the dependence of the random solution on the uncertain parameters, we try to investigate the influence of individual uncertain characteristics on the structure response by testing several numerical problems in plain strain or plane stress conditions