Uncertainty Quantification of a Nonlinear Aeroelastic System Using Polynomial Chaos Expansion With Constant Phase Interpolation

The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels

Cost-effectiveness of shifting breast cancer surveillance from a hospital setting to a community-based national screening programme setting

Background: In the Netherlands, breast cancer surveillance after breast conserving surgery (BCS) takes place in a hospital setting for at least five years to detect possible recurrences in early stage. As breast cancer incidence rises and mortality decreases, surveillance expenses increase. This study explores the effectiveness and cost-effectiveness of BCS surveillance as delivered in a hospital setting versus providing BCS surveillance as part of the community-based National Breast Cancer Screening Program (NBCSP). We hypothesise that the NBCSP-based strategy leads to lower costs and a lower proportion of true test results (TTR) compared to the hospital-based strategy and determine to what extent potential lower effectiveness may be balanced with expected cost savings. Materials and Methods: Both strategies are compared on effectiveness and cost-effectiveness in a decision tree from a healthcare perspective over a 5-year time horizon. Women aged 50–75 without distant metastases that underwent BCS in the years 2003–2006 with complete 5 year follow-up were selected from the Netherlands Cancer Registry (n = 14,093). Key input variables were mammography sensitivity and specificity, risk of loco regional recurrence (LRR), and direct healthcare costs. The primary outcome measure was the overall predictive value (measured in true test results). Secondary effectiveness measures were the positive predictive value (PPV) (LRRs detected or true positive test results) and the negative predictive value (NPV) (true negative test results) detected within five years post-treatment. Results are presented for low and high risk patients separately and expressed in incremental cost-effectiveness ratios (ICERs). Results: For low risk patients (with grade 1 tumours, no node involvement, and hormonal treatment), the PPV and NPV for the NBCSP strategy were 3.31% and 99.88%, and 2.74% and 99.95% for the hospital strategy respectively. For high risk patients (grade 3 tumours, over three nodes involved, without hormonal treatment), the PPV and NPV for the NBCSP strategy were 64.1% and 98.9%; and 51.0% and 99.7% for the hospital strategy respectively. For low risk patients the NBCSP saves €202 per patient leading to an ICER of €109/accurate test result. For high risk patients the cost savings are €72 per patient, leading to an ICER of €43/accurate test result. Conclusion: Although the NBCSP-based strategy is cheaper, it cannot replace the hospital-based strategy, since it leads to only half of the accurate test results compared to hospital-based strategy. This contradicts the goal of early detection of LRRs and improving outcomes

A novel penalty-based reduced order modelling method for dynamic analysis of joint structures

This work proposes a new reduced order modelling method to improve the computational efficiency for the dynamic simulation of a jointed structures with localized contact friction non-linearities. We reformulate the traditional equation of motion for a joint structure by linearising the non-linear system on the contact interface and augmenting the linearised system by introducing an internal non-linear penalty variable. The internal variable is used to compensate the possible non-linear effects from the contact interface. Three types of reduced basis are selected for the Galerkin projection, namely, the vibration modes (VMs) of the linearised system, static modes (SMs) and also the trial vector derivatives (TVDs) vectors. Using these reduced basis, it would allow the size of the internal variable to change correspondingly with the number of active non-linear DOFs. The size of the new reduced order model therefore can be automatically updated depending on the contact condition during the simulations. This would reduce significantly the model size when most of the contact nodes are in a stuck condition, which is actually often the case when a jointed structure vibrates. A case study using a 2D joint beam model is carried out to demonstrate the concept of the proposed method. The initial results from this case study is then compared to the state of the art reduced order modeling

Survival after Locoregional Recurrence or Second Primary Breast Cancer: Impact of the Disease-Free Interval

The association between the disease-free interval (DFI) and survival after a locoregional recurrence (LRR) or second primary (SP) breast cancer remains uncertain. The objective of this study is to clarify this association to obtain more information on expected prognosis. Women first diagnosed with early breast cancer between 2003–2006 were selected from the Netherlands Cancer Registry. LRRs and SP tumours within five years of first diagnosis were examined. The five-year period was subsequently divided into three equal intervals. Prognostic significance of the DFI on survival after a LRR or SP tumour was determined using Kaplan-Meier estimates and multivariable Cox regression analysis. Follow-up was complete until January 1, 2014. A total of 37,278 women was included in the analysis. LRRs or SP tumours were diagnosed in 890 (2,4%) and 897 (2,4%) respectively. Longer DFI was strongly and independently related to an improved survival after a LRR (long versus short: HR 0.65, 95% CI 0.48–0.88; medium versus short HR 0.81, 95% CI 0.65–1.01). Other factors related to improved survival after LRR were younger age (<70 years) and surgical removal of the recurrence. No significant association was found between DFI and survival after SP tumours. This is the first study to explore the association between the DFI and survival after recurrence in a nationwide population-based cancer registry. The DFI before a LRR is an independent prognostic factor for survival, with a longer DFI predicting better prognosi

The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions

[Abstract]: In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a few inversions of the original distribution plus independent samples from a standard normal variable. We will show that with this path-independent collocation approach the exact simulation of the Heston stochastic volatility model, as proposed in Broadie and Kaya [Oper. Res., 2006, 54, 217–231], can be performed efficiently and accurately. We also show how to efficiently generate samples from the squared Bessel process and perform the exact simulation of the SABR model

Uncertainty quantification and Heston model

[Abstract]: In this paper, we study the impact of the parameters involved in Heston model by means of Uncertainty Quantification. The Stochastic Collocation Method already used for example in computational fluid dynamics, has been applied throughout this work in order to compute the propagation of the uncertainty from the parameters of the model to the output. The well-known Heston model is considered and involved parameters in the Feller condition are taken as uncertain due to their important influence on the output. Numerical results where the Feller condition is satisfied or not are shown as well as a numerical example with real market data.This paper has been ERCIM “Alain Bensoussan Fellowship Programme” and partially funded by MCINN (Project MTM2010–21135–C02-01)