Robust inverse optimization

Given an observation of a decision-maker’s uncertain behavior, we develop a robust inverse optimization model for imputing an objective function that is robust against mis-specifications of the behavior. We characterize the inversely optimized cost vectors for uncertainty sets that may or may not intersect the feasible region, and propose tractable solution methods for special cases. We demonstrate the proposed model in the context of diet recommendation.     

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.     

Higher-order moments and spectra of velocity fluctuations in adverse-pressure-gradient turbulent boundary layer

The characteristics of turbulent boundary layer flows with adverse pressure gradients (APGs) differ significantly from those of canonical boundary layers. We have investigated the effects of an APG on the higher-order moments and spectra of velocity fluctuations. The local wavelet spectra reveal a large difference in energy-containing frequencies of streamwise and wall-normal components of turbulent velocities, which results in smaller Reynolds shear stress production. Moreover, an analysis of bispectra in the Fourier space has revealed that non-local interactions, consisting of streamwise fluctuating velocity with low frequency and wall-normal velocity with high frequency, occur in the APG flow. However, the small-scale motions are not affected by imposing an APG.     

Turbulent Heat and Fluid Flow over a Two-Dimensional Hill

Experimental investigation has been made on the flow and thermal fields over a heated two-dimensional hill with a cosine-squared shape. The detailed turbulent characteristics are measured by a backscatter-type two-component LDV, a PIV system, a fine thermocouple and a cold-wire probe. In the reverse-flow region on the leeward side of the hill, the turbulence intensities and the Reynolds shear stress show much larger values than in a canonical wall-bounded shear flow. The mean temperature maintains a relatively high value below the location where the horizontal mean velocity rapidly decreases. At the outer edge of the reverse-flow region, there exists a second maximum intensity of temperature fluctuations. The instantaneous temperature waveforms near the heated surface show very large amplitude consisting of high-frequency fluctuations superimposed on the low-frequency motions. Simultaneous measurement of velocity and temperature is also done using a combination of a two-component LDV and a fine-wire thermocouple together with digital response compensation. In the downstream region of the hill, the horizontal and vertical turbulent heat fluxes become maximum at the hill-top height, and tend to diffuse in the vertical direction. On the other hand, in the reverse-flow region formed behind the hill, both of the heat fluxes decrease remarkably. In particular, it is worth noting that the horizontal turbulent heat flux near the surface becomes opposite in sign to that in the forward flow region. This is mainly due to the reversal of the mean flow direction.     

A robust-CVaR optimization approach with application to breast cancer therapy

We present a framework to optimize the conditional value-at-risk (CVaR) of a loss distribution under uncertainty. Our model assumes that the loss distribution is dependent on the state of some system and the fraction of time spent in each state is uncertain. We develop and compare two robust-CVaR formulations that take into account this type of uncertainty. We motivate and demonstrate our approach using radiation therapy treatment planning of breast cancer, where the uncertainty is in the patient’s breathing motion and the states of the system are the phases of the patient’s breathing cycle. We use a CVaR representation of the tails of the dose distribution to the points in the body and account for uncertainty in the patient’s breathing pattern that affects the overall dose distribution.