Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data

To date the primary focus of most constrained approximate optimization strategies is that application of the method should lead to improved designs. Few researchers have focused on the development of constrained approximate optimization strategies that are assured of converging to a Karush-Kuhn-Tucker (KKT) point for the problem. Recent work by the authors based on a trust region model management strategy has shown promise in managing the convergence of constrained approximate optimization in application to a suite of single level optimization test problems. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, the authors have shown in application studies that the approximate optimization process converges to a KKT point for the problem. The approximate optimization strategy sequentially builds a cumulative response surface approximation of the augmented Lagrangian which is then optimized subject to a trust region constraint. In this research the authors develop a formal proof of convergence for the response surface approximation based optimization algorithm. Previous application studies were conducted on single level optimization problems for which response surface approximations were developed using conventional statistical response sampling techniques such as central composite design to query a high fidelity model over the design space. In this research the authors extend the scope of application studies to include the class of multidisciplinary design optimization (MDO) test problems. More importantly the authors show that response surface approximations constructed from variable fidelity data generated during concurrent subspace optimization (CSSOs) can be effectively managed by the trust region model management strategy. Results for two multidisciplinary test problems are presented in which convergence to a KKT point is observed. The formal proof of convergence and the successful MDO application of the algorithm using variable fidelity data generated by CSSO are original contributions to the growing body of research in MDO.Nomenclature k Lagrangian iteration - s approximate minimization iteration - i, j, l variable indices - m number of inequality constraints - n number of design variables - p number of equality constraints - f(x) objective function - g(x) inequality constraint vector - g _j (x) j-th inequality constraint - h(x) equality constraint vector - h _j (x) i-th equality constraint - c(x) generalized constraint vector - c _i (x) i-th generalized constraint - c ₁,c ₂,c ₃,c ₄ real constants - m(x) approximate model - q(x) approximate model - q(x) piecewise approximation - r _p penalty parameter - t, t ₁,t ₂ step size length - x design vector, dimensionn - x _l l-th design variable - x ^U upper bound vector, dimensionn - x _l ^U l-th design upper bound - x ^L lower bound vector, dimensionn - x _l ^L l-th design lower bound - B approximation of the Hessian - K constraints residual - S design space - , ₁, ₂, scalars - ₁, ₂ convergence tolerances - ₀, ₁, ₂, , trust region parameters - Lagrange multiplier vector, dimensionm+p - _i i-th Lagrange multiplier - trust region ratio - (x) alternative form for inequality constraints - (x, ,r _p ) augmented Lagrangian function - approximation of the augmented Lagrangian function - fidelity control - . Euclidean norm - , inner product - gradient operator with respect to design vector x - P(y(x)) projection operator; projects the vector y onto the set of feasible directions at x - trust region radius - x step size     

Monitoring trabecular bone microdamage using a dynamic acousto-elastic testing method

Dynamic acousto-elastic testing (DAET) is based on the coupling of a low-frequency (LF) acoustic wave and high-frequency ultrasound (US) pulses (probing wave). It was developed to measure US viscoelastic and dissipative non-linearity in trabecular bone. It is well known that this complex biphasic medium contains microdamage, even when tissues are healthy. The purpose of the present study was to assess the sensitivity of DAET to monitor microdamage in human calcanei. Three protocols were therefore performed to investigate the regional heterogeneity of the calcaneus, the correlation between DAET measurements and microdamage revealed by histology, and DAET sensitivity to mechanically induced fatigue microdamage. The non-linear elastic parameter beta was computed for all these protocols. The study demonstrated the presence of high viscoelastic and dissipative non-linearity only in the region of the calcaneus close to the anterior talocalcaneal articulation (region of high bone density). Protocols 1 and 2 also showed that most unsorted calcanei did not naturally exhibit high non-linearity, which is correlated with a low level of microcracks. Nevertheless, when microdamage was actually present, high levels of US non-linearity were always found, with characteristic non-linear signatures such as hysteresis and tension/compression asymmetry. Finally, protocol 3 demonstrated the high sensitivity of DAET measurement to fatigue-induced microdamage.     

Static and Dynamic Program Compilation by Interpreter Specialization

Interpretation and run-time compilation techniques are increasingly important because they can support heterogeneous architectures, evolving programming languages, and dynamically-loaded code. Interpretation is simple to implement, but yields poor performance. Run-time compilation yields better performance, but is costly to implement. One way to preserve simplicity but obtain good performance is to apply program specialization to an interpreter in order to generate an efficient implementation of the program automatically. Such specialization can be carried out at both compile time and run time.Recent advances in program-specialization technology have significantly improved the performance of specialized interpreters. This paper presents and assesses experiments applying program specialization to both bytecode and structured-language interpreters. The results show that for some general-purpose bytecode languages, specialization of an interpreter can yield speedups of up to a factor of four, while specializing certain structured-language interpreters can yield performance comparable to that of an implementation in a general-purpose language, compiled using an optimizing compiler.     

A Bayesian reconstruction method for micro-rotation imaging in light microscopy

The authors present a three-dimensional (3D) reconstruction algorithm and reconstruction-based deblurring method for light microscopy using a micro-rotation device. In contrast to conventional 3D optical imaging where the focal plane is shifted along the optical axis, micro-rotation imaging employs dielectric fields to rotate the object inside a fixed optical set-up. To address this entirely new 3D-imaging modality, the authors present a reconstruction algorithm based on Bayesian inversion theory and use the total variation function as a structure prior. The spectral properties of the reconstruction by simulations that illustrate the strengths and the weaknesses of the micro-rotation approach, compared with conventional 3D optical imaging, were studied. The reconstruction from real data sets shows that this method is promising for 3D reconstruction and offers itself as a deblurring method using a reconstruction-based procedure for removing out-of-focus light from the micro-rotation image series.     

Three‐dimensional numerical simulation of upflow bubbling fluidized bed in opaque tube under high flux solar heating

Solid particles can be used as a heat transfer medium in concentrated solar power plants to operate at higher temperature and achieve higher heat conversion efficiency than using the current solar heat transfer fluids that only work below 600°C. Among various particle circulation concepts, the dense particle suspension (DPS) flow in tubes, also called upflow bubbling fluidized bed (UBFB), was studied in the frame of the CSP2 FP7 European project. The DPS capacity to extract heat from a tube absorber exposed to concentrated solar radiation was demonstrated and the first values of the tube wall‐to‐DPS heat transfer coefficient were measured. A stable outlet temperature of 750°C was reached with a metallic tube, and a particle reflux in the near tube wall region was evidenced. In this article, the UBFB behavior is studied using the multiphase flow code NEPTUNE_CFD. Hydrodynamics of SiC Geldart A‐type particles and heat transfer imposed by a thermal flux at the wall are coupled in two‐dimensional unsteady numerical simulations. The convective/diffusive heat transfer between the gas and dispersed phase, and the inter‐particle radiative transfer (Rosseland approximation) are accounted for. Simulations and experiments are compared here and the temperature influence on the DPS flow is analyzed. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3857–3867, 2018     

A new step towards the lattice reconstruction in 3DAP

The spatial resolution of images produced by 3DAP is known not to be limited by the detector performance but by the physics of field ionisation and field evaporation. This resolution can be expressed by two parameters: the depth resolution and the lateral resolution, which have been shown to achieve, respectively, 0.06 and 0.2nm in an ideal case of a pure metal. By using this model and these values, the resolution along any crystallographic direction can be predicted. In addition, it is possible to predict the suitable sites of analysis where a given type of atomic planes can be resolved. Furthermore, it is shown that three types of planes with non-coplanar directions can be imaged in 3D reconstructed volumes. Thus, the reconstruction of the original tungsten lattice can be achieved with the use of Fourier Transform image analysis techniques. It is shown that the reliability of the method can be achieve the value of 90%.     

In vitro toxicoproteomic analysis of A549 human lung epithelial cells exposed to urban air particulate matter and its water-soluble and insoluble fractions

Background

Toxicity of airborne particulate matter (PM) is difficult to assess because PM composition is complex and variable due to source contribution and atmospheric transformation. In this study, we used an in vitro toxicoproteomic approach to identify the toxicity mechanisms associated with different subfractions of Ottawa urban dust (EHC-93).

Methods

A549 human lung epithelial cells were exposed to 0, 60, 140 and 200 μg/cm² doses of EHC-93 (total), its insoluble and soluble fractions for 24 h. Multiple cytotoxicity assays and proteomic analyses were used to assess particle toxicity in the exposed cells.

Results

The cytotoxicity data based on cellular ATP, BrdU incorporation and LDH leakage indicated that the insoluble, but not the soluble, fraction is responsible for the toxicity of EHC-93 in A549 cells. Two-dimensional gel electrophoresis results revealed that the expressions of 206 protein spots were significantly altered after particle exposures, where 154 were identified by MALDI-TOF-TOF-MS/MS. The results from cytotoxicity assays and proteomic analyses converged to a similar finding that the effects of the total and insoluble fraction may be alike, but their effects were distinguishable, and their effects were significantly different from the soluble fraction. Furthermore, the toxic potency of EHC-93 total is not equal to the sum of its insoluble and soluble fractions, implying inter-component interactions between insoluble and soluble materials resulting in synergistic or antagonistic cytotoxic effects. Pathway analysis based on the low toxicity dose (60 μg/cm²) indicated that the two subfractions can alter the expression of those proteins involved in pathways including cell death, cell proliferation and inflammatory response in a distinguishable manner. For example, the insoluble and soluble fractions differentially affected the secretion of pro-inflammatory cytokines such as MCP-1 and IL-8 and distinctly altered the expression of those proteins (e.g., TREM1, PDIA3 and ENO1) involved in an inflammatory response pathway in A549 cells.

Conclusions

This study demonstrated the impact of different fractions of urban air particles constituted of various chemical species on different mechanistic pathways and thus on cytotoxicity effects. In vitro toxicoproteomics can be a valuable tool in mapping these differences in air pollutant exposure-related toxicity mechanisms.

     

Estimating fractional cover of plant functional types in African savannah from harmonic analysis of MODIS time-series data

Assessments of tree/grass fractional cover in savannahs using remote sensing are challenging due to the heterogeneous mixture of the two plant functional types. Time-series decomposition models can be used to characterize vegetation phenology from satellite data, but have rarely been used for attributing phenological signal components to different plant functional types. Here, tree/grass dynamics are assessed in savannah ecosystems using time-series decomposition of 14 years of Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index data acquired from 2002 to 2015. The decomposition method uses harmonic analysis and tests the individual harmonic terms for statistical significance. Field data of fractional cover of trees and grasses were collected for 28 plots in Kruger National Park, South Africa. Matching MODIS pixels were analysed for their tree/grass phenological signals. Tree/grass annual and interannual variability were then assessed based on the harmonic models. In most harmonic cycles, grass-dominated sites had higher amplitudes than tree-dominated sites, while the tree green-up started earlier than grasses, before the start of the wet season. While changes in tree phenology are gradual, grasses present higher variability over time. Tree cover showed a significant correlation with the amplitude (r (correlation coefficient) = ?0.59, p = 0.001) and phase of the first harmonic term (r = ?0.73, p = 0.0001) and the number of cycles of the second harmonic term (r = 0. 56, p = 0.002). Grass cover was also significantly correlated with the amplitude (r = 0. 51, p = 0.005) and phase of the first harmonic term (r = 0.55, p = 0.002) and the number of cycles of the second harmonic term (r = ?0.52, p = 0.005). The positive correlation of grass cover with phase and negative correlation with number of cycles is indicating a late greening period and higher variability, respectively. Tree cover estimated from the phase of the strongest harmonic term showed a positive correlation with field-measured tree cover (R² (coefficient of determination) = 0.55, p < 0.01, slope = 0.93, root mean square error = 13.26%). The estimated tree cover also had a strong correlation with the woody cover map (r = 0.78, p < 0.01) produced by Bucini. The results show that MODIS time-series data can be used to estimate the fractional tree cover in heterogeneous savannahs from the phase of the plant functional type’s phenological behaviour. This study shows that harmonic analysis is able to discriminate between fractional cover by trees and grasses in savannahs. The quantitative analysis of tree/grass phenology from satellite time-series data enables a better understanding of the dynamics of the tree/grass competition and coexistence.