Search results for: quinazoline derivatives

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 128

Authors: Sam Weber, Deepak Mishra, Susan Wilde, Elizabeth Kramer

Abstract:

The frequency and severity of cyanobacteria harmful blooms (CyanoHABs) have been increasing over time, with point and non-point source eutrophication and shifting climate paradigms being blamed as the primary culprits. Excessive nutrients, warm temperatures, quiescent water, and heavy and less regular rainfall create more conducive environments for CyanoHABs. CyanoHABs have the potential to produce a spectrum of toxins that cause gastrointestinal stress, organ failure, and even death in humans and animals. To promote enhanced, proactive CyanoHAB management, risk modeling using geospatial tools can act as predictive mechanisms to supplement current CyanoHAB monitoring, management and mitigation efforts. The risk maps would empower water managers to focus their efforts on high risk water bodies in an attempt to prevent CyanoHABs before they occur, and/or more diligently observe those waterbodies. For this research, exploratory spatial data analysis techniques were used to identify the strongest predicators for CyanoHAB blooms based on remote sensing-derived cyanobacteria cell density values for 771 waterbodies in the Georgia Piedmont and landscape characteristics of their watersheds. In-situ datasets for cyanobacteria cell density, nutrients, temperature, and rainfall patterns are not widely available, so free gridded geospatial datasets were used as proxy variables for assessing CyanoHAB risk. For example, the percent of a watershed that is agriculture was used as a proxy for nutrient loading, and the summer precipitation within a watershed was used as a proxy for water quiescence. Cyanobacteria cell density values were calculated using atmospherically corrected images from the European Space Agency’s Sentinel-2A satellite and multispectral instrument sensor at a 10-meter ground resolution. Seventeen explanatory variables were calculated for each watershed utilizing the multi-petabyte geospatial catalogs available within the Google Earth Engine cloud computing interface. The seventeen variables were then used in a multiple linear regression model, and the strongest predictors of cyanobacteria cell density were selected for the final regression model. The seventeen explanatory variables included land cover composition, winter and summer temperature and precipitation data, topographic derivatives, vegetation index anomalies, and soil characteristics. Watershed maximum summer temperature, percent agriculture, percent forest, percent impervious, and waterbody area emerged as the strongest predictors of cyanobacteria cell density with an adjusted R-squared value of 0.31 and a p-value ~ 0. The final regression equation was used to make a normalized cyanobacteria cell density index, and a Jenks Natural Break classification was used to assign waterbodies designations of low, medium, or high risk. Of the 771 waterbodies, 24.38% were low risk, 37.35% were medium risk, and 38.26% were high risk. This study showed that there are significant relationships between free geospatial datasets representing summer maximum temperatures, nutrient loading associated with land use and land cover, and the area of a waterbody with cyanobacteria cell density. This data analytics approach to CyanoHAB risk assessment corroborated the literature-established environmental triggers for CyanoHABs, and presents a novel approach for CyanoHAB risk mapping in waterbodies across the greater southeastern United States.

Keywords: cyanobacteria, land use/land cover, remote sensing, risk mapping

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

Procedia PDF Downloads 224