A new framework for understanding systematic errors in cluster lens modelling. II. Constraint selection

Cluster lens models are affected by a variety of choices in the lens modelling process. We have begun a program to develop a systematics error budget for cluster lens modelling. Here we examine the selection of image constraints as a potential systematic effect. For constraining the mass model, we find that it is more important to have images be spatially distributed around the cluster than to have them distributed in redshift. We also find that some image sets appear to be more important than others in terms of how well they constrain the models; the ‘important’ image sets typically include an image that lies close to a lensing critical curve as well as an image that is relatively isolated from other images (providing constraints in a region that would otherwise lack lensing information). These conclusions can help guide observing programs that seek follow-up data for candidate lensed images.

Bayesian Input Design for Linear Dynamical Model Discrimination

A Bayesian design of the input signal for linear dynamical model discrimination has been proposed. The discrimination task is formulated as an estimation problem, where the estimated parameter indexes particular models. As the mutual information between the parameter and model output is difficult to calculate, its lower bound has been used as a utility function. The lower bound is then maximized under the signal energy constraint. Selection between two models and the small energy limit are analyzed first. The solution of these tasks is given by the eigenvector of a certain Hermitian matrix. Next, the large energy limit is discussed. It is proved that almost all (in the sense of the Lebesgue measure) high energy signals generate the maximum available information, provided that the impulse responses of the models are different. The first illustrative example shows that the optimal signal can significantly reduce error probability, compared to the commonly-used step or square signals. In the second example, Bayesian design is compared with classical average D-optimal design. It is shown that the Bayesian design is superior to D-optimal design, at least in this example. Some extensions of the method beyond linear and Gaussian models are briefly discussed.

Validation of the ASVDADD Constraint Selection Algorithm for Effective RCCE Modeling of Natural Gas Ignition in Air

The rate-controlled constrained-equilibrium (RCCE) model reduction scheme for chemical kinetics provides acceptable accuracies in predicting hydrocarbon ignition delays by solving a smaller number of differential equations than the number of species in the underlying detailed kinetic model (DKM). To yield good approximations, the method requires accurate identification of the rate controlling constraints. Until recently, a drawback of the RCCE scheme has been the absence of a systematic procedure capable of identifying optimal constraints for a given range of thermodynamic conditions and a required level of approximation. A recent methodology has proposed for such identification an algorithm based on a simple algebraic analysis of the results of a preliminary simulation of the underlying DKM, focused on the degrees of disequilibrium (DoD) of the individual chemical reactions. It is based on computing an approximate singular value decomposition of the actual degrees of disequilibrium (ASVDADD) obtained from the DKM simulation. The effectiveness and robustness of the method have been demonstrated for methane/oxygen ignition by considering a C1/H/O (29 species/133 reactions) submechanism of the GRI-Mech 3.0 scheme and comparing the results of a DKM simulation with those of RCCE simulations based on increasing numbers of ASVDADD constraints. Here, we demonstrate the new method for shock-tube ignition of a natural gas/air mixture, with higher hydrocarbons approximately represented by propane according to the full (53 species/325 reactions) GRI-Mech 3.0 scheme including NOx formation.