A Data Assimilation Framework that Uses the Kullback-Leibler Divergence

The process of integrating observations into a numerical model of an evolving dynamical system, known as data assimilation, has become an essential tool in computational science. These methods, however, are computationally expensive as they typically involve large matrix multiplication and inversion. Furthermore, it is challenging to incorporate a constraint into the procedure, such as requiring a positive state vector. Here we introduce an entirely new approach to data assimilation, one that satisfies an information measure and uses the unnormalized Kullback-Leibler divergence, rather than the standard choice of Euclidean distance. Two sequential data assimilation algorithms are presented within this framework and are demonstrated numerically. These new methods are solved iteratively and do not require an adjoint. We find them to be computationally more efficient than Optimal Interpolation (3D-Var solution) and the Kalman filter whilst maintaining similar accuracy. Furthermore, these Kullback-Leibler data assimilation (KL-DA) methods naturally embed constraints, unlike Kalman filter approaches. They are ideally suited to systems that require positive valued solutions as the KL-DA guarantees this without need of transformations, projections, or any additional steps. This Kullback-Leibler framework presents an interesting new direction of development in data assimilation theory. The new techniques introduced here could be developed further and may hold potential for applications in the many disciplines that utilize data assimilation, especially where there is a need to evolve variables of large-scale systems that must obey physical constraints

A new method for assessing the safety of ships damaged by collisions

The longitudinal strength of a ship decreases with the reduction in its bending moment capacity following a collision accident. This decrease may lead to the total loss of the ship in some cases due to its loss of hull girder strength, particularly when large vessels are involved. Therefore, the damaged ship should be able to reach the closest harbour safely without any catastrophic hull girder collapse. This paper aims to develop a method to predict the hull girder residual strength of double-hull oil tankers by considering probabilistic collision damage scenarios. The collision damage index is defined as the reduction ratio of the vertical hull girder moment of inertia, and the residual strength index is characterised as the reduction ratio of the hull girder ultimate bending moment. Four different as-built double-hull oil tankers (Panamax, Aframax, Suezmax and VLCC) were studied to demonstrate the proposed method and to formulate the collision damage index. The relationships between the residual strength index and the collision damage index are identified in the form of diagrams and linear-type regressions. The produced diagrams and regressions represent a first-cut assessment of a ship’s safety immediately after taking collision damage

Surgical cyst decortication in autosomal dominant polycystic kidney disease

PURPOSE: To provide a summary of the relevant literature regarding the impact of surgical cyst decortication on hypertension, renal function, and pain management in patients with autosomal dominant polycystic kidney disease (ADPKD). METHODS: Data collection was conducted via a Medline search using the subject headings autosomal dominant polycystic kidney disease, surgery, decortication, and marsupialization. Additional reports were derived from references included within these articles. RESULTS: Despite a trend for improved blood pressure control after cyst decortication in some studies, this cumulative review of the literature did not provide consistent evidence supporting the role of this procedure in blood pressure management in patients with ADPKD. Surgical cyst decortication was associated with renal deterioration in a subset of patients with compromised baseline renal function but did not otherwise appear to have a significant impact on renal function in the majority of studies reviewed. Improvement in chronic pain after this procedure was ubiquitously reported across all studies examined. CONCLUSIONS: Despite a potential role in blood pressure management in the setting of ADPKD, surgical cyst decortication has not been definitively shown to alleviate hypertension in this clinical setting. Renal function does not appear to improve following this surgery. Patients with compromised baseline renal function appear to be at increased risk for further deterioration in renal function after cyst decortication, although the role of this procedure in altering the natural trajectory of renal failure in this patient subset needs further investigation. Cyst decortication is highly effective in the management of disease-related chronic pain for the majority of patients with ADPKD, providing durable pain relief in this patient population

Prospectus, May 6, 2009

https://spark.parkland.edu/prospectus_2009/1014/thumbnail.jp