How do we understand and visualize uncertainty?

Geophysicists are often concerned with reconstructing subsurface properties using observations collected at or near the surface. For example, in seismic migration, we attempt to reconstruct subsurface geometry from surface seismic recordings, and in potential field inversion, observations are used to map electrical conductivity or density variations in geologic layers. The procedure of inferring information from indirect observations is called an inverse problem by mathematicians, and such problems are common in many areas of the physical sciences. The inverse problem of inferring the subsurface using surface observations has a corresponding forward problem, which consists of determining the data that would be recorded for a given subsurface configuration. In the seismic case, forward modeling involves a method for calculating a synthetic seismogram, for gravity data it consists of a computer code to compute gravity fields from an assumed subsurface density model. Note that forward modeling often involves assumptions about the appropriate physical relationship between unknowns (at depth) and observations on the surface, and all attempts to solve the problem at hand are limited by the accuracy of those assumptions. In the broadest sense then, exploration geophysicists have been engaged in inversion since the dawn of the profession and indeed algorithms often applied in processing centers can all be viewed as procedures to invert geophysical data

Multivariate adaptive regression splines for estimating riverine constituent concentrations

Regression-based methods are commonly used for riverine constituent concentration/flux estimation, which is essential for guiding water quality protection practices and environmental decision making. This paper developed a multivariate adaptive regression splines model for estimating riverine constituent concentrations (MARS-EC). The process, interpretability and flexibility of the MARS-EC modelling approach, was demonstrated for total nitrogen in the Patuxent River, a major river input to Chesapeake Bay. Model accuracy and uncertainty of the MARS-EC approach was further analysed using nitrate plus nitrite datasets from eight tributary rivers to Chesapeake Bay. Results showed that the MARS-EC approach integrated the advantages of both parametric and nonparametric regression methods, and model accuracy was demonstrated to be superior to the traditionally used ESTIMATOR model. MARS-EC is flexible and allows consideration of auxiliary variables; the variables and interactions can be selected automatically. MARS-EC does not constrain concentration-predictor curves to be constant but rather is able to identify shifts in these curves from mathematical expressions and visual graphics. The MARS-EC approach provides an effective and complementary tool along with existing approaches for estimating riverine constituent concentrations

Spatial Interpolation contribution to noise maps uncertainty

Noise maps results are usually presented as contour graphs or isophone curves, which describe the sound levels as functions of spatial location. These maps are added to Geographic Information Systems (GIS), allowing sound level evaluation as a function of the continuous coordinates x and y, for a given height above ground. Although the outcome of the system is a continuous variable, the calculations that allow its evaluation are obtained in discrete points that form a calculation grid, which is created by the application of spatial sampling techniques. Using spatial interpolation tools, values are assigned to the locations in which measures or calculations have not been performed. The application of sampling and interpolation techniques (the type of grid, its density, the interpolation algorithms…) contributes to the uncertainty of the results. This paper describes a calculation method to quantify the uncertainty associated to the spatial sampling and interpolation process. We also propose a revision of the classical meaning of noise mapping uncertainty, taking into account the final application of the results

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure

Real-time Monitoring of Uncertainty due to Refraction in Multibeam Echo Sounding

A software toolkit has been developed to objectively monitor uncertainty due to refraction in multibeam echosounding, specifically mapping systems that employ underway sound speed profiling hardware. The toolkit relies on the use of a raytrace simulator which mimics the sounding geometry of any given echosounder, specifically array type, angular sector, draft, and availability of a surface sound speed probe. The simulator works by objectively comparing a pair of consecutively collected sound speed profiles and reporting sounding uncertainty across the entire potential sounding space. Realtime visualizations of the uncertainty as a function of time and space allow the operator to tune the sound speed profile collection regime to maintain a desired sounding uncertainty while at the same time minimizing the number of casts collected