Multiscale nonlinear inversion of gravity data for depth-to-basement estimation via coupled stochastic-deterministic optimization

We have developed a multiscale approach for solving 2D and 3D nonlinear inverse problems of gravity data in estimating the basement topography. The inversion is carried out in two stages in which the long-wavelength features of the basement are first estimated from smoothed gravity data via a stochastic optimization algorithm. The solution of this stage is used as the starting model for a deterministic optimization algorithm to reconstruct the short-wavelength features from the full-spectrum gravity data. The forward problem is capable of handling lateral and vertical variations in the density of sediments. Two cases are considered regarding prior knowledge about the density: (1) The density contrast between sediments at the surface and the underlying basement and its vertical variations are a priori known, and (2) only the density contrast at the surface is known with its vertical gradient to be recovered in the inversion. In the former case, the unknowns of the problem are the depths, whereas in the latter case, they are the depths and density gradients defined individually for each prism. Therefore, the inverse problem is ill-posed and has many local minima. The stochastic optimization algorithm uses a random initial model and estimates a coarse model of the basement topography. By repeating the stochastic inversion, an ensemble of solutions is formed defining an equivalent domain in the model space supposed to be within the neighborhood of the global minimum of which several starting solutions are extracted for the secondary deterministic inversion. The presented methodology has been tested successfully in converging to the global minima in 2D and 3D cases with 50 and 2352 total number of prisms, respectively. Finally, the inversion algorithm is used to calculate the thickness of the sediments in the South Caspian Basin using the EIGEN-6c4 global gravity model.

From an Optimal Point to an Optimal Region: A Novel Methodology for Optimization of Multimodal Constrained Problems and a Novel Constrained Sliding Particle Swarm Optimization Strategy

The present work proposes a novel methodology for an optimization procedure extending the optimal point to an optimal area based on an uncertainty map of deterministic optimization. To do so, this work proposes the deductions of a likelihood-based test to draw confidence regions of population-based optimizations. A novel Constrained Sliding Particle Swarm Optimization algorithm is also proposed that can cope with the optimization procedures characterized by multi-local minima. There are two open issues in the optimization literature, uncertainty analysis of the deterministic optimization and application of meta-heuristic algorithms to solve multi-local minima problems. The proposed methodology was evaluated in a series of five benchmark tests. The results demonstrated that the methodology is able to identify all the local minima and the global one, if any. Moreover, it was able to draw the confidence regions of all minima found by the optimization algorithm, hence, extending the optimal point to an optimal region. Moreover, providing the set of decision variables that can give an optimal value, with statistical confidence. Finally, the methodology is evaluated to address a case study from chemical engineering; the optimization of a complex multifunctional process where separation and reaction are processed simultaneously, a true moving bed reactor. The method was able to efficiently identify the two possible optimal operating regions of this process. Therefore, proving the practical application of this methodology.

Numerical method for parameter inference of systems of nonlinear ordinary differential equations with partial observations

Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ordinary differential equations with partial observations. Our method combines fast Gaussian process-based gradient matching and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate, robust and efficient with partial observations and large noise.

D6.1 Deterministic optimization software

This deliverable focuses on the implementation of deterministic optimization algorithms and problem solvers within KRATOS open-source software. One of the main challenges of optimization algorithms in Finite-Element based optimization is how to get the gradient of response functions which are used as objective and constraints when this is not available in an explicit form. The idea is to use local sensitivity analysis to get the gradient of the response function(s)

Iliski, a software for robust calculation of transfer functions

1.AbstractUnderstanding the relationships between biological events is paramount to unravel pathophysiological mechanisms. These relationships can be modeled with Transfer Functions (TFs), with no need of a priori hypotheses as to the shape of the transfer function. Here we present Iliski, a software dedicated to TFs computation between two signals. It includes different pre-treatment routines and TF computation processes: deconvolution, deterministic and non-deterministic optimization algorithms that are adapted to disparate datasets. We apply Iliski to data on neurovascular coupling, an ensemble of biological events that link neuronal activity to local changes of blood flow, highlighting the software benefits and caveats in the computation and evaluation of TFs. We also propose a workflow that will help users to choose the best computation according to the dataset. Iliski is available under the open-source license CC BY 4.0 on GitLab (https://gitlab.com/AliK_A/iliski) and can be used on the most common operating systems, either within the MATLAB environment, or as a standalone application.

Reliability optimization of a large-size tubular negative Poisson’s ratio battery protection structure

The battery pack placed on the chassis of an electric vehicle is easily to be damaged in a side collision because of its large volume. Therefore, the power battery pack should comprise a protective structure that can cover the entire side. Because the traditional hollow structure has limited performance, this paper proposes a large-size tubular negative Poisson's ratio (LTNPR) protection structure. A 2D LTNPR structure that can protect the side of battery pack entirely is designed and its mechanical properties are calculated. Then, the FE model of the battery pack equipped with LTNPR structure is analyzed under side pole impact by CAE simulation, which verifies the superiority of the LTNPR structure over the traditional hollow structure. Finally, deterministic optimization and reliability optimization are applied. The study and results demonstrate that compared with traditional structure, the LTNPR structure can improve the crashworthiness of the power battery pack significantly. Furthermore, the specific energy absorption (SEA) of LTNPR structure is increased by 28.81% and the maximum acceleration of battery pack is reduced by 15.29% through deterministic optimization, while the σ level is increased from 2.8448 to 8 through reliability optimization. The passive safety of electric vehicle is improved.