Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

A linear-algebraic algorithm for identifying rigid-unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable-block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.

Modelling non-equillibrium unsaturated flow in soils during sudden pressure head changes by solving Richards' equation with a Method of lines approach

<p>The classical formulation of Richards' equation is relying on a unique functional relationship between water content, conductivity and pressure head. Some phenomena like hystersis effects in the water content during wetting and drying cycles and hydraulic non-equillibrium cannot be accounted for with this formulation. Therefor it has been extended in different ways in the past to be able to include these effects in the simulation. Each modification comes with its own challenges regarding implementation and numerical stability.<br>The Method Of Lines approach to solving the Richards' equation has already be shown to be an efficient and stable alternative to established solution methods, such as low-order finite difference and finite element methods applied to the mixed form of Richards' equation.<br>In this work a slightly modified Method Of Lines approach is used to solve the pressure based 1D Richards' equation. A finite differencing scheme is applied to the spatial derivative and the resulting system of ordinary differential equations is reformulated as differential-algebraic system of equations. The open-source code IDAS from the Sundials suite is used to solve the DAE system. Different extensions to Richards' equation have been incorporated into the model to address the shortcomings mentioned above. These extensions are a model able to simulate preferential flow using a coupled two domain approach, a simple hysteretic model to account for hysteresis in the water retention curve and also two models to either fully or partially calculate hydraulic non-equillibrium effects. To verify the numerical robustness of the extended model, stochastic parameterizations were generated that represent the full range of all soil types. Simulations were carried out using these parameter sets and real-world meteorological boundary conditions at 10 minutes time intervals, that exhibit drastic flux changes and poses numerical challenges for classical solution methods.</p><p>The results show that not only does the extended model converge for all parameterizations, but that numerical robustness and performance is maintained. Where applicable the results have been verified against solutions from the software Hydrus and show good agreement with those.</p>

Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models

We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The approach is underpinned by an inductive framework: this is structured as a sequential loop between a learner, which manipulates a candidate BC structured as a neural network, and a sound verifier, which either certifies the candidate’s validity or generates counter-examples to further guide the learner. We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: the outcomes show that we can synthesise sound BCs up to two orders of magnitude faster, with in particular a stark speedup on the verification engine (up to three orders less), whilst needing a far smaller data set (up to three orders less) for the learning part. Beyond improvements over the state of the art, we further challenge the new approach on a hybrid dynamical model and on larger-dimensional models, and showcase the numerical robustness of our algorithms and codebase.

A Conforming A-FEM for Modeling Arbitrary Crack Propagation and Branching in Solids

In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.

Hopsan: An Open-Source Tool for Rapid Modelling and Simulation of Fluid and Mechatronic Systems

Hopsan is an open-source simulation package developed as a collaboration project between industry and academia. The simulation methodology is based on transmission line modelling, which provides several benefits such as linear model scalability, numerical robustness and parallel simulation. All sub-models are pre-compiled, so that no compilation is required prior to starting a simulation. Default component libraries are available for hydraulic, mechanic, pneumatic, electric and signal domains. Custom components can be written in C++ or generated from Modelica and Mathematica. Support for simulation-based optimization is provided using population-based, evolutionary or direct-search algorithms. Recent research has largely focused on co-simulation with other simulation tools. This is achieved either by using the Functional Mock-up Interface standard, or by tool-to-tool communications. This paper provides a description of the program and its features, the current status of the project, and an overview of recent and ongoing use cases from industry and academia.

A RPCA-Based ISAR Imaging Method for Micromotion Targets

Micro-Doppler generated by the micromotion of a target contaminates the inverse synthetic aperture radar (ISAR) image heavily. To acquire a clear ISAR image, removing the Micro-Doppler is an indispensable task. By exploiting the sparsity of the ISAR image and the low-rank of Micro-Doppler signal in the Range-Doppler (RD) domain, a novel Micro-Doppler removal method based on the robust principal component analysis (RPCA) framework is proposed. We formulate the model of sparse ISAR imaging for micromotion target in the framework of RPCA. Then, the imaging problem is decomposed into iterations between the sub-problem of sparse imaging and Micro-Doppler extraction. The alternative direction method of multipliers (ADMM) approach is utilized to seek for the solution of each sub-problem. Furthermore, to improve the computational efficiency and numerical robustness in the Micro-Doppler extraction, an SVD-free method is presented to further lessen the calculative burden. Experimental results with simulated data validate the effectiveness of the proposed method.