On transmission Zeros of piezoelectric structures

The evaluation of transmission zeros is of great importance for the control engineering applications. The structures equipped with piezoelectric patches are complex to model and usually require finite element approaches supplemented by model reduction. This study rigorously investigates the influence of mesh size, model reduction, boundary conditions (free and clamped), and sensor/actuator configuration (collocated and non-collocated) on the evaluation of transmission zeros of the piezoelectric structures. The numerical illustrations are presented for a thin rectangular plate equipped with a single pair of piezoelectric voltage sensor/ voltage actuator. Through the examples considered in this study, a link is presented between the static response (or static deflected shape) and the transmission zeros of the piezoelectric structures. This interesting observation forms the basis of: (i) a local mesh refinement strategy for computationally efficient estimation of the transmission zeros and (ii) a physical interpretation of the pole-zero pattern in the case of piezoelectric structures. The physical interpretation developed in this study helps in qualitatively explaining the pole-zero patterns observed for different configurations. It is also shown that this understanding of the relation between the static deformed shape and the transmission zeros can be used by the practitioners to modify the pole-zero pattern through a careful selection of the orientation and the size of the piezoelectric patches.

Super-resolution for doubly-dispersive channel estimation

In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for example in radar and wireless communications. In particular, for information transmission in highly non-stationary environments the channel needs to be estimated quickly with identification signals of short duration and for vehicular application simultaneous high-resolution radar is desired as well. We consider the time-continuous setting and prove an exact resampling reformulation of the involved channel operator when applied to a trigonometric polynomial as identifier in terms of sparse linear combinations of real-valued atoms. Motivated by recent works of Heckel et al. we present an exact approach for off-the-grid super-resolution which allows to perform the identification with realizable signals having compact support. Then we show how an alternating descent conditional gradient algorithm can be adapted to solve the reformulated problem. Numerical examples demonstrate the performance of this algorithm, in particular in comparison with a simple adaptive grid refinement strategy and an orthogonal matching pursuit algorithm.

The influence of refinement strategies on the wavefunctions derived from an experiment

The synergy between theory and experiment found in X-ray wavefunction refinement (XWR) makes it one of the most compelling techniques available for chemical physics. The foremost benefit of XWR – obtaining wavefunctions constrained to experimental data – is at the same time its Achilles heel, because of the dependence of the results on the quality of both empirical and theoretical data. The purpose of this work is to answer the following: What is the effect of the refinement strategy and manipulation of input data on the physical properties obtained from XWR? With that in mind, cutoffs based on data resolution and F/σ(F) ratios were applied for both steps of XWR, the Hirshfeld atom refinement (HAR) and the X-ray constrained wavefunction fitting (XCW), for four selected systems: sulfur dioxide, urea, carbamazepine and oxalic acid. The effects of changing the weighting scheme or the method to transform σ(F 2) to σ(F) were also analysed. The results show that while HAR always reaches the same result, XCW is extremely sensitive to crystallographic data manipulation. This is a result of the variability of the experimental uncertainties for different resolution shells, and of not having proper standard uncertainties. Therefore, the use of distinct constraints for each resolution interval in XCW is proposed to fix this instability.

Formal Event-B Modeling of the MICONIC Application

Automatic planning has a de facto standard language called PDDL for describing planning problems. The dynamic analysis tools associated with this language do not allow sufficient verification and validation of PDDL descriptions. Indeed, these tools, namely planners and validators, allow a posteriori error detection. In this paper, we recommend a formal approach coupling the two languages Event-B and PDDL. Event-B supports a formal development process based on the refinement technique with mathematical proofs. Thus, we propose a refinement strategy for obtaining reliable PDDL descriptions from an ultimate Event-B model that is correct by construction. The correctness is guaranteed via the verification and validation tools supported by Event-B. We have chosen the MICONIC application managing modern elevators to illustrate our approach while recognizing that the MICONIC application is already modeled in PDDL without formal proof of its correctness.

On the Benefits of Using MVC Pattern for Structuring Event-B Models of WIMP Interactive Applications

This paper presents a formal development approach for designing interactive applications using a correct-by-construction approach. In this work, we propose a refinement strategy using model-view-controller (MVC) to structure and design Event-B formal models of the interactive application. The proposed MVC-based refinement strategy facilitates the development of an abstract model and a series of refined models by introducing the possible modes, controller’s behaviour and visual components of the interactive application while preserving the required interaction-related safety properties. To demonstrate the effectiveness, scalability, reliability and feasibility of our approach, we use a small example (from automotive domain) and real-life industrial case studies (from aviation). The entire development is realized in Event-B and the associated Rodin tool is used to analyse and verify the correctness of the formalized model. Finally, the developed Event-B models are used to generate source code using EB2ALL tool for going from the specification to the implementation of the interactive application.

Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems

We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We couple the perturbed inverse iteration approach with mesh refinement strategy based on residual estimators. We demonstrate our approach on model problems in two and three dimensions.