Fredrik Edelvik

Rational radial basis function interpolation with applications to antenna design

Functions with poles occur in many branches of applied mathematics which involve resonance phenomena. Such functions are challenging to interpolate, in particular in higher dimensions. In this paper we develop a technique for interpolation with quotients of two radial basis function (RBF) expansions to approximate such functions as an alternative to rational approximation. Since the quotient is not uniquely determined we introduce an additional constraint, the sum of the RBF-norms of the numerator and denominator squared should be minimal subjected to a norm condition on the function values. The method was designed for antenna design applications and we show by examples that the scattering matrix for a patch antenna as a function of some design parameters can be approximated accurately with the new method. In many cases, e.g. in antenna optimization, the function evaluations are time consuming, and therefore it is important to reduce the number of evaluations but still obtain a good approximation. A sensitivity analysis of the new interpolation technique is carried out and it gives indications how efficient adaptation methods could be devised. A family of such methods are evaluated on antenna data and the results show that much performance can be gained by choosing the right method.

Particle Swarm Optimization Applied to EEG Source Localization of Somatosensory Evoked Potentials

One of the most important steps in presurgical diagnosis of medically intractable epilepsy is to find the precise location of the epileptogenic foci. Electroencephalography (EEG) is a noninvasive tool commonly used at epilepsy surgery centers for presurgical diagnosis. In this paper, a modified particle swarm optimization (MPSO) method is used to solve the EEG source localization problem. The method is applied to noninvasive EEG recording of somatosensory evoked potentials (SEPs) for a healthy subject. A 1 mm hexahedra finite element volume conductor model of the subjects head was generated using T1-weighted magnetic resonance imaging data. Special consideration was made to accurately model the skull and cerebrospinal fluid. An exhaustive search pattern and the MPSO method were then applied to the peak of the averaged SEP data and both identified the same region of the somatosensory cortex as the location of the SEP source. A clinical expert independently identified the expected source location, further corroborating the source analysis methods. The MPSO converged to the global minima with significantly lower computational complexity compared to the exhaustive search method that required almost 3700 times more evaluations.

Application of particle swarm optimization in epileptic spike EEG source localization

Surgical therapy has become an important therapeutic alternative for patients with medically intractable epilepsy. Correct and anatomically precise localization of an epileptic focus is essential to decide if resection of brain tissue is possible. The inverse problem in EEG-based source localization is to determine the location of the brain sources that are responsible for the measured potentials at the scalp electrodes. We propose a new global optimization method based on particle swarm optimization (PSO) to solve the epileptic spike EEG source localization inverse problem. In a forward problem a modified subtraction method is proposed to reduce the computational time. The good accuracy and fast convergence are demonstrated for 2D and 3D cases with realistic head models. The results from the new method are promising for use in the pre-surgical clinic in the future.

Optimisation of robotised sealing stations in paint shops by process simulation and automatic path planning

Application of sealing materials is done in order to prevent water leakage into cavities of the car body, and to reduce noise. The complexity of the sealing spray process is characterised by multi-phase and free surface flows, multi-scale phenomena, and large moving geometries, which poses great challenges for mathematical modelling and simulation. The aim of this paper is to present a novel framework that includes detailed process simulation and automatic generation of collision free robot paths. To verify the simulations, the resulting width, thickness and shape of applied material on test plates as a function of time and spraying distance have been compared to experiments. The agreement is in general very good. The efficient implementation makes it possible to simulate application of one meter of sealing material in less than an hour on a standard computer, and it is therefore feasible to include such detailed simulations in the production preparation process and off-line programming of the sealing robots.

Non-invasive EEG source localization using particle swarm optimization: A clinical experiment

One of the most important steps of pre-surgical diagnosis in patients with medically intractable epilepsy is to find the precise location of the epileptogenic foci. An Electroencephalography (EEG) is a non-invasive standard tool used at epilepsy surgery center for pre-surgical diagnosis. In this paper a modified particle swarm optimization (MPSO) method is applied to a real EEG data, i.e., a somatosensory evoked potentials (SEPs) measured from a healthy subject, to solve the EEG source localization problem. A high resolution 1 mm hexahedra finite element volume conductor model of the subjects head was generated using T1-weighted magnetic resonance imaging data. An exhaustive search pattern and the MPSO method were then applied to the peak of the averaged SEPs data. The non-invasive EEG source analysis methods localized the somatosensory cortex area where our clinical expert expected the received SEPs. The proposed inverse problem solver found the global minima with acceptable accuracy and reasonable number of iterations.

Advances in neuro diagnostics based on microwave technology, transcranial magnetic stimulation and EEG source localization

Advances in neuro diagnostics based on microwave antenna system in terms of a helmet including a set of broad band patch antennas is presented. It is shown that classification algorithms can be used to detect internal bleeding in stroke patients. Transcranial magnetic stimulation has traditionally been used for brain mapping and treatment of depression. In this paper we discuss the use of the method for neuro diagnostics with the help of integrated image guidance. Surgical therapy has become an important therapeutic alternative for some patients with medically intractable epilepsy. Electroencephalography and the associated model based diagnostics as a non-invasive diagnostic tool is also discussed.

GEOMETRY ASSURANCE INTEGRATING PROCESS VARIATION WITH SIMULATION OF SPRING-IN FOR COMPOSITE PARTS AND ASSEMBLIES

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Improved Spray Paint Thickness Calculation From Simulated Droplets Using Density Estimation

Advancements in the simulation of electrostatic spray painting make it possible to evaluate the quality and efficiency of programs for industrial paint robots during Off-Line Programming (OLP). Simulation of the spray paint deposition process is very complex and requires physical simulation of the airflow, electric fields, breakup of paint into droplets, and tracking of these droplets until they evaporate or impact on a surface. The information from the simulated droplet impacts is then used to estimate the paint film thickness. The current common way of measuring paint thickness on complex geometrical shapes is to use histogram based methods. These methods are easy to implement but are dependent on good quality meshes. In this paper, we show that using kernel density estimation not only gives better estimates but it also is not dependent on mesh quality. We also extend the method using a multivariate bandwidth adapted using estimated gradients of the thickness. To show the advantages of the proposed method, all three methods are compared on a test case and with real thickness measurements from an industrial case study using a complex automotive part.

Multiobjective Optimization Applied to Design of PIFA Antennas

In this paper multiobjective optimization is applied to antenna design. The optimization algorithm is a novel response surface method based on approximation with radial basis functions. It is combined with CAD and mesh generation software, and electromagnetic solvers. To demonstrate the procedure we optimize the geometric design and feed position of a PIFA antenna located on a ground plane.

Simulations of 3D bioprinting: predicting bioprintability of nanofibrillar inks

3D bioprinting with cell containing bioinks show great promise in the biofabrication of patient specific tissue constructs. To fulfil the multiple requirements of a bioink, a wide range of materials and bioink composition are being developed and evaluated with regard to cell viability, mechanical performance and printability. It is essential that the printability and printing fidelity is not neglected since failure in printing the targeted architecture may be catastrophic for the survival of the cells and consequently the function of the printed tissue. However, experimental evaluation of bioinks printability is time-consuming and must be kept at a minimum, especially when 3D bioprinting with cells that are valuable and costly. This paper demonstrates how experimental evaluation could be complemented with computer based simulations to evaluate newly developed bioinks. Here, a computational fluid dynamics simulation tool was used to study the influence of different printing parameters and evaluate the predictability of the printing process. Based on data from oscillation frequency measurements of the evaluated bioinks, a full stress rheology model was used, where the viscoelastic behaviour of the material was captured. Simulation of the 3D bioprinting process is a powerful tool and will help in reducing the time and cost in the development and evaluation of bioinks. Moreover, it gives the opportunity to isolate parameters such as printing speed, nozzle height, flow rate and printing path to study their influence on the printing fidelity and the viscoelastic stresses within the bioink. The ability to study these features more extensively by simulating the printing process will result in a better understanding of what influences the viability of cells in 3D bioprinted tissue constructs.