The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.

This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.

The topic of force reconstruction has been studied quite extensively but most of the existing research work that has been done are in the domain of structural and civil engineering construction like bridges and beams. Considerable work in force reconstruction has also being done in fabrication of machines and structures like aircrafts, gear boxes etc. The topic of force reconstruction of the cutting forces during a machining process like turning or milling machines is a recent line of research to suffice the requirement of proactive monitoring of forces generated during the operation of the machine tool. The forces causing vibrations while machining if detected and monitored can enhance system productivity and efficiency of the process. The objective of this study was to investigate the algorithms available in literature for inverse force reconstruction and apply for reconstruction of cutting forces while machining on a computer numerically controlled (CNC) machine. This study has applied inverse force reconstruction technique algorithms 1) Deconvolution method, 2) Kalman filter recursive least square and 3) augmented Kalman filter for inverse reconstruction of forces for multi degree of freedom systems. Results from experiments conducted as part of this thesis work shows the effectiveness of the methods of force reconstruction to monitor the forces generated during the machining process on machine tools in real time without employing dynamometers which are expensive and complex to set-up. This study for developing a cost-effective method of force reconstruction will be instrumental in applications for improving machining efficiency and proactive preventive maintenance. / Graduate

No description available.

This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.

Introducing a new method for measureing ultra-short laser pulses, the research group "Solid State Light Sources" of the Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Berlin, encountered a new type of autoconvolution problem. The so called SD-SPIDER method aims for the reconstruction of the real valued phase of a complex valued laser pulse from noisy measurements. The measurements are also complex valued and additionally influenced by a device-related kernel function. Although the autoconvolution equation has been examined intensively in the context of inverse problems, results for complex valued functions occurring as solutions and right-hand sides of the autoconvolution equation and for nontrivial kernels were missing. The thesis is a first step to bridge this gap. In the first chapter, the physical background is explained and especially the autoconvolution effect is pointed out. From this, the mathematical model is derived, leading to the final autoconvolution equation. Analytical results are given in the second chapter. It follows the numerical treatment of the problem in chapter three. A regularization approach is presented and tested with artificial data. In particular, a new parameter choice rule making use of a specific property of the SD-SPIDER method is proposed and numerically verified. / Bei der Entwicklung einer neuen Methode zur Messung ultra-kurzer Laserpulse stieß die Forschungsgruppe "Festkörper-Lichtquellen" des Max-Born-Institutes für Nichtlineare Optik und Kurzzeitspektroskopie, Berlin, auf ein neuartiges Selbstfaltungsproblem. Die so genannte SD-SPIDER-Methode dient der Rekonstruktion der reellen Phase eines komplexwertigen Laserpulses mit Hilfe fehlerbehafteter Messungen. Die Messwerte sind ebenfalls komplexwertig und zusätzlich beeinflusst von einer durch das Messprinzip erzeugten Kernfunktion. Obwohl Selbstfaltungsgleichungen intensiv im Kontext Inverser Probleme untersucht wurden, fehlen Resultate für komplexwertige Lösungen und rechte Seiten ebenso wie für nichttriviale Kernfunktionen. Die Diplomarbeit stellt einen ersten Schritt dar, diese Lücke zu schließen. Im ersten Kapitel wird der physikalische Hintergrund erläutert und insbesondere der Selbstfaltungseffekt erklärt. Davon ausgehend wird das mathematische Modell aufgestellt. Kapitel zwei befasst sich mit der Analysis der Gleichung. Es folgt die numerische Behandlung des Problems in Kapitel drei. Eine Regularisierungsmethode wird vorgestellt und an künstlichen Daten getestet. Insbesondere wird eine neue Regel zur Wahl des Regularisierungsparameters vorgeschlagen und numerisch bestätigt, welche auf einer speziellen Eigenschaft des SD-SPIDER Verfahrens beruht.

Pass-by noise testing is an important step in vehicle design and regulation compliance. Finite element analysis simulations have been used to cut costs on prototyping and testing, but the high computational cost of simulating surface vibrations from complex geometries and the resulting airborne noise propagation is making the switch to digital twin methods not viable. This paper aims at investigating the use of equivalent source methods as an alternative to the before mentioned simulations. Through the use of a simple 2D model, the difficulties such as ill-conditioning of the transfer matrix and the required regularisation techniques such as TSVD and the Tikhonov L-curve method are tested and then applied to a mesh of a 3D engine model. Source and pressure field errors are measured and their origins are explained. A heavy emphasis is put on the model geometry as a source of error. Finally, rules of thumb based on the regularisation balance and the wavelength dependent pressure sampling positions are formulated in order to achieve usable results. / Bullerprovning vid passage är ett viktigt steg i fordonsdesign och regelefterlevnad. Simuleringar med finita elementanalyser har använts för att minska kostnaderna för prototypframtagning och provning, men de höga beräkningskostnaderna för att simulera ytvibrationer från komplexa geometrier och den resulterande luftburna bullerspridningen gör att övergången till digitala tvillingmetoder inte är genomförbar. Denna uppsats syftar till att undersöka användningen av ekvivalenta källmetoder som ett alternativ till de tidigare nämnda simuleringarna. Genom att använda en enkel 2D-modell testas svårigheterna som dålig konditionering av överföringsmatrisen och de nödvändiga regulariseringsteknikerna som TSVD och Tikhonov L-kurvmetoden och tillämpas sedan på ett nät av en 3D-motormodell. Käll- och tryckfältsfel mäts och deras ursprung förklaras. Stor vikt läggs vid modellgeometrin som en felkälla. Slutligen formuleras tumregler baserade på regulariseringsbalansen och de våglängdsberoende tryckprovtagningspositionerna för att uppnå användbara resultat.