Search results for "Full matrix"
showing 4 items of 4 documents
A Fast Imaging Technique Applied to 2D Electrical Resistivity Data
2014
A new technique is proposed to process 2D apparent resistivity datasets, in order to obtain a fast and contrasted resistivity image, useful for a rapid data check in field or as a starting model to constrain the inversion procedure. In the past some modifications to the back-projection algorithm, as well as the use of filtering techniques for the sensitivity matrix were proposed. An implementation of this technique is proposed here, considering a two-step approach. Initially a damped least squares solution is obtained after a full matrix inversion of the linearized geoelectrical problem. Furthermore, on the basis of the results, a subsequent filtering algorithm is applied to the Jacobian ma…
Ultrasonic phased array inspection of wire plus arc additive manufacture samples using conventional and total focusing method imaging approaches
2019
In this study, three aluminium samples produced by wire + arc additive manufacture (WAAM) are inspected using ultrasonic phased array technology. Artificial defects are machined using a centre drill, ø 3 mm, and electrical discharge machining (EDM), ø 0.5-1 mm, in a cylindrical through-hole topology. The samples are first inspected using a single-element wheel probe mounted on a KUKA robot in order to investigate the feasibility of using a conventional ultrasonic transducer approach. Unfortunately, the wheel probe is found to be unsuitable for scanning the WAAM specimens and ultrasonic phased arrays are employed next. The set-up includes 5 MHz and 10 MHz arrays (128 elements) in direct cont…
Numerical range and positive block matrices
2020
We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range $W(X)$ of the off-diagonal block $X$, especially the distance $d$ from $0$ to $W(X)$. A special consequence is an estimate, $$\begin{eqnarray}\text{diam}\,W\left(\left[\begin{array}{@{}cc@{}}A & X\\ X^{\ast } & B\end{array}\right]\right)-\text{diam}\,W\biggl(\frac{A+B}{2}\biggr)\geq 2d,\end{eqnarray}$$ between the diameters of the numerical ranges for the full matrix and its partial trace.
Ultrasonic phased array inspection of wire plus arc additive manufacture (WAAM) samples using conventional and total focusing method (TFM) imaging…
2018
In this study, three aluminium samples produced by wire + arc additive manufacture (WAAM) are inspected using ultrasonic phased array technology. Artificial defects are machined using a centre drill, ø3 mm, and electro-discharge machining (EDM), ø0.5-1 mm, in a cylindrical through hole topology. The sample was first inspected by a single element wheel probe mounted on a KUKA robot in order to investigate the feasibility of using a conventional ultrasonic transducer approach. Unfortunately, the wheel probe was found to be unsuitable for scanning of the WAAM specimens and ultrasonic phased arrays were employed next. The setup included 5 MHz and 10 MHz arrays (128 elements) in direct contact w…