A High-Frequency Phase Feature for the Measurement of Magnetic Permeability Using Eddy Current Sensor

Electromagnetic sensing has been used for diverse applications of non-destructive testing, including the surface inspection, measurement of properties, object characterization. However, the measurement accuracy could be significantly influenced by the lift-off between sensors and samples. To address the issue caused by lift-offs, various strategies have been proposed for the permeability measurement of ferromagnetic steels, which mainly involves different sensor designs and signal features (e.g., the zero-crossing feature). In this paper, a single high-frequency scenario for the permeability retrieval is introduced. By combining the signal of two sensing pairs, the retrieval of magnetic permeability is less affected by the lift-off of sensors. Unlike the previous strategy on reducing the lift-off effect (directly taking the phase term out of the integration) using the Dodd-Deeds analytical method, the proposed method is based on a high-frequency linear feature of the phase term. Therefore, this method has the merit of high accuracy and fast processing for the permeability retrieval (a simplified version of Dodd-Deeds analytical formulas after the integration). Experimental measurement has been carried out on the impedance measurement of designed sensors interrogating ferromagnetic dual-phase steels. For sensor lift-offs of up to 10 mm, the error of the permeability retrieval is controlled within 4 % under the optimal frequency.

Evaluation of the Economic Relationships on the Basis of Statistical Decision-Making in Complex Neutrosophic Environment

Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations (CNRs) and its types based on the idea of complex neutrosophic sets (CNSs). In addition, these concepts are supported by suitable examples. A CNR discusses the quality of a relationship using the degree of membership, the degree of abstinence, and the degree of nonmembership. Each of these degrees is a complex number from the unit circle in a complex plane. The real part of complex-valued degrees represents the amplitude term, while the imaginary part represents the phase term. This property empowers CNRs to model multidimensional variables. Moreover, some interesting properties and useful results have also been proved. Furthermore, the practicality of the proposed concepts is verified by an application, which discusses the use of the proposed concepts in statistical decision-making. Additionally, a comparative analysis between the novel concepts of CNRs and the existing methods is carried out.

A limit distribution for a quantum walk driven by a five-diagonal unitary matrix

In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is getting updated. The five-diagonal matrix contains a phase term and the quantum walk becomes a standard coined walk when the phase term is fixed at special values. Or, the phase term gives an effect on the quantum walk. As a result, we will see an explicit form of a long-time limit distribution for a quantum walk driven by the matrix, and thanks to the exact form, we understand how the quantum walker approximately distributes in space after the long-time evolution has been executed on the walk.

Extensions of power aggregation operators for decision making based on complex picture fuzzy knowledge

This article puts forward an innovative notion of complex picture fuzzy set (CPFS) which is particularly an extension and a generalization of picture fuzzy sets (PFSs) by the addition of phase term in the description of PFSs. The uniqueness of CPFS lies in the capability to manage the uncertainty and periodicity, simultaneously, due to the presence of phase term which broadens the range of CPFS from a real plane to the complex plane of unit disk. We describe and verify the fundamental operations and properties of CPFSs. We introduce the aggregation operators, namely; complex picture fuzzy power averaging and complex picture fuzzy power geometric operators in CPFSs environment, based on weighted and ordered weighted averaging and geometric operators. We construct multi-criteria decision making (MCDM) problem, using these operators and describe a numerical example to illustrate the validity and competence of this article. Finally, we discuss the advantages of this generalized concept of aggregation technique and analyze a comparative study to demonstrate the superiority and consistency of our model.

Extension of competition graphs under complex fuzzy environment

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

Thickness Measurement of Metallic Film Based on a High-Frequency Feature of Triple-Coil Electromagnetic Eddy Current Sensor

Previously, various techniques have been proposed for reducing the lift-off effect on the thickness measurement of the non-magnetic films, including the peak-frequency feature and phase feature in the Dodd-Deed analytical formulation. To realise a real-time feedback response on the thickness monitoring, the phase term in the Dodd-Deeds formulation must be taken off the integration. Previous methods were based on the slow change rate of the phase term when compared to the rest of the term – the magnitude term. However, the change rate of the phase term is still considerable for a range of working frequencies. In this paper, a high-frequency feature has been found. That is, the ratio between the imaginary and real part of the phase term is proportional to the integral variable under high frequencies. Based on this proportion relationship, the phase term has been taken out; and a thickness algorithm has been proposed. By combing the measured impedance from the custom-built sensor (three coils), the thickness of the metallic film can be reconstructed. Experiments have been carried out for the verification of the proposed scenario. Results show that the thickness of the metal film can be reconstructed with a small error of less than 2 %, and immune to a reasonable range of lift-offs.

Tandem Mach Zehnder Directional Coupler Design and Simulation on Silicon Platform for Optical Coherence Tomography Applications

We design and compare the splitting ratio wavelength flatness of directional coupler (DC), Mach-Zehnder directional coupler (MZDC), and tandem MZDC. All coupler responses are analyzed, and tandem MZDC performance is the best in the wavelength insensitivity compared with the other two. An MZDC with any coupling ratio could be utilized to match the maximum flatness in a 40-nm wavelength range. To extend a broad flatness range, the tandem MZDC is proposed and still follows the Mach Zehnder structure taking two MZDCs as couplers connected through a decoupled region. Unlike DC, MZDC with the flat wavelength response has a non-linear output phase. Hence, using two wavelength-insensitive MZDCs as the coupling function in a tandem MZDC could demonstrate a more extensive decoupled phase term to maximize the flat wavelength response. The tandem MZDC theoretically demonstrates the splitting ratio with 100-nm flatness in the wavelength range from 1250 nm to 1350 nm. Finally, a point spread function through the tandem MZDC shows a 24-dB signal-to-noise ratio improvement in optical coherence tomography applications.

Moving Target Indication for Dual-Channel Circular SAR/GMTI Systems

In a dual-channel circular synthetic aperture radar (CSAR) and ground moving target indication (GMTI) system, the antenna baseline is not parallel with the flight path due to a yaw angle. The angle causes a varying group-phase shift between the dual-channel signals and therefore degrades the correlation between the image pair. Therefore, the group-phase shift needs to be removed before channel equalization. To resolve the problem, the interferometric phase term was deduced and analyzed based on the geometry of a dual-channel CSAR system. Then, the varying phase term with respect to the Doppler frequency and the varying group-phase shift over the range were compensated for in the channel registration. Furthermore, blind channel equalization, including two-dimensional calibration and amplitude equalization, was applied to eliminate the amplitude and residual phase differences between the channels. Finally, the amplitude image obtained using a displaced phase center antenna (DPCA) was multiplied by the phase image obtained with along-track interferometry (ATI) to detect moving targets. The experimental results verified the effectiveness of the method for both uniform and non-uniform clutter suppression.