Finite Measurements Research Articles

Determination of the Operating Temperature of the Gas-Insulated Transmission Line

Gas-insulated lines (GILs) have been increasingly used as high-current busducts for high-power transmission. Temperature is one of the most important factors affecting the performance and ampacity of GILs. In this paper, an analytical method was proposed to determine the temperature of a three-phase high-current busduct in the form of a single pole GIL. First, power losses in the phase conductors and enclosures were determined analytically with the skin, and proximity effects were taken into account. The determined power losses were used as heat sources in thermal analysis. Considering the natural convection and radiation heat transfer effects, the heat balance equations on the surface of the phase conductors and the screens were established, respectively. Subsequently, the temperature of the phase conductors and the enclosures were determined. The validation of the proposed method was carried out using the finite element method and laboratory measurements.

Performance Testing of a Large-Format X-ray Reflection Grating Prototype for a Suborbital Rocket Payload

The soft X-ray grating spectrometer on board the Off-plane Grating Rocket Experiment (OGRE) hopes to achieve the highest resolution soft X-ray spectrum of an astrophysical object when it is launched via suborbital rocket. Paramount to the success of the spectrometer are the performance of the [Formula: see text] reflection gratings populating its reflection grating assembly. To test current grating fabrication capabilities, a grating prototype for the payload was fabricated via electron-beam lithography at The Pennsylvania State University’s Materials Research Institute and was subsequently tested for performance at Max Planck Institute for Extraterrestrial Physics’ PANTER X-ray Test Facility. Bayesian modeling of the resulting data via Markov chain Monte Carlo (MCMC) sampling indicated that the grating achieved the OGRE single-grating resolution requirement of [Formula: see text] at the 94% confidence level. The resulting [Formula: see text] posterior probability distribution suggests that this confidence level is likely a conservative estimate though, since only a finite [Formula: see text] parameter space was sampled and the model could not constrain the upper bound of [Formula: see text] to less than infinity. Raytrace simulations of the tested system found that the observed data can be reproduced with a grating performing at [Formula: see text]. It is therefore postulated that the behavior of the obtained [Formula: see text] posterior probability distribution can be explained by a finite measurement limit of the system and not a finite limit on [Formula: see text]. Implications of these results and improvements to the test setup are discussed.

Design and Fabrication of a MEMS-Based Break Junction Device for Mechanical Strain-Correlated Optical Characterization of a Single-Molecule

Here, we propose a robust lab-on-a-chip system for multi-dimensional (electrical, optical, and mechanical) characterization of a single-molecule utilizing a Si micromachined micro-electromechanical-system (MEMS) chip. Our MEMS-based break junction (MEMS-BJ) utilizes conventional MEMS chip fabrication techniques to create an electrostatic comb actuator capable of trapping a single-molecule between two nanoscale metal electrodes with sub-nanometer displacement resolution. In order to achieve this functionality, components of the chip (e.g flexural spring, comb drive fingers) are delicately designed based on an analytical model and basic performance parameters are verified using a finite element analysis simulation and capacitive sensor measurements. Using this system, we are able to perform combined single-molecule Raman spectroscopy and molecular conductance measurements in real-time. Finally, we present a representative case study of the multi-dimensional characterization of a single-molecule junction by analyzing correlated electrical, optical, and mechanical information while mechanically modulating the strain on the junction which allows for direct observation of the interplay between molecular structure and electron transport. We believe that our MEMS-BJ system will enable a deeper multi-dimensional study at a single-molecule level promoting the development of new methods for chemical and biological sensor applications.

Improving the Accuracy of Wound-Rotor Resolvers Under Inter-Turn Short Circuit Faults

The performance of the resolver as a position sensor is significantly influenced by electrical and mechanical faults. Among different faults, short circuit in the stator windings has more destructive effect than others on accuracy of resolver. Furthermore, due to thin wires of the stator it is highly likely to occur. Therefore, in this paper a robust design is proposed for wound-rotor resolvers to not only suppress the influence of short circuit fault in the stator/rotor winding, but also improve the accuracy of the sensor under mechanical faults. The effectiveness of the proposed robust design is demonstrated by an analytical model based on winding function method and then approved by time stepping finite element analysis (TSFEA) and experimental measurements on a prototype sensor.

Nonstationary force sensing under dissipative mechanical quantum squeezing

We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves non-thermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise much greater than the maximum possible in a stationary measurement scenario. We analyse two different measurement schemes in the nonstationary transient regime, a back-action evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.

Analytical Modeling of Slotted, Surface-Mounted Permanent Magnet Synchronous Motors With Different Rotor Frames and Magnet Shapes

This article presents an analytical solution procedure to investigate the geometrical impact of the magnet and the rotor core on the performance of slotted, surface-mounted permanent magnet (PM) synchronous motors. In particular, four different motor configurations with loaf-shape/regular arc-shape magnets mounted on the octagon/circular rotor surface are investigated, and their no-load (i.e., PM flux density, back EMF, and the cogging torque) and on-load (i.e., armature flux density, winding inductance, and electromagnetic torque) performance metrics are compared. The analysis is carried out analytically by using the concept of the surface magnetization current (SMC) and the superposition theorem. First, the stator slots are nullified, and Poisson's equation is solved on a slot-less surface. The effect of the stator slots is then included by injecting equivalent SMC on the stator bore. For verification purposes, analytical results are validated via the finite element (FE) and experimental measurements on the motor prototype.

Development and Assessment of Novel Multiligament Knee Injury Reconstruction Graft Constructs and Techniques.

Multiligament knee injury (MLKI) typically requires surgical reconstruction to achieve the optimal outcomes for patients. Revision and failure rates after surgical reconstruction for MLKI can be as high as 40%, suggesting the need for improvements in graft constructs and implantation techniques. This study assessed novel graft constructs and surgical implantation and fixation techniques for anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), posterior medial corner (PMC), and posterior lateral corner (PLC) reconstruction. Study objectives were (1) to describe each construct and technique in detail, and (2) to optimize MLKI reconstruction surgical techniques using these constructs so as to consistently implant grafts in correct anatomical locations while preserving bone stock and minimizing overlap. Cadaveric knees (n = 3) were instrumented to perform arthroscopic-assisted and open surgical creation of sockets and tunnels for all components of MLKI reconstruction using our novel techniques. Sockets and tunnels with potential for overlap were identified and assessed to measure the minimum distances between them using gross, computed tomographic, and finite element analysis-based measurements. Percentage of bone volume spared for each knee was also calculated. Femoral PLC-lateral collateral ligament and femoral PMC sockets, as well as tibial PCL and tibial PMC posterior oblique ligament sockets, were at high risk for overlap. Femoral ACL and femoral PLC lateral collateral ligament sockets and tibial popliteal tendon and tibial posterior oblique ligament sockets were at moderate risk for overlap. However, with careful planning based on awareness of at-risk MLKI graft combinations in conjunction with protection of the socket/tunnel and trajectory adjustment using fluoroscopic guidance, the novel constructs and techniques allow for consistent surgical reconstruction of all major ligaments in MLKIs such that socket and tunnel overlap can be consistently avoided. As such, the potential advantages of the constructs, including improved graft-to-bone integration, capabilities for sequential tensioning of the graft, and bone sparing effects, can be implemented.

Tight bound on finite-resolution quantum thermometry at low temperatures

Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound can be saturated by monitoring the non-equilibrium dynamics of a single-qubit probe. We support this finding by accurate numerical simulations of a spin-boson model. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

Eccentric position diagnosis of static eccentricity fault of external rotor permanent magnet synchronous motor as an in‐wheel motor

An eccentric position diagnosis method of static eccentricity (SE) fault of external rotor permanent magnet synchronous motor (ER-PMSM) is presented. Firstly, an analytical model of no-load radial magnetic field of ER-PMSM is established. Analytical models of no-load Back-EMF of both unit motors and the whole motor are carried out and are verified by finite element method (FEM) and experimental measurements. Then, the influences of SE ratio, SE circumferential angle, winding distribution mode and number of parallel branches on no-load radial magnetic field and no-load Back-EMF are analyzed based on these analytical models. The results show that SE does not affect the frequency characteristics of no-load radial magnetic field, but changes space order characteristics. On one hand, for ER-PMSM, of which the number of unit motors is equal to 1, SE causes no-load Back-EMF distortion. On the other hand, for ER-PMSM, of which the number of unit motors is greater than 1, SE does not affect no-load Back-EMF of the whole motor, but it still leads to no-load Back-EMF distortion of unit motors. Therefore, based on total harmonic distortion (THD) of no-load Back-EMF of unit motor, a projection method of intersection lines for SE fault diagnosis of ER-PMSM is proposed finally.

Frequency Response Function Measurements via Local Rational Modeling, Revisited

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. This article presents an overview of the existing methods and gives an in-depth bias and variance analysis of the FRF and disturbing noise variance estimates. In addition, a new local modeling approach is described, which combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model-order selection procedure applied to a specific subclass of rational functions.

Locating small inclusions in diffuse optical tomography by a direct imaging method

Abstract Optical tomography is a typical non-invasive medical imaging technique, which aims to reconstruct geometric and physical properties of tissues by passing near infrared light through tissues for obtaining the intensity measurements. Other than optical properties of tissues, we are interested in finding locations of small inclusions inside the object from boundary measurements, based on the time-dependent diffusion model. First, we analyze the asymptotic behavior of the boundary measurements weighted by the fundamental solution of a backward diffusion equation as the diameters of inclusions go to zero. Then, we derive an efficient algorithm for locating small inclusions by finite boundary measurements. This algorithm is direct, simple and easy to be implemented numerically, since it only involves matrix operations and has no iteration process. Finally, some numerical results are presented to illustrate the feasibility and robustness of the algorithm. A new observation of the algorithm is that we can take the source points and test points independently and increase the resolution of numerical results by taking more test points.

Modeling of Attractive Force by Magnetic Wheel Used for Mobile Robot

Mobile robots that are required to climb inclined ferromagnetic surfaces typically employ magnetic wheels. In order to design magnetic wheels and to properly size the permanent magnet as magnetizing source without the need for finite element analyses, a model that predicts the attractive magnetic force is necessary. In this paper, an analytical force model is derived by estimating the reluctance between the wheel and the surface. A magnetic circuit is constructed, incorporating the leakage flux from the side of the wheel. The model is validated against the results from finite element analyses and measurements from a test rig and a wheel prototype. Within the limitations of the model, it can adequately predict the force and can be used for initial design of magnetic wheels.

A Second-Order Statistics-Based Mixed Sources Localization Method With Symmetric Sparse Arrays

This letter proposes a localization method for mixed far-field (FF) and near-field (NF) sources based on second-order statistics (SOS) with generalized symmetric sparse linear arrays. First, the DOAs of the FF sources are estimated by using MUSIC method. Then, we use the oblique projection technique to isolate the NF sources from the FF ones and the atomic norm minimization is employed to retrieve the DOAs of the NF sources. Finally, the range information of the NF sources are determined by one-dimensional searching. To against the effect of finite measurements, an iterative procedure is employed to alternatively updating the DOA and range information of NF sources and the oblique projector. Closed-form expression of Crammer-Rao lower bound (CRLB) is derived from the coarray perspective for the sparse arrays. Simulations are carried out to demonstrate the effectiveness of our proposed method.

Improved magnetic circuit analysis of a laminated magnetorheological elastomer device featuring both permanent magnets and electromagnets

As an essential and critical step, magnetic circuit modelling is usually implemented in the design of efficient and compact magnetorheological (MR) devices, such as MR dampers and MR elastomer isolators. Conventional magnetic circuit analysis simplifies the analysis by ignoring the magnetic flux leakage and magnetic fringing effect. These assumptions are sufficiently accurate in dealing with less complicated designs, featuring short magnetic path lengths such as in an MR damper. However, when dealing with MR elastomer devices, such simplification in magnetic circuit analysis results in inaccuracy of dimensioning and performance estimation of the devices due to their sophisticated design and complex magnetic paths. Modelling permanent magnets also imposes challenges in the magnetic circuit analysis. This work proposes an improved approach to include magnetic flux fringing effect in magnetic circuit analysis for MR elastomer devices. An MRE-based isolator containing multiple MRE layers and both a permanent magnet and an exciting coil was designed and built as a case study. The results of the proposed method are compared to those of conventional magnetic circuit modelling, finite element analysis and experimental measurements to demonstrate the effectiveness of the proposed approach.

A multifunctional honeycomb metastructure for vibration suppression

In this study, a multifunctional metastructure is proposed for vibration suppression by combining a honeycomb sandwich structure and a locally resonant metastructure. To localize the low-frequency bandgaps, an analytical model based on Hamilton's principle and the energy averaging technique is developed and is confirmed by a three-dimensional numerical simulation. Moreover, the effective mass density is determined analytically to give a physical insight into the wave control mechanism. Then, the dynamic behavior of the finite structure is investigated analytically. A finite element (FE) simulation and experimental measurements are performed to demonstrate the validity and accuracy of this dynamic model. Results show that the proposed metastructure exhibits an excellent vibration suppression performance, as well as a significant tunability. Furthermore, to claim multifunctionality, the out-of-plane compression behavior is analyzed experimentally. Experimental results indicate that mechanical properties of the proposed metastructure are significantly improved in comparison with a traditional square honeycomb sandwich structure. The proposed strategy is a novel multi-functional combination, which can help realize vibration control and high mechanical efficiency. This will significantly impact multiple research areas in vibration analysis and provide engineering applications.

Robust Control for the Detection Threshold of CFAR Process in Cluttered Environments.

The constant false alarm rate (CFAR) process is essential for target detection in radar systems. Although the detection performance of the CFAR process is normally guaranteed in noise-limited environments, it may be dramatically degraded in clutter-limited environments since the probabilistic characteristics for clutter are unknown. Therefore, sophisticated CFAR processes that suppress the effect of clutter can be used in actual applications. However, these methods have the fundamental limitation of detection performance because there is no feedback structure in terms of the probability of false alarm for determining the detection threshold. This paper presents a robust control scheme for adjusting the detection threshold of the CFAR process while estimating the clutter measurement density (CMD) that uses only the measurement sets over a finite time interval in order to adapt to time-varying cluttered environments, and the probability of target existence with finite measurement sets required for estimating CMD is derived. The improved performance of the proposed method was verified by simulation experiments for heterogeneous situations.

Magnet System for the Quantum Electromechanical Metrology Suite

The design of the permanent magnet system for the new Quantum Electro-Mechanical Metrology Suite (QEMMS) is described. The QEMMS, developed at the National Institute of Standards and Technology (NIST), consists of a Kibble balance, a programmable Josephson voltage standard, and a quantum Hall resistance standard. It will be used to measure masses up to $100\,\mathrm{g}$ with relative uncertainties below $2\times 10^{-8}$. The magnet system is based on the design of the NIST-4 magnet system with significant changes to adopt to a smaller Kibble balance and to overcome known practical limitations. Analytical models are provided to describe the coil-current effect and model the forces required to split the magnet in two parts to install the coil. Both models are compared to simulation results obtained with finite element analysis and measurement results. Other aspects, such as the coil design and flatness of $Bl$ profile are considered.

Trapped air metamaterial concept for ultrasonic sub-wavelength imaging in water

Acoustic metamaterials constructed from conventional base materials can exhibit exotic phenomena not commonly found in nature, achieved by combining geometrical and resonance effects. However, the use of polymer-based metamaterials that could operate in water is difficult, due to the low acoustic impedance mismatch between water and polymers. Here we introduce the concept of “trapped air” metamaterial, fabricated via vat photopolymerization, which makes ultrasonic sub-wavelength imaging in water using polymeric metamaterials highly effective. This concept is demonstrated for a holey-structured acoustic metamaterial in water at 200–300 kHz, via both finite element modelling and experimental measurements, but it can be extended to other types of metamaterials. The new approach, which outperforms the usual designs of these structures, indicates a way forward for exploiting additive-manufacturing for realising polymer-based acoustic metamaterials in water at ultrasonic frequencies.

Frequency characteristics and thermal compensation of MEMS devices based on geometric anti-spring

This paper presents the analytical modeling, simulation and experimental validation of sensitivity, temperature variation and active controllability of MEMS geometric anti-spring (GAS) devices. Two models, the elasticity model and the thermal drift model, were proposed and analyzed, based on the study of asymmetrical and symmetrical geometric anti-spring structures. With the elasticity model, structural optimization led to analytical frequency-prestress design formula and a dedicated MEMS structure. An independent pre-stress and frequency shift effect is the result of thermal changes, so a thermal drift analytical model was built for the geometric anti-spring device, showing thermal sensitivities of 82.5 ppm/°C and 58.4 ppm/°C for the 3-spring and 4-spring devices, respectively. The analytical model was validated by both finite element analyses and experimental measurements. The designed devices (3-springs and 4-springs) were tested afterward in a dedicated setup, for both positive and negative electrostatically induced pre-stresses. Without electrical compensation, the thermal drift of the symmetrical 4-spring GAS device, for temperatures in the range +25°C to +110°C, is about 2138 ppm, and it is reduced to only 8.35 ppm when the electrostatic temperature compensation is active. Similarly, the asymmetrical structure has an uncompensated thermal sensitivity of its resonant frequency of 2254 ppm in the temperature operation range, and it is reduced to 51.5 ppm with electrical compensation within the easily controlled range of the temperature span, from +25°C to +75°C. As a result, although the benefits of the asymmetrical structure would lead to a higher sensitivity, trade-offs related to thermally-induced drift behavior and controllability also should be taken into consideration in the selection of the structural topology and application environment.

Electric Field and Thermal Analysis of 132 kV Ceramic Oil-Filled Cable Sealing Ends

This paper reports on a method combining the use of finite element simulations and external measurements to provide preliminary condition diagnosis of oil-filled cable sealing ends (CSEs) without requiring downtime. Good agreement has been obtained between the predictions from the electric field and thermal simulations and the measurements on a 132 kV oil-filled CSE. The electrostatic computation combined with electric field measurements can provide information regarding the electric field distribution inside the CSE and help in identifying potential issues with the CSE design, the materials or the cable termination process. The thermal computation combined with thermal imaging can reveal potential problems, such as high resistance connection to the busbar, and provide information regarding the cooling efficiency of the liquid dielectric. The method presented can provide the starting point for prioritizing maintenance operations on CSEs.