Capacitance Matrix Research Articles

Cleanroom-free fabrication of flexible capacitive pressure sensors using paintable silver electrodes on stationery paper and random microstructured polydimethylsiloxane dielectric layer

Abstract In this work, we propose a facile, low-cost, and cleanroom-free approach for fabricating flexible capacitive pressure sensors based on paintable Ag electrodes on stationery paper substrates (Ag–paper electrodes) and a random microstructured polydimethylsiloxane (PDMS) dielectric layer transferred from emery paper. COMSOL Multiphysics simulations and experimental investigations suggest that the pressure sensor with random microstructured PDMS dielectric layer performs better than the sensor with ordered micropyramidal dielectric layer. The developed Ag–paper electrode and random microstructured PDMS dielectric layer-based pressure sensors are workable in a wide pressure range (up to 630 kPa) and exhibit a high sensitivity of 0.132 kPa−1 up to 1 kPa, low hysteresis (6.6%) with loading–unloading of ∼500 kPa pressure, high stability during a ∼5250 cyclic test, and the ability to sense a low pressure of ∼27 Pa. The developed sensor also successfully transduces arterial pulse wave forms when it is properly attached to the wrist. Using the proposed process, a flexible capacitive pressure sensor matrix of 4 × 4 array is also successfully developed for single- and multiple-point pressure mapping with minimal cross-talk. The proposed sensor process is simple and inexpensive to implement, and offers spatial pressure mapping for e-skin applications.

Finite element analysis for the measurement error of electrostatic accelerometer due to the electrode misalignment

Abstract The electrostatic accelerometer is the key payload of many space missions, such as satellite gravity measurements, space gravitational experiments, with a typical precision requirement from nano-g to femto-g. The measurement error model analysis is an important issue for the electrostatic accelerometer with numerous error sources. The traditional method by theoretical analysis is complicated to evaluate the complete measurement error models quantitatively especially when the machining and assembly errors of the sensor head are considered. Limited by the earth gravity and seismic noise which is much higher than the intrinsic noise, the complete error model of electrostatic accelerometers can also hardly be tested on ground. In this paper, the method by using finite element analysis of the sensor head is studied. The simulation model for an electrostatic accelerometer sensor head is built, and the multi-conductor capacitance matrix data is simulated. The accuracy of the capacitance simulation is evaluated in three ways including the convergence check of the capacitance with the mesh size, the symmetry verification, and the sensitivity comparison with the theoretical model. Finally, the accelerometer measurement model is analyzed based on the simulation data, using the case of rotating installation misalignment of the upper electrode as an example. The measurement model and error items of one horizontal axis and one rotating axis are quantitatively evaluated. The method proposed in this paper provide a new effective approach to the measurement model analysis of the electrostatic accelerometers in complex working scenarios both in orbit and on ground, which could be helpful to enhance the performance and the efficiency of application.

A new approach towards more accurate modeling of mechanical defects in power transformer windings

In many cases, power transformers can continue their normal operation despite mechanical defects in their windings. However, estimating the lifespan and assessing the risk of using a transformer with mechanical defects depend on detailed studies of insulation aging and the distribution of transient voltages along the winding, and consequently, the likelihood of partial discharge. Risk assessment studies can only be effectively conducted through accurate modeling of transformers across a wide frequency range. In this study, an attempt has been made to investigate the impact of winding mechanical defects on the transformer equivalent circuits parameters using finite element method precisely modeling of transformer windings, without applying approximation or common simplifications. To compare the effect of each mechanical defect on the resistance, inductance, and capacitance matrices arrays, an index called fault classification accuracy has been used. The investigations have shown that the capacitance matrix arrays undergo the most significant changes for all types of modeled defects in this research. To examine the impact of defects on the transformer frequency response, a π coupled model that directly uses output matrices of finite element modeling has been employed. The sensitivity of various components of frequency response has also been investigated for the used model.

Measure for intensity of electrostatic interaction between two disjoint sets of charged conductors

Measure for intensity of electrostatic interaction between two disjoint sets of charged conductors is introduced, and it is called relative intensity of interaction (RII). Firstly, we examine properties and we found various forms and upper bounds for RII between charged conductors and neutral conductors. The most important derived expression for RII is in terms of Schur complement of original capacitance matrix and capacitance matrix of system without neutral conductors. RII between two disjoint sets S1 and S2 of arbitrarily charged conductors is bounded above by sum of RII’s between charged set S1 and neutral set S2, and vice versa.

Finite Element Analysis of Flow-Electrode Capacitive Deionization

As access to freshwater diminishes due to climate change and population growth, drought-stricken regions across the globe continue to turn to groundwater and desalination. A largely untapped water resource in many parts of the world is brackish water - defined as water with total dissolved solids (TDS) in the range of 500 ppm to 10,000 ppm. Flow Capacitive Deionization (FCDI) is an electrochemical ion removal technology that is well-suited for the continuous desalination of brackish waters. Traditional Capacitive Deionization (CDI) consists of two fixed capacitive electrodes which are charged and discharged cyclically to capture ions from the solution being treated, and then regenerated to create a waste brine stream. During FCDI operation however, an applied potential drives ions out of a center water channel, typically through a pair of cation and anion exchange membranes (CEM/AEM), and into two flowing capacitive slurry electrodes (Figure 1). Because the electrodes are mobile, they can be moved into an adjacent cell for regeneration, thus enabling continuous operation of the desalination system without cyclical charge/discharge. The cathode and anode slurries typically consist of activated carbon suspended in a salt solution.Because the electrodes are flowing in FCDI, models describing this system must translate the Eulerian derivative to describe transient capacitive charge/discharge to a Lagrangian material derivative following the electrode material flowing through space. A flowing capacitive electrode is a significantly more complex system than a stationary porous and capacitive electrode matrix, incorporating the fluid dynamics of the slurries, ion transport within the slurry’s electrolyte medium, etc. Despite nearly a decade of research into FCDI, few researchers have probed the transient and spatially dependent mechanisms of ion transport and electro-adsoprtion within flow electrodes. While the overall electrodialytic contributions to ion capture within FCDI systems have been studied (1,2), the mechanism of competition between the electrodialysis and capacitive ion capture within the flow electrodes remains somewhat elusive. Additional analysis of the ion transport phenomena within these flow electrodes could bring forth insights into optimal design of FCDI devices and/or electrode formulations.In this study, an existing 2-dimensional mathematical model (3,4) for electrochemical flow capacitors is adapted to FCDI and solved via finite element analysis in COMSOL Multiphysics. Transport equations describing the advection of overpotential along with the flowing electrode are coupled with the Nernst-Planck equations which govern ion transport within the CEM/AEM, center water channel, and slurry electrolyte medium. This study investigates the effect of slurry flow velocity and sodium chloride concentration in the influent water on electrical potential profiles within an FCDI cell, and illustrates the active regions of capacitive electro-adsorption through the depth of the flow channel. Models of electrodialysis and FCDI are compared to understand the fundamental differences in driving forces for ion removal between the two technologies. The model shows agreement with experimental data through prediction of salt adsorption rate trends (mmol NaCl m-2 s-1) vs. influent sodium chloride concentrations. Through this analysis, it is shown that this model may serve as a valuable groundwork for expansion of FCDI modeling capabilities to include three dimensional cell geometries and subsequent optimization of operational parameters and cell dimensions. P. Nativ, Y. Badash, and Y. Gendel, Electrochem. Commun., 76, 24–28 (2017). J. Ma, C. He, C. Zhang, and T. D. Waite, Water Res., 144, 296–303 (2018). N. C. Hoyt, J. S. Wainright, and R. F. Savinell, J. Electrochem. Soc., 152, A652–A657 (2015). N. C. Hoyt, R. F. Savinell, and J. S. Wainright, Chem. Eng. Sci., 144, 288–297(2016). Figure 1

High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation

We propose a high precision algorithm for solving the Gelfand–Levitan–Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson’s type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.

Mesh‐free Monte Carlo method for electrostatic problems with floating potentials

AbstractNumerical simulation plays a crucial role in the analysis and design of power equipment, such as lightning protection devices, which may become inefficient using traditional grid‐based methods when handling complex geometries of large problems. The authors propose a grid‐free Monte Carlo method to handle electrostatic problems of complex geometry for both the interior and exterior domains, which is governed by the Poisson equation with a floating potential boundary condition that is neither a pure Dirichlet nor a Neumann condition. The potential and gradient at any given point can be expressed in terms of integral equations, which can be estimated recursively within the walk‐on‐sphere algorithm. Numerical examples have been demonstrated, including the evaluation of the mutual capacitance matrix of multi‐conductor structures and lighting striking near real fractal trees. The proposed method shows advantages in terms of geometric flexibility and robustness, output sensitivity, and parallelism, which may become a candidate for game‐changing numerical methods and exhibit great potential applications in high‐voltage engineering.

The hybrid anti-symmetrized coupled channels method (haCC) for the tRecX code

We present a new implementation of the hybrid antisymmetrized Coupled Channels (haCC) method in the framework of the tRecX (Scrinzi, 2022 [6]). The method represents atomic and molecular multi-electron functions by combining CI functions, Gaussian molecular orbitals, and a numerical single-electron basis. It is suitable for describing high harmonic generation and the strong-field dynamics of ionization. Fully differential photoemission spectra are computed by the tSurff method. The theoretical background of haCC is outlined and key improvements compared to its original formulation are highlighted. We discuss control of over-completeness resulting from the joint use of the numerical basis and Gaussian molecular orbitals by pseudo-inverses based on the Woodbury formula. Further new features of this tRecX release are the iSurff method, new input features, and the AMOS gateway interface. The mapping of haCC into the tRecX framework for solving the time-dependent Schrödinger equation is shown. Use, performance, and accuracy of haCC are discussed on the examples of high-harmonic generation and strong-field photo-emission by short laser pulses impinging on the Helium atom and on the linear molecules N2 and CO. Program summaryProgram title: tRecX — time-dependent Recursive indeXing (tRecX=tSurff+irECS)CPC Library link to program files:https://doi.org/10.17632/m9g2jc82sw.1Developer's repository link:https://gitlab.physik.uni-muenchen.de/AG-Scrinzi/tRecXLicensing provisions: GNU General Public License 2Programming language: C++External libraries: Eigen, arpack, lapack, blas, boost, FFTW (optional)Journal Reference of previous version: A. Scrinzi, Comp. Phys. Comm., 270:108146, 2022.Does the new version supersede the previous version: YesReasons for the new version: Major new functionality: haCC — hybrid antisymmetrized coupled channels methodSummary of revisions: Main additions are haCC and iSurff. Code usage and compilation were improved.Nature of problem: tRecX is a general solver for time-dependent Schrödinger-like problems, with applications mostly in strong field and attosecond physics. There are no technical restrictions on the spatial dimension of the problem with up to 6 spatial dimensions realized in the strong-field double ionization of Helium. Gaussian-based quantum chemical multi-electron atomic and molecular structure can be combined with the numerical basis. A selection of coordinate systems is available and any Hamiltonian involving up to second derivatives and arbitrary up to three dimensional potentials can be defined on input by simple scripts.Solution method: The method of lines is used with spatial discretization by a flexible combination of one dimensional basis sets, DVR representations, discrete vectors, expansions into higher-dimensional eigenfunctions of user-defined operators, and Gaussian based molecular orbitals. Multi-electron Gaussian-based CI (configuration interaction) functions for neutrals and ions are combined with the numerical basis. Photo-emission spectra are calculated using the time-dependent surface flux method (tSurff) in combination with infinite range exterior complex scaling (irECS) for absorption. The code is object oriented and makes extensive use of tree-structures and recursive algorithms. Parallelization is by MPI. Code design and performance allow use in production as well as for graduate level training.

Scattering from time-modulated subwavelength resonators

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We consider the one-dimensional setting. In order to understand the energy of the system, we prove a novel higher-order discrete, capacitance matrix approximation of the subwavelength resonant quasi-frequencies. Further, we perform numerical experiments to support and illustrate our analytical results and show how periodically time-dependent material parameters affect the scattered wave field.

Efficient and Accurate Separable Models for Discretized Material Optimization: A Continuous Perspective Based on Topological Derivatives

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models constructed from convex separable first order approximations have a long and successful tradition in the design optimization community and have led to powerful optimization tools like the prominently used method of moving asymptotes (MMA). In this paper, we introduce several new separable approximations to a model problem and examine them in terms of accuracy and fast evaluation. The models can, in general, be nonconvex and are based on the Sherman–Morrison–Woodbury matrix identity on the one hand, and on the mathematical concept of topological derivatives on the other hand. We show a surprising relation between two models originating from these two—at a first sight—very different concepts. Numerical experiments show a high level of accuracy for two of our proposed models while also their evaluation can be performed efficiently once enough data has been precomputed in an offline stage. Additionally it is demonstrated that suboptimal decisions can be avoided using our most accurate models.

Tracking Modal Parameters of Structures Online Using Recursive Stochastic Subspace Identification under Ambient Excitations

Continuous and autonomous system identification is an alternative to regular inspection during operations, which is essential for structural integrity management (SIM) as well as structural health monitoring (SHM). In this regard, online (or real-time) system identification techniques that have recently received considerable attention can be used to assess the current condition and performance during operations and, in the meantime, can be utilized to detect any damage or deterioration. For example, stochastic subspace identification (SSI), based on recursive formulation, has proven its capability in tracking modal parameters as well as time-variant dynamic behaviors. This study proposes the implementation of recursive SSI (RSSI) using the matrix inversion lemma to track slow time-varying parameter changes under ambient excitations. Subsequently, some investigations for practical implementation are examined and discussed. For verifying the reliability of SHM applications based on the proposed methods, two datasets measured from different experiments are exploited to identify the modal parameters reclusively. The results from both numerical simulations and experimental investigations demonstrated the effectiveness of tracking the modal parameters exhibiting time-varying dynamic characteristics under white noise excitations (or ambient excitations).

An LMI-based robust state-feedback controller design for the position control of a knee rehabilitation exoskeleton robot: Comparative analysis

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equation solver for non-rectangular geometries. We advect the potential vorticity (PV) with finite volumes to ensure global PV conservation using a staggered discretization of the PV and stream function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need to define the PV on the domain boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The discretization presented here does not require tuning of any additional parameter, e.g., additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. Subsequently, we validate our solver on a vortex-shear instability test case in a circular domain, on a vortex–wall interaction test case, and on an idealized wind-driven double-gyre configuration in an octagonal domain at an eddy-permitting resolution. Finally, we release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments on this new discretization, e.g., machine-learning parameterization or data-assimilation techniques.

Efficient super-resolution image reconstruction of electrical capacitance tomography for gas–solid fluidized bed measurement

Electrical capacitance tomography (ECT) has been widely used to investigate the flow dynamics of the gas–solid fluidized bed. Deep learning-based tomographic imaging of ECT is of great potential to reconstruct the particle concentration distribution with compatible image quality and reconstruction speed. However, it suffers from low model construction efficiency as numerous data samples need to be collected for training the deep neural network. Here a super-resolution (SR) imaging model based on a two-stage imaging network is proposed to improve the model construction efficiency. A low-resolution (LR) imaging network is used to reconstruct the LR image with the measured capacitance matrix while a subsequent high-resolution (HR) network calculates the HR image with the reconstructed LR image. The imaging performance, construction efficiency, and generalization ability of the trained SR imaging model are evaluated by reconstructing the samples in the test set and the unseen typical flow patterns. Considering the training set includes 100,000 data samples, the time consumption of numerically collecting the dataset for training the SR imaging model is 2.70 h, 2.2 % of that for a conventional deep learning-based imaging model of ECT, and the overall model construction time is only 4.44 h when the grid numbers of the LR and HR images are 246 and 8053, respectively. Experimental measurements are further carried out on a fluidized bed and the preliminary results show good prediction and generality of the trained model for reconstructing the particle concentration distribution.

Efficient contingency analysis of power systems using linear power flow with generalized warm-start compensation

Contingency analysis (CA) is fundamental to power system planning and operation. The compensation method and linear power flow (LPF) models are frequently used in CA to boost efficiency. However, the conventional compensation scheme fails to adapt to modern LPF models with novel structures. To bridge this gap, this paper proposes a generalized warm-start compensation algorithm (GWSCA) for LPFs. To efficiently calculate the inversion of a perturbed coefficient matrix in LPF models, a generalized decomposition method is devised based on the matrix inverse lemma and full rank decomposition. A warm-start strategy is developed to improve the computational accuracy by using the precontingency operating point of a power grid. The proposed GWSCA is incorporated with an LPF model based on logarithmic transformation of voltage magnitudes to implement fast and accurate CA. Simulation results show that GWSCA outperforms the conventional algorithms in terms of computational efficiency and accuracy.

On the Features of Calculating Linear Parameters and Characteristics of Multi-Wire Transmission Lines

The features of calculating the matrices of linear parameters and characteristics of multi-wire transmission lines have been considered. The method of calculation of the matrices of primary linear parameters of multi-wire transmission lines has been presented. The criteria for the accuracy of the calculation of the capacitive matrix have been formulated. It has been noted that it is necessary to accurately account for the mutual influence between the transmission line conductors for a correct estimation of the distortions of thesignals propagated in it. The influence of the linear parameters of multi-wire transmission lines on responses and eye diagrams at the end of their active conductors has been demonstrated. The influence of the distances from the extreme conductors to the boundaries of the cross-sections of transmission lines on the accuracy ofcalculating their capacitive matrices has been studied. Using the method of moments, it has been shown that known approaches to determining these distances do not always give accurate or efficient results. On the example of several transmission lines with different numbers of dielectric layers and conductors, as well as with the screen and without it, the minimum values of this distance at which it is possible to achieve an accurate and efficient calculation of their capacitive matrices have been determined.

Transmission properties of time-dependent one-dimensional metamaterials

We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically using Muller’s method. We prove a formula in the form of an ODE using a capacitance matrix approximation. Comparison of the exact results with the approximations reveals that the method of capacitance matrix approximation is accurate and significantly more efficient. We prove various transmission properties in the aforementioned structure and illustrate them with numerical simulations. In particular, we investigate the effect of time-modulated material parameters on the formation of degenerate points, band gaps and k-gaps.

Landscape of wave focusing and localization at low frequencies

AbstractHigh‐contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high‐contrast systems that resonate in a subwavelength regime. Our from‐first‐principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving a discrete approximation of the three‐dimensional scattering problem. We develop landscape theory for the generalized capacitance matrix and use it to predict the positions of three‐dimensional wave focusing and localization in random and non‐periodic systems of subwavelength resonators.

Kernel Geometric Mean Metric Learning

Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space through nonlinear transformation, and use the integral representation of the weighted geometric mean and the Woodbury matrix identity in new feature space to generalize the analytical solution obtained in the GMML algorithm as a form represented by a kernel matrix, and then the KGMML algorithm is obtained through operations. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems

The large overhead arising from conventional channel estimations in reconfigurable intelligent surface (RIS) aided millimeter-wave communication systems, may offset the performance gain brought by the RIS. To tackle this issue, we propose a location information assisted beamforming design without the requirement of the channel training process. First, we establish the geometrical relationship between the channel model and the user location, and mathematically derive an approximate channel state information (CSI) error bound based on the user location error region. Then, for combating the negative impact of the location error on the communication performance, we formulate a worst-case robust beamforming optimization problem to optimize the beamformer at the base station (BS) and the phase-shift matrix at the RIS. To solve this non-convex problem, we develop a novel relaxed alternating optimization process (RAOP) by utilizing various optimization tools, such as the Lagrange multiplier, the matrix inversion lemma, the semidefinite relaxation (SDR), as well as the branch-and-bound (BnB). Additionally, we prove sufficient conditions for the SDR to yield rank-one solutions, and modify the BnB to acquire the phase-shift solution under an arbitrary constraint of possible phase-shift values. Finally, we analyse the convergence and complexity of the proposed RAOP, and carry out simulations for performance evaluations. Compared to the conventional non-robust beamforming, our method performs better and shows strong robustness against the location-error-related CSI uncertainty. Compared to the robust beamforming based on the S-procedure and penalty convex-concave procedure (CCP), our method with BnB shows the advantages of being able to converge faster and handle arbitrary phase-shift argument sets.