Approximate Analysis Research Articles

Research on AC Electronic Load with Energy Recovery Based on Finite Control Set Model Predictive Control

Nowadays, AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment. To tackle the problems of control difficulty, strategy complexity, and poor dynamic performance of AC electronic load with energy recovery of the conventional control strategy, a control strategy of AC electronic load with energy recovery based on Finite Control Set Model Predictive Control (FCS-MPC) is developed. To further reduce the computation burden of the FCS-MPC, a simplified FCS-MPC with transforming the predicted variables and using sector to select expected state is proposed. Through simplified model and equivalent approximation analysis, the transfer function of the system is obtained, and the stability and robustness of the system are analyzed. The performance of the simplified FCS-MPC is compared with space vector control (SVPWM) and conventional FCS-MPC. The results show that the FCS-MPC method performs better dynamic response and this advantage is more obvious when simulating high power loads. The simplified FCS-MPC shows similar control performance to conventional FCS-MPC at less computation burden. The control performance of the system also shows better simulation results.

Theoretical and Numerical Estimate of Signal-to-Noise Ratio in the Analysis of Josephson Junctions Lifetime for Photon Detection

The performances of a Josephson junction employed to reveal a train of pulses (a rough model for single photon detection) are analyzed with a theoretical estimate that exploits an index employed in statistical decision theory, the Kumar–Carroll index. The approximate analysis compares the numerically simulated performances of the device through the receiver operating characteristics, that offer an overview of the rate of false detection, as well as the probability to miss a signal (in this case, a pulse train). It is thus demonstrated the usefulness and the limits of the succinct Kumar–Carroll parameter. On the first side, it is proven that an increase of the parameter corresponds to an improvement of the detection. However, on the side of the limitations, the expected performances are not quite accurate, for the actual performances are systematically worse than the theoretical estimates. The results may be relevant to characterize Josephson junctions as detectors of weak signals, as those stemming from axions.

Composite wing vibration coupling control

The paper discusses the possibility to control coupled bending-twisting vibrations of composite wing by means of the monoclinic structures in the reinforcement of the plating. Decomposing the potential straining energy and kinetic energy of natural vibration modes into interacting and non-interacting parts, it became possible to introduce the two coefficients that integrally consider the effect of geometry and reinforcement structure upon the dynamic response parameters of the wing. The first of these coefficients describes the elastic coupling of the natural vibration modes, the second coefficient describes the inertial one. The paper describes the numerical studies showing how the orientation of considerably anisotropic CRP layers in the plating affects natural frequencies, loss factors, coefficients of elastic and inertial coupling for several lower tones of natural bending-twisting vibrations of the wing. Besides, for each vibration mode, partial values of the above mentioned dynamic response parameters were determined by means of the relationships for orthotropic structures where instead of “free” shearing modulus in the reinforcement plant, “pure” shearing modulus is used. Joint analysis of the obtained results has shown that each pair of bendingtwisting vibration modes has its orientation angle ranges of the reinforcing layers where the inertial coupling caused by asymmetry of the cross-section profile with respect to the main axes of inertia decreases, down to the complete extinction, due to the generation of the elastic coupling in the plating material. These ranges are characterized by the two main features: 1) the difference in the natural frequencies of the investigated pair of bendingtwisting vibration modes is the minimum and 2) natural frequencies of bending-twisting vibrations belong to a stretch restricted by corresponding partial natural frequencies of the investigated pair of vibration modes. This result is of practical importance because it enables approximate analysis of real composite wings with complex geometry in the existing commercial software packages.

축류펌프의 입구 안내깃 모사에 따른 성능 및 내부 유동장에 관한 수치해석적 연구

In this study, an absolute flow angle was numerically assigned to the inlet of an axial pump in order to predict its performance and internal flow field prior to the design process of an inlet guide vane. The finite volume method, which is an approximate analysis method based on the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equation, was applied for discretization of governing equations. The shear stress transport (SST) model was used as the turbulence model and the hexahedral grid system was selected as the appropriate number of nodes through the grid dependency test. The change in the performance curve and internal flow field was found with respect to the difference in the absolute flow angle at the impeller inlet. When installing a variable inlet guide vane of an axial flow pump, an efficient operation plan by adjusting the angle of an inlet guide vane might be established with the results of this study.

Single-nucleus RNA and ATAC sequencing uncovers the molecular and cellular characteristics in the musk gland of Chinese forest musk deer (Moschus berezovskii).

The Chinese forest musk deer (FMD; Moschus berezovskii) is an endangered artiodactyl mammal. Musk secreted by the musk gland of male has extremely high economic and medicinal value. However, the molecular and cellular characteristics of the musk gland have not been studied. Here, we investigated the diversity and transcriptional composition of musk gland cell types and the effect of cell type-specific chromatin accessibility on gene expression using single-nucleus RNA sequencing (snRNA-seq) and single-nucleus ATAC sequencing (snATAC-seq) association analysis. Based on uniform manifold approximation and projection (UMAP) analysis, we identified 13 cell types from the musk gland, which included two different acinar cells (cluster 0 and cluster 10). Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis indicated that many pathways related to musk secretion were enriched in acinar cells. Our analysis also revealed acinar cell core transcription factors and core target genes, and further constructed acinar cell-specific regulatory networks. In cluster 0, 11 core target genes (Nedd4l, Adcy9, Akr1c1, Vapb, Me1, Acsl1, Acss3, Srd5a1, Scnn1a, Acadm, and Nceh1) possibly related to musk secretion were regulated by 24 core transcription factors (SP3, NFIC, NR6A1, EHF, RUNX1, TFAP2A, RREB1, GRHL2, NFIB, ELF1, MAX, KLF5, REL, HES1, POU2F3, TFDP1, NR2C1, ATF7, MEIS1, NR4A2, NFIA, PBX1, ZNF652, and NFKB1). In cluster 10, four core target genes (Akr1c1, Pcca, Atp1b1, and Sgk1) possibly related to musk secretion were regulated by 10 core transcription factors (BARX2, EHF, PBX1, RUNX1, NFIB, FOXP1, KLF3, KLF6, ETV6, and NR3C2). Moreover, the credibility of snRNA-seq and snATAC-seq data was verified by fluorescence in situ hybridization and immunohistochemistry. Finally, cell communication analysis demonstrated that the two types of acinar cells mainly have communications in musk secretion-related processes. In conclusion, we provided important insights and invaluable resources for the molecular and cellular characteristics of the musk gland, which will lay a foundation for the study of musk secretion mechanism in the future.

A Symbolic Approach to Detecting Hardware Trojans Triggered by Don’t Care Transitions

Due to the globalization of Integrated Circuit supply chain, hardware Trojans and the attacks that can trigger them have become an important security issue. One type of hardware Trojans leverages the “don’t care transitions” in Finite-state Machines (FSMs) of hardware designs. In this article, we present a symbolic approach to detecting don’t care transitions and the hidden Trojans. Our detection approach works at both register-transfer level (RTL) and gate level, does not require a golden design, and works in three stages. In the first stage, it explores the reachable states. In the second stage, it performs an approximate analysis to find the don’t care transitions and any discrepancies in the register values or output lines due to don’t care transitions. The second stage can be used for both predicting don’t care triggered Trojans and for guiding don’t care aware reachability analysis. In the third stage, it performs a state-space exploration from reachable states that have incoming don’t care transitions to explore the Trojan payload and to find behavioral discrepancies with respect to what has been observed in the first stage. We also present a pruning technique based on the reachability of FSM states. We present a methodology that leverages both RTL and gate-level for soundness and efficiency. Specifically, we show that don’t care transitions and Trojans that leverage them must be detected at the gate-level, i.e., after synthesis has been performed, for soundness. However, under specific conditions, Trojan payload exploration can be performed more efficiently at RTL. Additionally, the modular design of our approach also provides a fast Trojan prediction method even at the gate level when the reachable states of the FSM is known a priori . Evaluation of our approach on a set of benchmarks from OpenCores and TrustHub and using gate-level representation generated by two synthesis tools, YOSYS and Synopsis Design Compiler (SDC), shows that our approach is both efficient (up to 10× speedup w.r.t. no pruning) and precise (0% false positives both at RTL and gate-level netlist) in detecting don’t care transitions and the Trojans that leverage them. Additionally, the total analysis time can achieve up to 1.62× (using YOSYS) and 1.92× (using SDC) speedup when synthesis preserves the FSM structure, the foundry is trusted, and the Trojan detection is performed at RTL.

Analytic structure of the Landau gauge quark propagator from Padé analysis

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Pad\'e approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e., for a Minkowski type of momentum. This pole occurs at Euclidean momenta $p\ensuremath{\sim}\ensuremath{-}300\text{ }\text{ }\mathrm{MeV}$ and it reproduces typical quark mass values used in phenomenological effective quark models. The Pad\'e approximant analysis also gives hints on the presence of a branch cut. Our results also show a clear correlation between the position of this pole, understood as an effective quark mass, and the pion mass that is compatible with partial conservation of the axial current. Slightly differences between the poles for the two quark form factors are observed which can be viewed either as a limitation of the method or as a suggestion that the quark propagator has no spectral representation.

String stability in traffic flows

String stability or instability is a fundamental issue in traffic flow about whether the speed oscillations of the leading vehicle are damped or amplified as such oscillations pass through the platoon. If they are amplified, then traffic jams will occur. In this paper, we propose a suitable notion of string stability for continuum models of traffic flows, and study what kinds of driving behaviors lead to string stability or instability. We find that the well-known Lighthill-Whitham-Richards model and Aw-Rascle-Zhang model are string stable for wide classes of perturbations. As a consequence, the driving behaviors described by these models suppress speed oscillations and hence do not cause traffic jams. Once the hysteresis behavior is added to the Lighthill-Whitham-Richards model, an example is given to show that string instability can occur for large perturbations, leading to phantom jams. Under small perturbations, however, examples as well as approximate solution analysis suggest that the hysteretic traffic flow is string stable. The approximation solution analysis is developed to replace linear stability analysis, as hysteretic flow model cannot be linearized.

Approximate entropy analysis across electroencephalographic rhythmic frequency bands during physiological aging of human brain.

Aging is the inevitable biological process that results in a progressive structural and functional decline associated with alterations in the resting/task-related brain activity, morphology, plasticity, and functionality. In the present study, we analyzed the effects of physiological aging on the human brain through entropy measures of electroencephalographic (EEG) signals. One hundred sixty-one participants were recruited and divided according to their age into young (n = 72) and elderly (n = 89) groups. Approximate entropy (ApEn) values were calculated in each participant for each EEG recording channel and both for the total EEG spectrum and for each of the main EEG frequency rhythms: delta (2-4Hz), theta (4-8Hz), alpha 1 (8-11Hz), alpha 2 (11-13Hz), beta 1 (13-20Hz), beta 2 (20-30Hz), and gamma (30-45Hz), to identify eventual statistical differences between young and elderly. To demonstrate that the ApEn represents the age-related brain changes, the computed ApEn values were used as features in an age-related classification of subjects (young vs elderly), through linear, quadratic, and cubic support vector machine (SVM). Topographic maps of the statistical results showed statistically significant difference between the ApEn values of the two groups found in the total spectrum and in delta, theta, beta 2, and gamma. The classifiers (linear, quadratic, and cubic SVMs) revealed high levels of accuracy (respectively 93.20 ± 0.37, 93.16 ± 0.30, 90.62 ± 0.62) and area under the curve (respectively 0.95, 0.94, 0.93). ApEn seems to be a powerful, very sensitive-specific measure for the study of cognitive decline and global cortical alteration/degeneration in the elderly EEG activity.

Analysis of using Newton’s ring to test lens surface radius of curvature

When using Newton’s ring to test lens surface radius of curvature, the air gap in between the master plate and the lens can have either a positive or a negative meniscus shape. The optics for the negative meniscus shape air gap has been widely analyzed and the results are assumed to be valid for the positive meniscus shape air gap. Accurate and approximate analysis are performed in this paper for the positive meniscus shape air gap. Analysis results of this paper show that for the same parameters involved, the Newton’s ring number for the positive meniscus shape air gap is larger than the Newton’s ring number for the negative meniscus shape air gap. The difference between these two Newton’s ring numbers increases as the value of h / r increases, where h is the lens half diameter and r is the master plate surface radius of curvature. For h / r = 0.87, the ratio of these two numbers can be as large as 2.

DETERMINATION, ANALYSIS AND SYNTHESIS OF THE ROOTS OF VALID ALGEBRAIC EQUATIONS USING LOGARITHMIC AMPLITUDE-PHASE FREQUENCY CHARACTERISTICS

The article considers the method of approximate determination, analysis and synthesis of the roots of real algebraic equations of high order. The solution of such problems is relevant in the case of designing information-measuring and control systems, studying the dynamics of movement of various mechanisms (industrial robots, quadrocopters, etc.), determining the trajectories of aircraft, etc. The analytical solution of such problems is limited to equations of the third (sometimes fourth) degree, in other cases it is necessary to use either special sequential algorithms or packages of applied computer programs such as "Wolfram.Matematica", which allow only to find the roots of the equations, but not to synthesize them. The proposed method is based on the application for the decomposition of the studied polyomial (corresponding to the equation) into the simplest multipliers corresponding to aperiodic and/or oscillatory links, asymptotic logarithmic amplitude and phase-frequency characteristics. The form and values of the roots of the equation are proposed to be judged by the slopes at the fracture points of the logarithmic amplitude and phase-frequency characteristics of the polyparticle under study. The construction of logarithmic amplitude and phase-frequency characteristics is carried out by discarding the "small" terms of the polygamy at separate frequency intervals. A feature of the method is the possibility of its use both in conjunction with the computer and without it. Manual use of the method assumes that the user has a calculator and a ruler. The method allows to determine not only the roots of real algebraic equations (both real and complex), but also to establish a visual relationship between the coefficients for the terms of the equations with the type and values of the roots and purposefully change the necessary coefficients to change the parameters and type of roots. The possibilities of the method are not limited to solving real algebraic equations with positive coefficients and integer powers, it shows quite satisfactory results for equations with mixed coefficients and fractional powers. The method is quite simple, clear, has a small error in the case of far spaced roots, but in the case of closely spaced roots, its error increases, although it remains quite acceptable. The article presents the substantiation of the method, shows numerous examples of its capabilities, compares the results obtained with the results obtained with the help of the package of applied computer programs "Wolfram.Matematica".

Convergence rate analysis of Galerkin approximation of inverse potential problem

In this work we analyze the inverse problem of recovering a space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very mild conditions on the problem data. Then we provide an error analysis of a standard reconstruction scheme based on the standard output least-squares formulation with Tikhonov regularization (by an H 1-seminorm penalty), which is then discretized by the Galerkin finite element method with continuous piecewise linear finite elements in space (and also backward Euler method in time for parabolic problems). We present a detailed error analysis of the discrete scheme, and provide convergence rates in a weighted for discrete approximations with respect to the exact potential. The error bounds explicitly depend on the noise level, regularization parameter and discretization parameter(s). Under suitable conditions, we also derive error estimates in the standard and interior L 2 norms. The analysis employs sharp a priori error estimates and nonstandard test functions. Several numerical experiments are given to complement the theoretical analysis.

Phase reduction of strongly coupled limit-cycle oscillators

The phase reduction method has played a key role in the theoretical and experimental analysis of synchronization dynamics of coupled oscillators, but its applicability is limited to the case of weak coupling. In this study, a phase equation that describes strongly coupled limit-cycle oscillators is derived, where the orbit of each oscillator can deform largely depending on the strong parametric coupling. We extend the phase reduction theory for strongly perturbed limit-cycle oscillators and develop an approximate self-consistency analysis to obtain a reduced description of the oscillator dynamics using only the phase variables of the oscillators. Numerical simulations show that the proposed phase equation improves the accuracy to predict the dynamics of strongly coupled oscillators over the conventional description.

Designing Cladded Components for High Temperature Nuclear Service: Part II—Design Rules

AbstractThe challenge of using existing ASME Section III, Division 5, class A metallic materials for the construction of structural components of advanced reactors with corrosive coolants could be mitigated by allowing designers to use cladding to protect the base material from corrosion. However, the existing Section III, Division 5 rules provide no guidance on the evaluation of strain accumulation and creep-fatigue damage in cladded components. The availability of design rules for cladded components that do not require long-term clad material testing could promote the application of the cladding approach to accelerate the deployment schedule of these advanced reactor systems. To avoid long-term properties for the clad materials Part I of this work proposes two approximate design analysis methods for two types of clad materials—soft clads that creep much faster and have lower yield stress than the class A base material, and hard clads that creep much slower and have higher yield stress than the class A base material. The proposed analysis methods approximate the response of a soft clad by treating it as perfectly compliant and of a hard clad by treating it as linear elastic. Based on these approximate design analysis strategies this Part II develops a complete set of design rules for class A components cladded with either soft or hard clad materials. Part II discusses the reasoning behind the proposed design rules and uses example finite element analyses of representative reactor components to illustrate the use of these design methods.

Designing Cladded Components for High Temperature Nuclear Service: Part I—Analysis Methods

AbstractUse of corrosion-resistant cladding can greatly extend the design life of structural components in many advanced reactor systems. However, there are currently no ASME design rules for cladded components to guard against creep-fatigue failure and ratcheting strain accumulation in elevated temperature nuclear service. This paper, presented in two parts, addresses this gap by proposing a design strategy for cladded components that do not require long-term testing of clad materials. The proposed approach relies on approximate design analysis methods for two types of clad materials—a soft clad that creeps much faster than and has lower yield stress than the class A base material and a hard clad that creeps much slower than and has higher yield stress than the class A base material. Part I discusses the approximate analysis strategies for the clad materials—treat a soft clad as perfectly compliant and a hard clad as linear elastic—and Part II develops a complete set of design rules for each of the two types of cladded components. Finite element analyses of representative high temperature reactor components show that the proposed design analysis methods can bound the design quantities in soft cladded components and approximate the design quantities in hard cladded components.

Nine-Point Iterated Rectangle Dichotomy for Finding All Local Minima of Unknown Bounded Surface

Abstract A method is suggested to find all local minima and the global minimum of an unknown two-variable function bounded on a given rectangle regardless of the rectangle area. The method has eight inputs: five inputs defined straightforwardly and three inputs, which are adjustable. The endpoints of the initial intervals constituting the rectangle and a formula for evaluating the two-variable function at any point of this rectangle are the straightforward inputs. The three adjustable inputs are a tolerance with the minimal and maximal numbers of subintervals along each dimension. The tolerance is the secondary adjustable input. Having broken the initial rectangle into a set of subrectangles, the nine-point iterated rectangle dichotomy “gropes” around every local minimum by successively cutting off 75 % of the subrectangle area or dividing the subrectangle in four. A range of subrectangle sets defined by the minimal and maximal numbers of subintervals along each dimension is covered by running the nine-point rectangle dichotomy on every set of subrectangles. As a set of values of currently found local minima points changes no more than by the tolerance, the set of local minimum points and the respective set of minimum values of the surface are returned. The presented approach is applicable to whichever task of finding local extrema is. If primarily the purpose is to find all local maxima or the global maximum of the two-variable function, the presented approach is applied to the function taken with the negative sign. The presented approach is a significant and important contribution to the field of numerical estimation and approximate analysis. Although the method does not assure obtaining all local minima (or maxima) for any two-variable function, setting appropriate minimal and maximal numbers of subintervals makes missing some minima (or maxima) very unlikely.

Efficient steady state analysis of the grid using electromagnetic transient models

• Time-domain steady-state (TDSS) methodology efficiently solves for an accurate steady-state of the grid using EMT models. • The paper presents a decoupling approach that iterates on a waveform to efficiently solve for the steady-state. • The simulation results highlight improvement in accuracy over power flow while solving in fewer iterations compared to EMT analysis. Modern grids contain an increasing number of non-linear grid devices that are accurately modeled only in the time domain. Performing an accurate steady-state analysis with such models requires a transient simulation to infinite (sufficiently long) time, which can be computationally prohibitive. Power flow provides an efficient, but approximate steady state analysis using models based on a single nominal frequency, which fails to represent the true steady-state. We present a new method for efficiently analyzing the steady state response using traditional transient models that is inspired by harmonic balance methods. Rather than solving the underlying ODE by discretizing time, our method iterates on the entire waveform to find an accurate time domain waveform that captures the steady-state dynamics for all three phases. This presents a novel, efficient methodology for accurately studying the steady-state of the power grid. We introduce the concept by studying the steady state of a 14-bus system under various scenarios and highlight the difference between the steady-states achieved through power-flow and our method that uses EMT models.

Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics

Calibrating mathematical models to describe ecological data provides important insight via parameter estimation that is not possible from analysing data alone. When we undertake a mathematical modelling study of ecological or biological data, we must deal with the trade-off between data availability and model complexity. Dealing with the nexus between data availability and model complexity is an ongoing challenge in mathematical modelling, particularly in mathematical biology and mathematical ecology where data collection is often not standardised, and more broad questions about model selection remain relatively open. Therefore, choosing an appropriate model almost always requires case-by-case consideration. In this work we present a straightforward approach to quantitatively explore this trade-off using a case study exploring mathematical models of coral reef regrowth after some ecological disturbance, such as damage caused by a tropical cyclone. In particular, we compare a simple single species ordinary differential equation (ODE) model approach with a more complicated two-species coupled ODE model. Univariate profile likelihood analysis suggests that the both models are practically identifiable. To provide additional insight we construct and compare approximate prediction intervals using a new parameter-wise prediction approximation, confirming both the simple and complex models perform similarly with regard to making predictions. Our approximate parameter-wise prediction interval analysis provides explicit information about how each parameter affects the predictions of each model. Comparing our approximate prediction intervals with a more rigorous and computationally expensive evaluation of the full likelihood shows that the new approximations are reasonable in this case. All algorithms and software to support this work are freely available as jupyter notebooks on GitHub so that they can be adapted to deal with any other ODE-based models.

Analysis and Optimization of Energy Variations in MMCs With Variable DC Voltages

The modular multilevel converter (MMC) containing full-bridge submodules (FBSMs) can increase the modulation index to reduce the energy storage requirement. The MMCs containing FBSMs can also adjust the dc voltage to fit special applications. However, limited research explores the energy storage characteristics of MMCs with variable dc voltages, and few effective approaches can ensure low-energy storage requirements. This study proposes an approximate analysis method for the energy storage requirement in MMC with variable dc voltages. Results reveal that the energy variation under low dc voltages restricts the reduction effects of the increased modulation index on the energy storage requirement. Then, on the basis of the fact that the low ac component of the arm current under low dc voltages provides a large current margin, an optimal circulating current (OCC) is proposed to optimize the energy variation under low dc voltages. In addition, a practical curve-fitting approach is proposed to facilitate the calculation of OCC in real-time controllers. With these approaches, the energy storage requirement with variable dc voltage becomes similar to that with constant rated dc voltage. Simulation and experimental results verify the analysis.

Operational signature-based symbolic hierarchical clustering for building energy, operation, and efficiency towards carbon neutrality

Buildings are considered the enormous source of untapped energy efficiency potential in the global carbon neutrality. It is necessary to ensure that buildings are energy-efficient using operational pattern analytics and diagnostics. Therefore, this study proposes a novel symbolic hierarchical clustering method (named HOS-SAX) to evaluate the building system operation, efficiency, and energy usage patterns. The proposed HOS-SAX method is intended to enhance the existing methods that focus only on the energy usage characteristics and thus offer limited insights on the building system and operational efficiency. The proposed method consists of: (1) Holistic Operational Signature (HOS) and (2) HOS-based symbolic aggregate approximation (SAX) analyses. A HOS analysis is conducted to derive the representative operational signatures for building operation and efficiency using system-, building-, and weather-level data. Then, SAX is performed with the operational signatures derived from the HOS to cluster the building operation patterns. In a case study for a district heating substation serving residential buildings, the HOS-SAX cluster analysis showed 15 sections in the cluster map that visualize the: (1) energy usage, (2) design efficiency, and (3) control efficiency. The cluster map revealed that the sections that operated inefficiently account for approximately 71% of the entire operation period. Moreover, it is expected that the supply temperature of 0.87 °C can be reduced in the most inefficient sections.