First-order Approximation Method Research Articles

Numerical analysis and validation on the phased evacuation time in high-rise buildings

The main aim of this study is to investigate the numerical analysis of phased evacuation and validate the feasibility of high-rise buildings using the control volume model. Based on the same spatial configuration, the number of participants on each floor, and four-phased evacuations of an actual fire drill conducted by a Japanese academic group in 2018, the numerical analysis results for these phased evacuations of this high-rise building have been investigated. The numerical results are in good agreement with the fire drill data in the aspects of the total number of people reaching the ground floor, the space-time feature curve and the first participant on each floor descending to the ground floor. The changes in the number of waiting participants versus time on each floor were obtained and compared in this study with the fire drill data to comprehend the transient situations of the internal participants in this high-rise building during the phased evacuation. Furthermore, the results of the first-order approximation method of NFPA, the Melinek and Booth method and the Route B calculation of the Japanese Building Center Verification Method for the total building evacuation are presented to discuss the differences between the phased evacuation and the total building evacuation.

DC Voltage Source Based on a Battery of Supercapacitors with a Regulator in the Form of an Isolated Boost LCC Resonant Converter

Studies have been conducted on Energy storage systems (ESS) that replaced lithium-ion batteries (LIB) by the thermal runaway of the existing LIB. Using only the supercapacitor (SC) as a direct current power source in applications such as supercapacitor-based ESSs and mobile electric vehicle charging stations (MCSs) reduces the output voltage of the SC linearly. To solve this problem, this paper combines a boost converter capable of achieving regulatable constant voltage from an input of an SC bank to an output of a rectifier and an inductor/capacitor/capacitor (LCC) resonance converter. In this paper, an electrical double-layer capacitor (EDLC) known as SC was constructed as 64.8-V 400-FEDLC for experimental analysis. This EDLC is a high-capacity EDLC bank using 120 EDLCs with 30 serial connections and 4 parallel connections. In addition, resonance compensation circuits are analyzed and designed using a first-order harmonic approximation method (FHA). The analysis shows that the LCC resonance compensation converter is more suitable for EDLC standalone systems as an energy storage system, for LCC resonance converter topologies combined with EDLC discharge characteristics, constant voltage discharge is designed under an efficient discharge strategy, i.e., variable load conditions after the first constant voltage discharge. Based on LCC compensation analysis, the system has an optimum frequency, which allows the system to operate at the maximum efficiency point. By combining constant voltage power characteristics, constant voltage power becomes the same as the optimal power point, and thus high efficiency could be maintained in the constant voltage stage. Finally, the above design is verified through experiments.

A Meta Reinforcement Learning-Based Task Offloading Strategy for IoT Devices in an Edge Cloud Computing Environment

Developing an effective task offloading strategy has been a focus of research to improve the task processing speed of IoT devices in recent years. Some of the reinforcement learning-based policies can improve the dependence of heuristic algorithms on models through continuous interactive exploration of the edge environment; however, when the environment changes, such reinforcement learning algorithms cannot adapt to the environment and need to spend time on retraining. This paper proposes an adaptive task offloading strategy based on meta reinforcement learning with task latency and device energy consumption as optimization targets to overcome this challenge. An edge system model with a wireless charging module is developed to improve the ability of IoT devices to provide service constantly. A Seq2Seq-based neural network is built as a task strategy network to solve the problem of difficult network training due to different dimensions of task sequences. A first-order approximation method is proposed to accelerate the calculation of the Seq2Seq network meta-strategy training, which involves quadratic gradients. The experimental results show that, compared with existing methods, the algorithm in this paper has better performance in different tasks and network environments, can effectively reduce the task processing delay and device energy consumption, and can quickly adapt to new environments.

A propensity-based framework for measurement uncertainty analysis

We regard the measurand (or influence quantity) as a random variable characterized by central tendency and dispersion. We define ‘propensity’ as the sum of the central tendency and dispersion. We argue that the state of propensity can be described by a probability density function (PDF) that we name ‘propensity spectrum’. This paper proposes a propensity-based framework for measurement uncertainty analysis of the measurand that is related to influence quantities through a measurement model. The proposed framework encodes the state of propensity of the measurand in the form of a PDF (propensity spectrum) based on all available information about influence quantities. This can be achieved by an “exact” method based on the principle of propagation of distributions, or a first-order approximation method (the law of propagation of uncertainty). A case study is presented to demonstrate the methods provided by the proposed framework, compared to the GUM method and Bayesian methods.

Confidence Intervals by Bootstrapping Approach: A Significance Review

A confidence interval is an interval estimate of a parameter of a population calculated from a sample drawn from the population. Bootstrapping method, which involves producing several new data sets that are resampled from the original data in order to estimate parameter for each newly created data set, allowing an empirical distribution for the parameter to be estimated. Since certain statistics are harder to estimate, confidence intervals are rarely employed. Several statistics might necessitate multi-step formulas assuming that are impractical for calculating confidence intervals. This paper reviews research on the concept of bootstrapping and bootstrap confidence interval. The current narrative analysis was developed to answer the main research question: (1) What is the concept of the bootstrap method and bootstrap confidence interval? (2) What are the methods of bootstrapping to obtain confidence interval? This study has found general bootstrap method idea, various techniques of bootstrap methods, its advantages and disadvantages, and its limitations. There are normal interval method, percentile bootstrap method, basic method, first-order normal approximation method, bias-corrected bootstrap, accelerated bias-corrected bootstrap and bootstrap-t method. This study concludes that the advantages of using bootstrap CI is that it does not require any assumptions about the shape of distribution and universality of the approach. Bootstrapping is a computer-intensive statistical technique that relies significantly on modern high-speed digital computers to do massive computations.

Distributed sliding mode consensus control for multiple discrete-Time Euler-Lagrange systems

This paper studies the consensus problem for multiple discrete-time Euler-Lagrange (DTEL) systems via distributed sliding mode control under a directed graph. Different from the existing work, we transform the DTEL system into a discrete-time second-order nonlinear system through the famous Euler’s first-order approximation method, and a local discrete-time disturbance observer (DTDO) is introduced to estimate both model uncertainties and external disturbances. In addition, a novel integral sliding surface is proposed to guarantee that the consensus error is asymptotically stable when agents move on the sliding surface. Based on such a sliding manifold combined with the proposed DTDO, a distributed sliding mode controller is constructed. Meanwhile, a sufficient condition is derived to ensure the existence of the quasi-sliding mode motion. Finally, numerical simulations of the two-link robot arm’s system are carried out to verify the effectiveness of the proposed control algorithm.

Assessment of predicted aircraft engine non-volatile particulate matter emissions at Hangzhou Xiaoshan International Airport using an integrated method

ABSTRACT Assessing the aircraft engine nonvolatile particulate matter (nvPM) emissions during landing and take-off (LTO) cycles is significant for airport air quality management. However, presently few prior studies have examined aircraft engine nvPM emissions on a daily basis for optimizing flight operations at airports. Therefore, based on the latest first-order approximation method of engine nvPM emissions, we introduce the engine emission data and aircraft flight data to establish an integrated method for estimating daily aircraft engine nvPM emissions at airports. This method can be applied to obtain different engine nvPM mass and number emissions in each phase of the LTO cycle, and therefore the total nvPM mass and number emissions in different time periods can be estimated for the analysis of the sources and trends of daily aircraft engine nvPM emissions during LTO cycles at Hangzhou Xiaoshan International Airport. Results show that the highest aircraft engine nvPM mass and number emissions are generally predicted to occur in the climb and taxi/ground idle phase, respectively. The proportion of total engine nvPM mass and number emissions in each phase of the LTO cycle could also be estimated, specifically the take-off phase (21% & 6%), climb phase (52% &15%), approach phase (8% & 27%), and taxi/ground idle phase (19% & 52%). In addition, the trends of hourly engine nvPM mass and number emissions during LTO cycles within a day are similar, but the predicted highest total hourly engine nvPM mass and number emissions occur in different time periods (7:00–8:00 a.m. & 11:00–12:00 a.m.) at the airport, and the total hourly engine nvPM mass and number emissions at 6:00 a.m. to 17:00 p.m. are generally higher than those of the rest periods. These results are valuable for optimizing flight operations for mitigating the environmental impact of aircraft engine nvPM emissions. Implications: The integrated method for estimating engine nvPM mass and number emissions in the LTO cycle based on FOA4.0 method reported in this study is effective to assess the sources and trends of daily aircraft engine nvPM emissions during LTO cycles at airports, which is valuable for optimizing flight operations considering the environmental impact of aircraft engine nvPM emissions. When the relevant aircraft flights, engine parameters, and engine nvPM emission databases embedded in the integrated method for any airport are established, the method is feasible to assess the sources and trends of aircraft engine nvPM emissions during LTO cycles at any time period in the airport.

Ellipsoid non-probabilistic reliability analysis of the crack growth fatigue of a new titanium alloy used in deep-sea manned cabin

Reliability analysis of crack growth fatigue of titanium alloy is one of the important guarantees for the safety of deep-sea manned cabin. However, the traditional probabilistic fatigue reliability analysis methods often need accurate parameter statistics information. In this paper, under the condition of the limited test data, a first-order approximate ellipsoid non-probabilistic reliability analysis method for fatigue crack growth of a titanium alloy was proposed. A limit state equation of the crack growth correction model, considering the small crack effect, is formulated according to the fatigue life model. The uncertain parameters are constructed by the interval model, normal distribution, and Khachiyan algorithm. The different limit state equations are obtained by changing the coefficient κ. The first-order approximation and Monte Carlo methods are used to solve the reliability of the ellipsoid model. Calculations demonstrate that the results of the ellipsoid non-probabilistic reliability method are more conservative than that of the probabilistic reliability method. When κ is less than or equal to 2, the Khachiyan algorithm is preferred to build the ellipsoid model, and when κ is greater than 2, the interval model is preferred. Through parameter sensitivity analysis, the uncertain parameters KC, n, m, A, and ΔKthR are found to significantly affect the crack growth rate.

Approximated dielectric tensor of the biaxial α-SnSe crystal

We present the principal components of the dielectric tensor for α-SnSe biaxial single crystal in the spectral range from 0.74 to 6.42 eV at room temperature (300 K) using spectroscopic ellipsometry. Aspnes’ first-order approximation method was applied to obtain approximated pseudodielectric response from the pseudodielectric tensor measured at an angle of incidence of ϕ = 68.8°. Multilayer calculations were then performed to extract the pure dielectric tensor without surface roughness artifacts. The Tauc–Lorentz model was applied to describe the critical point structures, and the optical constants along the principal axes of biaxial α-SnSe single crystal can be now calculated at arbitrary wavelength for device applications.

Numerical and Analytical Analysis of Stochastic Electromagnetic Fields Coupling to a Printed Circuit Board Trace

Stochastic electromagnetic fields coupling to printed circuit board (PCB) traces are important to the understanding of electromagnetic compatibility at high frequencies when the circuits or systems are electrically large. In this article, it is studied both numerically and analytically, and the factors affecting the absorbed power are investigated. We present new methods to determine the level of coupling on PCB traces or other transmission lines on a dielectric substrate. A Monte Carlo method is applied to generate random uniform fields, and the quasi-TEM transmission line model is employed to compute the response of the trace for each plane wave numerically. In the analytical method, the closed-form expressions of the zero-order and the first-order approximations are established for the PCB trace. Based on the first-order approximation method and the numerical results, a computationally efficient empirical method is developed to estimate the power received. The absorbed power increases with frequency in the electrically short case after which multiple resonances can be seen. The absorbed power in the matched case is neither the largest nor the smallest among all the cases. It increases with the square of the substrate height but decreases with the permittivity of the substrate.

Three Calculation Methods of the WGM Cylindrical Cavity Diameter

WGM mode in cylindrical cavity can be rapidly calibrated with analytical approximate formulas based on cylindrical micro-cavity WGM resonance peaks position. On this basis, the diameter of circular cavity can be calculated by applying the three methods, which are the first-order approximation method, the second-order approximation method and mode field radius. When comparing the results which are got from the three methods with the actual geometric diameter, we find that the deviation is within 3%, 2%, 1% respectively. As a result, the diameter of circular cavity can be correctly worked out by making use of these three ways mentioned.

A new efficient Bayesian parameter inference strategy: Application to flow and pesticide transport through unsaturated porous media

Statistical calibration of flow and transport models in unsaturated porous media is often carried out with Markov Chain Monte Carlo (MCMC) methods. However, the practicality of these methods is limited by their computational requirement, particularly when large prior intervals are assigned to the model parameters. In this work, a new operational strategy is investigated to alleviate the computational burden of MCMC samplers using results from a preliminary calibration performed with the First-Order Approximation (FOA) method. With the new strategy, the posterior distribution is approximated using a high-order Polynomial Chaos Expansion (PCE) surrogate model constructed over reduced parameter ranges. The latter are obtained from the 99.9 FOA confidence intervals.Two challenging test cases are investigated to assess efficiency and accuracy of the new strategy. The first test case considers estimation of flow and pesticide transport parameters from a synthetic infiltration experiment. The second test case deals with the assessment of unsaturated hydraulic soil parameters from a real-word laboratory drainage experiment. The results of the proposed strategy are compared to those of FOA, of the standard MCMC method and of an improved MCMC method in which the sampler is preconditioned with draws from the FOA posterior distribution. For both test cases, the new strategy provides accurate mean estimated parameter values and uncertainty regions and is much more efficient than the other MCMC methods. It is up to 50 times more efficient than the standard MCMC method.

A defender-attacker model and algorithm for maximizing weighted expected hitting time with application to conservation planning

ABSTRACTThis article studies an interdiction problem in which two agents with opposed interests, a defender and an attacker, interact in a system governed by an absorbing discrete-time Markov chain. The defender protects a subset of transient states, whereas the attacker targets a subset of the unprotected states. By changing some of the transition probabilities related to the attacked states, the attacker seeks to minimize the Weighted Expected Hitting Time (WEHT). The defender seeks to maximize the attacker’s minimum possible objective, mitigating the worst-case WEHT. Many applications can be represented by this problem; this article focuses on conservation planning. We present a defender–attacker model and algorithm for maximizing the minimum WEHT. As WEHT is not generally a convex function of the attacker’s decisions, we examine large-scale integer programming formulations and first-order approximation methods for its solution. We also develop an algorithm for solving the defender’s problem via mixed-integer programming methods augmented by supervalid inequalities. The efficacy of the proposed solution methods is then evaluated using data from a conservation case study, along with an array of randomly generated instances.

Robust output feedback attitude tracking control for rigid-flexible coupling spacecraft

This paper investigates the robust attitude tracking control problem for a rigid-flexible coupling spacecraft. First, the dynamic model for a rigid-flexible coupling spacecraft is established based on the first-order approximation method to fully reveal the coupling effect between rigid movement and flexible displacement when the spacecraft is in rapid maneuver. In the condition that flexible vibration measurements are not available, an robust output feedback controller which is independent of model is presented using Lyapunov method with considering state-independent disturbances. To resolve the chattering problem caused by the discontinuous sign function, a modified continuous output feedback controller is proposed by introducing functions with continuous property. Rigorous proof is achieved showing that the proposed control law ensures asymptotic stability and guarantees the attitude of a rigid-flexible spacecraft to track a time-varying reference attitude based on angle and angular velocity measurements only. Finally, simulations are carried out to verify the simplicity and effectiveness of the proposed control scheme.

A Weighted Saddlepoint Approximation Method for System Reliability Analysis

The relationship between the reliability probabilities of the component and the system is hard to get. If this relationship can be obtained easily, the reliability of the system can be calculated by using the reliability structures of the components. The common method to express this relationship is using the linear correlation index, which only shows the linear correlation between the components failure rather than the relationship between high nonlinear functions. In order to describe this relationship accurately and calculate the system reliability using the component reliability structures, a Uniform Design (UD)-Saddlepoint Approximation (SA)-based system reliability analysis method is proposed. The system reliability analysis method is decomposed to three simple steps: (1) calculating the weight coefficient which represents the contribution rate of each component to system reliability, (2) approximating Cumulant Generation Function (CGF) of each component, (3) calculating CGF of the system and approximating the system reliability with SA method. The weight coefficient of each component is derived from UD method, and a variable interval selection method is developed to decrease the required number of samples and increase the accuracy of the weight coefficients. First-Order Saddlepoint Approximation (FOSA) method or Mean-Value First-Order Saddlepoint Approximation (MVFOSA) method is used to analyze the CGF of a component performance function. Then the CGF of the system can be obtained by the weighted addition law by combining the CGFs of components performance functions with the weight coefficients. Finally, the system reliability can be approximated by SA method. Four examples are employed to demonstrate that the new method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

An Improvement on SSA Method for EM Scattering From Electrically Large Rough Sea Surface

An improved facet model for the predication of the normalized radar cross section (NRCS) of electrically large rough sea surface was proposed based on the first-order small slope approximation (SSA-1) method, the Bragg scattering mechanism, and the specular scattering mechanism. The proposed method is able to evaluate both the complex reflective function and NRCS of electrically large sea surfaces from as low as ultrahigh frequency band to as high as Ka-band. The main idea is that a tilt sea facet can be regarded as the superposition of a planner facet and the microscopic profile; the latter is assumed to be a set of sinusoidal ripple patches. Thus, the integration kernel in SSA-1 over several small facets can be replaced by a large facet with a short wave modification. The efficiency increases because of the much larger mesh size than SSA. Then, both the backscattering and bistatic scattering NRCS results calculated by the proposed method were compared with those predicated by SSA-1, and all of the results show that the proposed method has the merits of high calculation efficiency as well as calculation accuracy.

R-based reproduction of the estimation process hidden behind NONMEM® Part 1: first-order approximation method

NONMEM® is the most-widely used nonlinear mixed effects modelling tool introduced into popu - lation PK/PD analysis. Even though thousands of pharmaceutical scientists utilize NONMEM® rou- tinely for their data analysis, the various estimation methods implemented in NONMEM® remain a mystery for most users due to the complex statistical and mathematical derivations underlying the algorithm used in NONMEM®. In this tutorial, we demonstrated how to directly obtain the objec- tive function value and post hoc η for the first order approximation method by the use of R. We hope that this tutorial helps pharmacometricians understand the underlying estimation process of nonlinear mixed effects modelling.

Frame frequency prediction for Risley-prism-based imaging laser radar.

A dual-wedge scanner has potential applications in laser imaging radar. To realize fast scanning imaging without a blind region, the rotation rates of the wedges have to be controlled to perform beam scanning along appropriate track paths. The first-order paraxial approximation method is employed to investigate the 2D scan patterns and path density for different angular frequency ratios of the wedges rotating steadily in the same and opposite directions. The frame rate of no-blind-region scanning imaging is estimated in terms of the imaging coverage requirement. The internal relations between the rotation rates, the instantaneous field of view (IFOV), and the imaging velocity are revealed. The results show that the spiral scanning trace, resulting from co-rotating wedges, is dense in the center and sparse at the edge of the scanning field. The reverse results can be obtained for the rosette scanning trace, resulting from counter-rotating wedges. The denser the scanning trace is, the longer the scan period is. The faster the wedges rotate and the wider the IFOV is, the higher the frame rate is. When the ratio of the width of IFOV to the angular radius of the scanning field is 0.15, the frame rate of no-blind-region spiral scanning imaging can be up to 18 fps for wedge rotation rate of 12000 r/min, and that for rosette scanning imaging can be up to 20 fps.

Estimation of uncertainty propagation in flood inundation mapping using a 1-D hydraulic model

A need for more accurate flood inundation maps has recently arisen because of the increasing frequency and extremity of flood events. The accuracy of flood inundation maps is determined by the uncertainty propagated from all of the variables involved in the overall process of flood inundation modelling. Despite our advanced understanding of flood progression, it is impossible to eliminate the uncertainty because of the constraints involving cost, time, knowledge, and technology. Nevertheless, uncertainty analysis in flood inundation mapping can provide useful information for flood risk management. The twin objectives of this study were firstly to estimate the propagated uncertainty rates of key variables in flood inundation mapping by using the first-order approximation method and secondly to evaluate the relative sensitivities of the model variables by using the Hornberger–Spear–Young (HSY) method. Monte Carlo simulations using the Hydrologic Engineering Center's River Analysis System and triangle-based interpolation were performed to investigate the uncertainty arising from discharge, topography, and Manning's n in the East Fork of the White River near Seymour, Indiana, and in Strouds Creek in Orange County, North Carolina. We found that the uncertainty of a single variable is propagated differently to the flood inundation area depending on the effects of other variables in the overall process. The uncertainty was linearly/nonlinearly propagated corresponding to valley shapes of the reaches. In addition, the HSY sensitivity analysis revealed the topography of Seymour reach and the discharge of Strouds Creek to be major contributors to the change of flood inundation area. Copyright © 2014 John Wiley & Sons, Ltd.

Analytical quality assessment of iteratively reweighted least-squares (IRLS) method

The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.