Approximate Estimation Research Articles

A statistical interpretation of the EN 1993-1-10 brittle fracture criteria

EN 1993-1-10 contains tables for selection of steel quality class with respect to avoidance of brittle fracture. The conservatism of the method has not previously been examined statistically. The original verification of the method has been established basically on a deterministic assessment of 19 double edge cracked specimen tests. This verification has not accounted for e.g. constraint effects and the treatment of nominal data versus measured data is not fully satisfactory. Therefore, here the confidence of the procedure is examined statistically using more up to date information regarding the Charpy-V vs fracture toughness correlation and a quantitative assessment of the constraint effect. The study has two main purposes. First, to present a method by which consistent statistically defined criteria for a standard like EN 1993-1-10 can be developed and second, to obtain an approximate estimate of the conservatism contained in the present methodology. The statistical treatment is applied to the same 19 specimens originally used for the verification of the method.

Stability of Fixed Points of Partial Contractivities and Fractal Surfaces

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces.

On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations

Abstract In this paper, we propose and analyze a discontinuous Galerkin finite element method for solving the transient Boussinesq incompressible heat conducting fluid flow equations. This method utilizes an upwind approach to handle the nonlinear convective terms effectively. We discuss new a priori bounds for the semidiscrete discontinuous Galerkin approximations. Furthermore, we establish optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in L 2 \mathbf{L}^{2} and energy norms, the temperature approximation in L 2 L^{2} and energy norms and pressure approximation in L 2 L^{2} -norm for t > 0 t>0 . Additionally, under the smallness assumption on the data, we prove uniform in time error estimates. We also consider a backward Euler scheme for full discretization and derive fully discrete error estimates. Finally, we provide numerical examples to support the theoretical conclusions.

Projective tensor products of approximation spaces associated with positive operators

In this paper the projective tensor products of approximation spaces associated with positive operators in Banach spaces are characterized. We show that the tensor products of approximation spaces can be considered as the interpolation spaces generated by $K$-method of real interpolation. The inequalities that provide a sharp estimates of best approximations by analytic vectors of positive operators on projective tensor products are established. Application to spectral approximations of the regular elliptic operators on projective tensor products of Lebesgue spaces is shown.

Seismic structure of the Balmuccia Peridotite from a high-resolution refraction and reflection survey

SUMMARY In anticipation of a forthcoming scientific deep drilling initiative within the Western Alps near Balmuccia, Italy, a high-resolution seismic survey is performed at the proposed drill site. This site is situated within the Ivrea Verbano Zone (IVZ), characterized by lower crustal materials and fragments of upper-mantle rocks exposed adjacent to the Insubric Line. The 2-km-long seismic survey crosses an isolated km-scale outcrop of peridotite near the town of Balmuccia. Applying P-wave traveltime tomography, a substantial contrast in seismic velocities is identified, with velocities in the range of 1–8 km s−1. The peridotite displays velocities ranging from 6 to 8 km s−1. The higher velocities near 8 km s−1 are consistent with laboratory measurements on small-scale samples, while the low-velocity areas within the peridotite body reflect the influence of fractures and faults. The mean velocity derived for the peridotite body is ca. 7 km s−1. The reflection seismic analysis reveals subvertical reflectors positioned at the peridotite boundaries mapped at the surface, converging at a depth of ca. 0.175 km b.s.l. which images a lens-like structure for the peridotite body. However, the area beneath the imaged lens and the deeper Ivrea Geophysical Body (IGB) suggested by earlier studies is not well imaged, which leaves room for other interpretations regarding the relationship of these two bodies. Prior geophysical investigations provide only approximate depth estimates for the top of the IGB, spanning between 1–3 km depth b.s.l. Although the reflection data do not exhibit a series of continuous reflectors beneath the peridotite, a prominent reflection at ca. 1.3 km depth may indicate the top of the IGB.

Calculation of electrical energy losses in distribution networks for power supply using oil and vacuum circuit breakers

A method for approximate estimation of load losses in distribution networks from 6 to 10 kV, as well as for lower voltage networks, has been proposed. The main advantage of this method is that the root mean square current is calculated only once for a series of calculations. This approach significantly reduces the time required for calculations and improves their accuracy, as it eliminates the need for multiple determinations of the root mean square current for each individual calculation. The proposed approach contributes to a better understanding of the influence of various factors on load losses, which allows for more effective planning and management of distribution networks. This is particularly important in the context of increasing loads on electrical networks and higher demands for their reliability and efficiency. In the calculation of electrical energy losses in distribution networks from 6 to 10 kV, methods that use generalized coefficients of electrical circuits and operating modes in the form of regression equations are widely applied. The most significant and independent factors, such as the input of active energy, total line length, number of line sections, total number of transformers, and their total installed capacity, must be taken into account and are included in the calculation equation. Additionally, the components used and their regular maintenance play an important role in electrical energy losses in electrical networks. The main direction of research is the optimization of distribution network parameters, taking into account the latest technologies and materials, as well as the implementation of automated monitoring and control systems that will allow timely detection and elimination of problems associated with electrical energy losses. The proposed method for estimating load losses in distribution networks is a promising direction for the development of the energy sector, which will contribute to improving the efficiency and reliability of electrical networks, as well as reducing the costs of their operation and maintenance.

A simple Cox approach to estimating risk ratios without sharing individual-level data in multi-site studies.

Epidemiologic studies frequently use risk ratios to quantify associations between exposures and binary outcomes. When the data are physically stored at multiple data partners, it can be challenging to perform individual-level analysis if data cannot be pooled centrally due to privacy constraints. Existing methods either require multiple file transfers between each data partner and an analysis center (e.g., distributed regression) or only provide approximate estimation of the risk ratio (e.g., meta-analysis). Here we develop a practical method that requires a single transfer of eight summary-level quantities from each data partner. Our approach leverages an existing risk-set method and software originally developed for Cox regression. Sharing only summary-level information, the proposed method provides risk ratio estimates and confidence intervals identical to those that would be provided - if individual-level data were pooled - by the modified Poisson regression. We justify the method theoretically, confirm its performance using simulated data, and implement it in a distributed analysis of COVID-19 data from the U.S. Food and Drug Administration's Sentinel System.

Efficiency and Mechanism of Catalytic Siloxane Exchange in Vitrimer Polymers: Modeling and Density Functional Theory Investigations.

Of late, siloxane-containing vitrimers have gained significant interest due to their fast dynamic characteristics over a reasonable temperature range (180-220 °C), making them well-suited for diverse applications. The exchange reaction pathway in the siloxane vitrimers is accountable for the covalent adaptive network, with the reaction's effectiveness being regulated by either organic or organometallic catalysts. However, directly studying the exchange reaction pathway in the bulk phase using experimental approaches is challenging because of the intricate and interconnected structure of these vitrimers. Here, we perform comprehensive density functional theory (DFT) and experimental investigations to discover the detailed catalytic efficacy of siloxane exchange and provide direction for the reaction process using a 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) catalyst. The calculated transition barrier energy and catalytic efficiency of hexamethyldisiloxane and dihydroxy-dimethylsilane exchange derived from the nudged elastic band with transition-state calculations strongly agree with the experimental findings. In addition, Fukui indices, along with partial charges, are employed to evaluate the nucleophilic and electrophilic behaviors of silanol and siloxane molecules. Our analysis revealed that by utilizing the Fukui indices of both the acid and the base, we can make an approximate estimation of the respective kinetics of the SN2 process in the siloxane exchange reaction mechanism. These findings establish a foundation for comprehending a crucial aspect of the exchange mechanism in siloxane vitrimer systems and could aid in the development of novel catalysts.

Site Characterization and Shallow Shear Velocity through HVSR Measurements around the Hyderabad Metropolitan Region, India

ABSTRACT We investigate the site characterization and shallow shear velocity profiles from the analysis of the Horizontal to Vertical Spectral ratio (HVSR) around the Hyderabad metropolitan region (HMR), which falls under the southern Indian shield. This work uses both the ambient noise and microearthquake data to compute the HVSR, and additionally the Random Decrement technique to compute the HVSR of extracted Rayleigh waves. This study indicates comparable HVSR curves at each station with the three different datasets, from which we obtain the average dominant frequency (f0) and amplification value (A0). They are further used to calculate the seismic vulnerability index value (Kg). We observe that the value of f0 around the HMR is not fixed, but is varying in the range of 3.4 to 18 Hz, whereas the value of A0 is in the range of 1.7 to 12 approximately and Kg in the range of 0.16 to 1.68 approximately, with an exception of ∼ 33 at VKB (Vikarabad) station, which may be due to a local unconsolidated sub-surface structure. Based on the Diffused Field Assumption (DFA), we invert the average HVSR curves and average dispersion curves of Rayleigh waves, and provide the shallow shear velocity profiles up to 300 m, along with an approximate estimate of VS30 (in upper 30 m depth). The estimated VS30 values vary between 911 to 3143 m/s, falling under the classifications A and B (mostly Hard Rock and Rock type) of National Earthquake Hazards Reduction Program (NEHRP) (BSSC, 2001). However, our study shows some stations with shear velocity inversions at shallow depths within 300 m, indicating layers of low velocity, needing further study. In the absence of detailed near-surface findings, these findings are valuable inputs for geotechnical engineering studies and urban-city planning around the HMR, and emphasizes the effectiveness the HVSR method to determine sub-surface topography and/or unknown soil structures as an economical investigation viability.

Monte Carlo simulation of UV-driven synthesis of complex organic molecules on icy grain surfaces

Context. Complex organic molecules (COMs) have been widely observed in molecular clouds and protostellar environments. One of the formation mechanisms of COMs is radical reactions on the icy grain surface driven by UV irradiation. While many experiments have reported that various COMs (including biomolecules) can be synthesized under such ice conditions, the majority of the reaction processes are unclear. Complementary numerical simulations are necessary to unveil the synthetic process behind the formation of COMs. Aims. In this study, we develop a chemical reaction simulation using a Monte Carlo method. To explore the complex reaction network of COM synthesis, the model was designed to eliminate the need to prepare reaction pathways in advance and to keep computational costs low. This allows for broad parameter surveys and a global investigation of COM synthesis reactions. With this simulation, we investigate the chemical reactions occurring on icy dust surfaces during and after UV irradiation, assuming a protoplanetary disk environment. We aim to reveal the types of organic molecules produced in a disk and the formation mechanisms of COMs, in particular, amino acids and sugars. Methods. The Monte Carlo method we developed here produces reaction sequences by selecting a reaction from all candidate reactions at each calculation step, based on Arrhenius-type weighting. For our purpose, we significantly accelerated the calculation by adopting an approximate estimation of activation energy without expensive quantum chemical calculations. Results. The results show that photodissociation and subsequent radical-radical reactions cause random rearrangement of the covalent bonds in the initial molecules composed of methanol, formaldehyde, ammonia, and water. Consequently, highly complex molecules such as amino acids and sugars were produced in a wide range of the initial conditions. We found that the final abundances of amino acids and sugars have extremely similar dependence on the atomic ratios of the initial molecules, which peak at C/H ~ 0.1–0.3 and O/H ~ 0.3–0.5, although the amino acids abundance is usually more than ten times higher than that of sugars. To understand this dependence, a semi-analytical formula was derived. Additionally, parameter surveys of temperature, photon energy, and other factors have suggested that the decomposition reactions of amino acids and sugars undergo a rapid transition within the threshold of a given parameter.

A priori estimates of the unsteady incompressible thermomicropolar fluid equations and its numerical analysis based on penalty finite element method

In this paper, the unsteady incompressible thermomicropolar fluid (UITF) equations are considered. Theoretically, some a priori regularity conclusions are presented firstly, which seem to be not available in the literatures. Numerically, a penalty finite element method (PFEM) for the UITF equations is studied, the Euler semi-implicit temporal semi-discrete method of the penalty UITF equations is proposed, the stability and the L2-H1 error estimates of the temporal discrete solutions are proved. Finally, the stability and the L2-H1 error estimates for the finite element fully-discrete approximation of the penalty UITF equations are rigorously proved. The accuracy and efficiency of the fully-discrete PFEM are demonstrated by some numerical examples.

On estimates of M-term approximations of the Sobolev class in the Lorentz space

On estimates of M-term approximations of the Sobolev class in the Lorentz space

Resilient Factor Graph-Based GNSS/IMU/Vision/Odo Integrated Navigation Scheme Enhanced by Noise Approximate Gaussian Estimation in Challenging Environments

The signal blockage and multipath effects of the Global Navigation Satellite System (GNSS) caused by urban canyon scenarios have brought great technical challenges to the positioning and navigation of autonomous vehicles. In this paper, an improved factor graph optimization algorithm enhanced by a resilient noise model is proposed. The measurement noise is resilient and adjusted based on an approximate Gaussian distribution-based estimation. In estimating and adjusting the noise parameters of the measurement model, the error covariance matrix of the multi-sensor fusion positioning system is dynamically optimized to improve the system accuracy. Firstly, according to the approximate Gaussian statistical property of the GNSS/odometer velocity residual sequence, the measured data are divided into an approximate Gaussian fitting region and an approximate Gaussian convergence region. Secondly, the interval is divided according to the measured data, and the corresponding variational Bayesian network and Gaussian mixture model are used to estimate the innovation online. Further, the noise covariance matrix of the adaptive factor graph-based model is dynamically optimized using the estimated noise parameters. Finally, based on low-cost inertial navigation equipment, GNSS, odometer, and vision, the algorithm is implemented and verified using a simulation platform and real-vehicle road test. The experimental results show that in a complex urban road environment, compared with the traditional factor graph fusion localization algorithm, the maximum improvement in accuracy of the proposed algorithm can reach 65.63%, 39.52%, and 42.95% for heading, position, and velocity, respectively.

ROUTE OF SOUTH SECTION OF BUDVA BYPASS - REVIEW OF PRELIMINARY DESIGN OF ORGANIZATION AND TECHNOLOGY CONSTRUCTION

<p class="ABSTRACT">The Budva bypass, spanning approximately 30 kilometers, is divided into three distinct sections: North, Middle, and South. The Terms of reference required the preparation of a Preliminary design for the construction elements of all structures along the section and route. The Southern section, which is the subject of this article, begins at the end of the Middle section in Vrijesno. The route of the Southern Section goes through the hilly hinterland above the Budva coast, from Kamenovo to Petrovac. In Petrovac, it is connected to the main road M-2 Petrovac-Sotonići-Virpazar via the intersection "Petrovac". The total length of the Southern section is 8.56km. There are five bridges and one tunnel in this route. There are, also, retaining structures and slope protection, conection routes and deviations, one interchange, and noise protection walls on this section of bypass. In this article, parts of Preliminary Design of organization and technology construction are showned. Network plan structure, approximate estimation of the duration of the works, approximate cost estimation, and approximate cash flow estimation during construction are presented.</p>

Problem-Based Learning for Calculating Kinetic Parameters from Michaelis-Menten Equation

In “Advanced Enzymology” at the University of Barcelona, we teach various methods for identifying uni-uni irreversible reactions. Kinetic constants such as maximum velocity (Vmax) and Michaelis constant (Km) are calculated using non-linear regression with the Michaelis-Menten equation. However, if a computer is not available, students must calculate these kinetic parameters using linear regressions with Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf plots. Michaelis-Menten equation: v = (Vmax [S]) / (Km + [S]), Lineweaver-Burk equation: 1/v = (Km/Vmax) (1/[S]) + 1/Vmax, Eadie-Hofstee equation: v = – Km (v/[S]) + Vmax, Hanes-Woolf equation: [S]/v = (1/Vmax) [S] + (Km/Vmax). The objective of this work was that students explore various methods for calculating kinetic constants and determine the most effective approach. A problem was prepared with data on substrate concentrations ([S]) and reaction rates (v). Data points with lower substrate concentration, and also with lower velocities had higher errors. The Michaelis-Menten plot provided only an approximate estimation of the kinetic constants, as it is not a linear graph. The Lineweaver-Burk plot generated maximum velocities that were too low due to the higher errors for low substrate concentrations, rendering impossible values of the kinetic parameters. The Eadie-Hofstee plot provided better results, as the values of v/[S] compensated their errors. Furthermore, kinetic constants were obtained directly from the slope and intersection of the line equation. The Hanes-Woolf plot also produced correct values for kinetic parameters, since high substrate concentrations were less erroneous than lower ones. After completing this computer class, students were very satisfied and learned the different methods for obtaining kinetic parameters. Non-linear regression is undoubtedly the most accurate method for obtaining kinetic parameters values. However, in the absence of computers, the Eadie-Hofstee plot is the best and most commonly used plot in kinetic papers.

Dynamic ant colony optimization algorithm for parameter estimation of PEM fuel cell

Proton Exchange Membrane Fuel Cells (PEMFCs) provide a reliable, pollution-free, sustainable, and stable power generating alternative to non-renewable resources, and they do not self-discharge. Proton exchange membrane fuel cells (PEMFCs) necessitate correct parameter estimates for effective investigation, modelling and designing effective fuel cells, highlighting the importance of exact modelling for successful use in many industries. The present research aims to determine the approximate parameters estimation of PEMFC using a modified algorithm derived from the Ant Colony Optimization (ACO) meta-heuristic algorithm. In order to provide justification for the algorithm, it is initially benchmarked against 10 functions. The study compares the outcomes of PEMFC parameter estimation through the Dynamic Ant Colony Optimisation (DACO) algorithm including some additional metaheuristic algorithms such as Ant Colony Optimisation (ACO), Particle Swarm Optimisation (PSO), Artificial Bee Colony (ABC), Differential Evolution (DE) algorithm, and an algorithm known as Grey Wolf Optimisation - Cuckoo Search (GWOCS) which is hybrid in nature. The suggested algorithm’s performance evaluation is based on minimising the Square Error (SSE). The modified proposed optimization algorithm exhibits superior performance compared to other alternative meta-heuristic algorithms due to its minimal SSE value. The effectiveness and efficiency of the modified method based on the Ballard Mark V datasheet were evaluated using statistical error analysis and non-parametric testing. The convergence curves of DACO demonstrate a faster convergence compared to the other optimization algorithms.

Reliability inference based on inverted exponentiated Rayleigh lifetime distribution under unified hybrid censored scheme

In this study, we investigated the Inverted Exponentiated Rayleigh Distribution (IERD), a significant and efficient continuous lifetime distribution commonly applied in lifespan research. Our focus was on estimating unknown parameters for a two-parameter inverted exponentiated Rayleigh distribution using unified hybrid censored data. We considered both maximum likelihood and Bayesian estimation approaches. Specifically, we employed the Gibbs within Metropolis–Hastings samplers method to develop approximate Bayes estimators utilizing informative and non-informative priors, along with symmetric and asymmetric loss functions. In addition, we utilized Markov chain Monte Carlo (MCMC) samples to derive maximum posterior density credible intervals. Simulation experiments were conducted to assess the efficacy of the proposed methodologies, and actual data analysis was performed to validate the proposed estimators.

Space-time error estimates for approximations of linear parabolic problems with generalized time boundary conditions

Abstract We first give a general error estimate for the nonconforming approximation of a problem for which a Banach–Nečas–Babuška (BNB) inequality holds. This framework covers parabolic problems with general conditions in time (initial value problems as well as periodic problems) under minimal regularity assumptions. We consider approximations by two types of space-time discretizations, both based on a conforming Galerkin method in space. The first one is the Euler $\theta -$scheme. In this case, we show that the BNB inequality is always satisfied, and may require an extra condition on the time step for $\theta \le \frac 1 2$. The second one is the time discontinuous Galerkin method, where the BNB condition holds without any additional condition.

Evaluation of the Xtb Semiempirical Method for the Prediction of Antioxidant Properties in Alzheimer’s Disease: Salen-Type Ligands

Alzheimer’s disease (AD) stands as the predominant form of dementia, accounting for up to 70% of all cases worldwide. AD is a complex disease with various contributing factors. Evidence suggests that the metalliccomplexes formed by the β-amyloid peptide (Aβ) and extraneuronal copper can catalyze the generation ofreactive oxygen species, consequently increasing oxidative stress and contributing to the decline of neurons. This interaction underscores the significance of bioavailable copper as a crucial redox-active target in exploring protocols for multifunctional agents in AD treatment. In the field of computational chemistry, density functional theory (DFT) is widely accepted as a standard method across different disciplines. Despite this, DFT presents computational challenges, particularly in screening extensive molecular sets during the initial phases of drug research. Recent advances in semiempirical quantum mechanical methods (SQM) offer a promising alternative, providing rapid molecular geometry optimization and approximate estimation of thermodynamical properties, being at least two orders of magnitude faster than traditional DFT calculations. In this work, we present an evaluation of the GFNn-xTB SQM methods in the rapid screening of antioxidant properties in AD, performed on a set of salen ligands by calculating the standard reduction potentials of their copper complexes as key property. Results show that the implementation of GFNn-xTB SQM calculations before DFT evaluations is

A preventive maintenance policy and a method to approximate the failure process for multi-component systems

Numerous maintenance policies have been proposed in the reliability mathematics and engineering literature. Nevertheless, little has been reported on their practical applications in industries. This gap is largely due to restrictive assumptions of the maintenance policies. Two of the main assumptions are that maintenance is conducted on typical components and that the reliability of an item under maintenance is known (where the item can be a component or a system composed of multiple components). These assumptions do not often hold in the real world: maintenance is often performed on a collection of components such as an integrated circuit plate and the reliability of each individual component may not be known. To reduce these gaps, this paper develops a new maintenance policy for a collection of components and an approximate method to estimate the reliability of this collection based on the failure data collected from the field. The maintenance policy considers that a system is composed of three subsystems with different levels of maintenance effectiveness (i.e, minimal, imperfect, and perfect). The approximate estimate of the reliability of each subsystem is derived based on the failure data that are time between failures of the system but not those of the components that cause the system to fail. An algorithm for simulating the superposition of generalised renewal processes is then proposed. Numerical examples are used to illustrate the proposed approximation method.