Deterministic Results Research Articles

Assessment of the Current Collection Quality of Pantograph–Catenary With Contact Line Height Variability in Electric Railways

The numerical tools are widely used to facilitate the design of the railway catenary. Only radical results are obtained as the current assessment is generally performed without any practical errors. In this article, the most common error, the contact line height variability, is appropriately included in evaluating the current collection quality. Based on the real-life contact line height data collected from a high-speed network, the heights of the key points in the contact line are extracted, of which the pointwise stochastics is represented by the power spectrum density (PSD) function. Random samples are generated by the inverse Fourier transform based on the Monte Carlo method. An advanced initialization procedure is presented to properly include the contact line height variability in the initial configuration. A stochastic analysis with a high cutoff frequency is performed to evaluate a double pantograph–catenary system’s current collection quality. Unlike the deterministic result obtained by the perfect design data, the contact line height variability causes uncertainty. The present analysis method indicates some risks of safety accident and contact loss that the traditional simulation cannot capture with ideal design data or low cutoff frequency.

Systoles and Lagrangians of random complex algebraic hypersurfaces

Let n\geq 1 be an integer, and \mathcal L \subset \mathbb{R}^n be a compact smooth affine real hypersurface, not necessarily connected. We prove that there exist c>0 and d_0\geq 1 such that for any d\geq d_0 , any smooth complex projective hypersurface Z in \mathbb{C} P^n of degree d contains at least c\dim H_{*}(Z, \mathbb{R}) disjoint Lagrangian submanifolds diffeomorphic to \mathcal L , where Z is equipped with the restriction of the Fubini–Study symplectic form (Theorem 1.1). If moreover all connected components of \mathcal L have non-vanishing Euler characteristic, which implies that n is odd, the latter Lagrangian submanifolds form an independent family in H_{n-1}(Z, \mathbb{R}) (Corollary 1.2). These deterministic results are consequences of a more precise probabilistic theorem (Theorem 1.23) inspired by a 2014 result by J.-Y. Welschinger and the author on random real algebraic geometry, together with quantitative Moser-type constructions (Theorem 3.4). For n=2 , the method provides a uniform positive lower bound for the probability that a projective complex curve in \mathbb{C} P^2 of given degree equipped with the restriction of the ambient metric has a systole of small size (Theorem 1.6), which is an analog of a similar bound for hyperbolic curves given by M. Mirzakhani (2013). In higher dimensions, we provide a similar result for the (n-1) -systole introduced by M. Berger (1972) (Corollary 1.14). Our results hold in the more general setting of vanishing loci of holomorphic sections of vector bundles of rank between 1 and n tensored by a large power of an ample line bundle over a projective complex n -manifold (Theorem 1.20).

Slab dielectric waveguide with randomly fluctuating refractive indices

The three-layer slab dielectric waveguide is perhaps the most basic structure for designing optical and electronic devices. Deterministic results, assuming constant refractive indices, on the propagation of an electromagnetic wave within this structure are well known and they are reported in papers and textbooks, however to the best of the authors knowledge, there are no works reported in the literature on the stochastic propagation. In order to describe the stochastic propagation, we propose a model in which the refractive indices are variables fluctuating randomly. Our main objective is to show the student the significant difference between the deterministic and stochastic response of the system, when constant or random refractive indices are considered. In particular the dispersion curves, the distribution of the fields and the energy flow are presented and discussed. Our results show that the asymmetry factor associated with the dispersion curves can be easily modified by means of the magnitude of the induced fluctuation. Another interesting property shows that both TE0 and TM0 fundamental modes propagate only for small fluctuations. In the core of the guide, the amplitude of the electric and magnetic fields exhibits damped oscillations due to the randomness of the system. The energy flow is high in the substrate region, but it is vanishing in the cladding region. We conclude that those deterministic results are a particular case of our stochastic results.

Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-Mixing Nonuniformly Hyperbolic Maps

Consider a nonuniformly hyperbolic map T:Mrightarrow M modelled by a Young tower with tails of the form O(n^{-beta }) , beta >2 . We prove optimal moment bounds for Birkhoff sums sum _{i=0}^{n-1}vcirc T^i and iterated sums sum _{0le i<j<n}vcirc T^i, wcirc T^j , where v,w:Mrightarrow {{mathbb {R}}} are (dynamically) Hölder observables. Previously iterated moment bounds were only known for beta >5. Our method of proof is as follows; (i) prove that T satisfies an abstract functional correlation bound, (ii) use a weak dependence argument to show that the functional correlation bound implies moment estimates. Such iterated moment bounds arise when using rough path theory to prove deterministic homogenisation results. Indeed, by a recent result of Chevyrev, Friz, Korepanov, Melbourne & Zhang we have convergence to an Itô diffusion for fast-slow systems of the form xk+1(n)=xk(n)+n-1a(xk(n),yk)+n-1/2b(xk(n),yk),yk+1=Tyk\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} x^{(n)}_{k+1}=x_k^{(n)}+n^{-1}a(x_k^{(n)},y_k)+n^{-1/2}b(x_k^{(n)},y_k) , \\quad y_{k+1}=Ty_k \\end{aligned}$$\\end{document}in the optimal range beta >2.

Ensemble technique application to an XBeach-based coastal Early Warning System for the Northwest Adriatic Sea (Emilia-Romagna region, Italy)

During the last three decades, ensemble modelling has switched the focus from deterministic to probabilistic outcomes after its successful application in meteorological forecasting. This work involves the application of Ensemble Prediction System (EPS)-based results as forcing for a coastal EWS employing the morphodynamic model XBeach in a so-called (semi-)probabilistic way. First, calibration following the GLUE approach is performed for a profile in Cesenatico (Emilia-Romagna coast, Italy), while the (semi-)probabilistic system is implemented subsequently for two nearby locations. Ensemble mean and standard deviation from the Transnational Multi-Model Ensemble (TMES) forecasting system are combined in varied ways and used to force XBeach. A testing period of two months is analyzed (March and April 2020) together with the already operational deterministic implementation with one specific day of high sea conditions being used to assess the performance of the system. The deterministic results present higher outcome variability compared to the usage of the TMES mean and mean plus/minus one standard deviation (SD). Adding two SDs to the TMES mean results in higher variability than the deterministic approach. The (semi-)probabilistic system shows high potential as it provides more information on possible outcomes. However, its implementation has to be carefully designed as the application of the TMES mean plus SDs might result in false threshold exceedance and unproportionate responses.

Reliability-based topology optimization of piezoelectric smart structures with voltage uncertainty

Currently, most of the piezoelectric structures are designed under deterministic conditions, where the influence of uncertain factors on the output motion accuracy is ignored. In this work, a probabilistic reliability-based topology optimization method for piezoelectric structure is proposed to deal with the working voltage uncertainty. A nested double-loop optimization algorithm of minimizing the total volume while satisfying the reliability requirement of the displacement performance is established, where the PEMAP-P (piezoelectric material with penalization and polarization) model is used for parameterization of stiffness matrix, piezoelectric coupling matrix, and polarization direction. This strategy consists of an inner loop for reliability analysis and an outer loop for topology optimization. The reliability index approach based on most probable point (MPP) is used for realizing the evaluation of reliability constraint in reliability analysis. The sensitivities of reliability constraint with respect to the random variables and design variables are detailed using the adjoint variable method. Typical examples are performed to illustrate the effectiveness of the proposed RBTO method. A comparison of the optimization results for different reliability indexes, standard deviations of the voltage, spring stiffnesses, and displacement limits are conducted, as well as the deterministic topology optimization results.

Hierarchical Trust-Tech-Enhanced K-Means Methods and Their Applications to Power Grids

K-means has been widely used in solving a wide range of clustering problems arising in engineering and industrial applications, but it still suffers from several issues. To address these issues, a hierarchical K-means method enhanced by Trust-Tech (H-KTT) is presented in this paper. The proposed H-KTT method is composed of two stages. The first stage of H-KTT is a hierarchical K-means (H-K-means) method for enhancing K-means with better initial points. Second, the H-K-means method is further enhanced to find multiple high-quality clustering results by the Trust-Tech methodology. The H-KTT method was evaluated on several test datasets including the clustering of Automatic Meter Reading (AMR), popular in power grids, with promising results. In particular, the evaluation results indicate that the proposed H-KTT method can significantly improve both the quality and stability of the clustering results by the K-means method. Furthermore, while the K-means gives stochastic clustering results, the proposed H-KTT method usually gives deterministic clustering results.

Development of a stochastic bioeconomic model for the red octopus fishery on the Yucatan Peninsula: Implications for management

Although much effort has been dedicated to the management of the red octopus fishery on the Yucatan Peninsula (Mexico), managers have yet to incorporate economic aspects to ensure sustainable and profitable exploitation of this fishery resource. We developed a bioeconomic model that incorporated the uncertainty for the r and K parameters. We fit 3 models (Schaefer, Fox, and Pella–Tomlinson) to abundance index survey data and used the Akaike information criterion for model selection. The best fit corresponded to the Schaefer model. We built deterministic and stochastic versions of the Gordon–Schaefer model. Economic data (costs and prices) were determined from inter[1]views with fishermen. To estimate the posterior distributions of parameters and indicators, we used Bayesian methods with Markov chain Monte Carlo (MCMC) simulations. The deterministic results suggested that the maximum sustainable income was Mex$851.70 million, with a fishing effort of 3,650 fishing boats, while the maximum sustainable profit was $390.8 million, with a fishing effort of 2,472 fishing boats. The equilibrium point corresponded to an effort of 4,945 fishing boats. Regarding the stochastic model, the MCMC simulation results suggest that the maximum sustainable income distribution was not normal; its average was $856.1 million (SE 1.8) and the most likely value was $849.50 million. The most likely fishing effort at equilibrium was 4,970 fishing boats. Our results suggest the fishery could be operating close to the economic equilibrium point; if this is the case, fishing effort must decrease in order for annual profit to increase. Our approach will help make periodical re-evaluations of the fishery and establish management strategies to ensure the profitable and sustainable exploitation of the red octopus on the Yucatan Peninsula.

Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

An exact formula for the joint probability of pair neutron detection for the Rossi-α method, which is composed of the sum of a large number of higher harmonics, is verified in this study by comparing it with a Monte Carlo simulation. A simple conventional formula for the Rossi-α method cannot yield an accurate fundamental mode time-decay constant α owing to the effect of higher harmonics. Dynamic mode decomposition (DMD) is applied to the eigendecomposition of autocorrelation functions in a subcritical system. Through DMD, the autocorrelations obtained from the deterministic exact formula, which is free from stochastic noise, are accurately decomposed into major higher harmonic components. The DMD results obtained from a Monte Carlo simulation are inferior to the deterministic results due to stochastic noise. These findings suggest that if detection positions are properly allocated within a subcritical system, DMD can yield a satisfactorily accurate fundamental mode α-eigenvalue.

ALGORITHM AUTOMATION METHODS FOR WORKING WITH NETWORK EQUIPMENT

Relevance of the topic: methods of automating algorithms for the operation of network equipment are currently carried out using various tools and solutions for faster and more efficient execution of routine tasks, as well as for obtaining deterministic results. Production processes need algorithmization of ACS as a tool for saving time resource for management, coordinating production schedules, technical and technological limitations. You can form an alternative to quickly respond to precedents in production that have not predicted to change the course of technological processes. Most automation options today have disadvantages and advantages. The most popular way is queuing theory. Optimization of global search, additive method of criteria convolution, APS (Advanced Planning and Scheduling) systems for the most perfect planning are relevant. The specified software systematically synchronizes the planning process deployed for optimization and combines actions on the links that make up the supply chain, accentuates the framework and specifics determined by production and the industry. Most often, the network equipment is controlled by a software module that loads the machines and mechanisms needed by the enterprise for the production of products. Developers design systems to control timeslots and production lines. Known for the high efficiency of algorithms, the execution of which occurs through the automated control system, and the installation is carried out at an industrial enterprise to control loading operations. In the structure of external software, an algorithm is required. The program module contains commands for loading operations. They are distributed for technological lines, divided along the time axis. We see a rational solution to simulate a complex using simulation and analytics based on an automation product within the network equipment configured by the program. This will allow, under the conditions of the experiment, to determine how most likely traffic will be distributed in time, to prepare methods for automatic collection of information. Input traffic parameters, settings or the current load arriving at the equipment are set arbitrarily.

A robust risk assessment method for energy planning scenarios on smart islands under the demand uncertainty

Energy systems with a high share of variable renewable energy are more vulnerable to sudden changes in the system operation. This is especially emphasized on small systems such as energy systems on geographical islands. Because of these reasons, there is a need for quantifying the risk of energy scenarios of such systems. This paper presents a novel robust risk assessment method under demand uncertainty for energy planning scenarios for the islands. The method uses graph theory for the representation of power system topology. The Poisson distribution is used for calculating the probability of power system element failure. The robust modelling approach is applied by the introduction of auxiliary variables and compared to the deterministic model results. Four energy planning scenarios for Unije island are modelled and subjugated to several power system outages resulting in a risk vector calculated as the product of probability vector and damage matrix. The study also presents a zero-import risk energy planning scenario for Unije island that is achieved for a system of 0.5 MW photovoltaic plant and 3.55 MWh battery storage system.

Convergence results for stochastic convex feasibility problem using random Mann and simultaneous projection iterative algorithms in Hilbert space

Real life problems are entrenched in ambiguities. To deal with these ambiguities, stochastic functional analysis has emerged as one of the mathematical tools for solving these kinds of problems. The purpose of this paper is to extend the convergence results of deterministic convex feasibility problems to a stochastic convex feasibility problem and prove that the solution of a convex feasibility problem generated by random Mann-type and Simultaneous projection iterative algorithms with firmly non-expansive mapping converge in quadratic mean and consequently in probability to random fixed point in Hilbert space. These results extend, unify, and generalize different established deterministic results in the literature.

Quantitative Risk Analysis of Tunnel Instability in Layered Rock Mass Considering the Spatial Variability of Elastic Modulus

Layered rock mass is a typical excavation disturbance sensitive rock mass, which is prone to the large deformation and collapse of soft rock mass under tunnel unloading. This in turn causes the construction safety risk and delays the project construction. As the spatial variability of rock mechanics parameters existed widely, which could make the deterministic calculation results cannot really reflect the safety reserve of the rock mass by supports. Therefore, considering the spatial variability of elastic modulus of layered rock mass for study the risk of tunnel instability both has the theoretical and practical significance. According to the transverse anisotropy characteristics of layered rock mass in Baokang tunnel, China, elastic wave velocities were determined by the acoustic test method at different broken surrounding rock mass. Meanwhile, the elastic modulus was converted into the elastic modulus based on theoretical formula, and a database of the elastic modulus was set up. Using the variograms model of geostatistics, the autocorrelation distances of elastic modulus along the strike and dip of rock strata were determined, respectively. Furthermore, a two-dimensional parameter random field which can characterize the spatial variability of elastic modulus of layered rock mass was constructed by the Karhunen-Loève (K-L) expansion method. Taking the standard value of tunnel allowable deformation as the evaluation index, the limit state equation of tunnel allowable deformation in the soft rock was established. Finally, considering the spatial variability of elastic modulus of layered rock mass, a quantitative risk analysis of surrounding rock instability was realized by the Monte Carlo method and numerical simulation method. The engineering example shows that, this quantitative risk analysis method can effectively evaluate the safety state of the surrounding rock mass, and it can provide a theoretical guidance and technical support for the tunnel construction. This work could provide a reference for other layered rock mass tunnel construction.

Mixed layer acoustic propagation with small scale ocean dynamics

The effects of dynamic oceanographic processes in the upper ocean mixed layer on acoustic propagation are investigated using at-sea sound speed observations and acoustic transmission simulations. The sound speed environment is based on a 400 m deep and 1000 km long East-West salinity and temperature transect that was collected during April of 2005 in the North Pacific where there is a mixed layer acoustic duct with a mean depth of 89 m. The deterministic baseline of this sound speed measurement is first estimated from the observations using a spatial lowpass filter with a cut off length scale of 50-km. The remaining small length scale variations in sound speed are assumed to have two physically distinct contributions: one due to the vertical displacement of isopycnals caused by eddies and internal waves and another due to compensating temperature and salinity anomalies along isopycnals termed spice. These two contributions can be separated yielding three distinct sound speed fields: i(1) the deterministic background; (2) thedisplacement field; and (3) the spice field. Acoustic transmission loss calculations are carried out on these three fields for frequencies of 400 and 1000 Hz for sources both in and below the mixed layer duct. Statistical and deterministic results for acoustic normal modes and full field transmission loss are presented, which quantify the relative importance of displacement and spice for acoustic propagation in the upper ocean.

Operation Rule Derivation of Hydropower Reservoirs by Support Vector Machine Based on Grey Relational Analysis

In practical applications, the rational operation rule derivation can lead to significant improvements in the middle and long-term joint operation of cascade hydropower stations. The key issue of actual optimal operation is to select effective attributions from the deterministic optimal operation results, however, there is still no general and mature method to solve this problem. Firstly, the joint optimal operation model of hydropower reservoirs considering backwater effects are established. Then, the dynamic programming and progressive optimality algorithm are applied to solve the joint optimal operation model and the deterministic optimization results are obtained. Finally, the grey relational analysis method is applied to select more effective factors from the obtained results as the input of a support vector machine for further operation rule derivation. The Xi Luo-du and Xiang Jia-ba cascade reservoirs in the upper Yangtze river of China are selected as a case study. The results show that the proposed method can obtain better input factors to improve the performance of SVM, and smallest value of root mean square error by the proposed method of Xi Luo-du and Xiang Jia-ba are 94.33 and 21.32, respectively. The absolute error of hydropower generation for Xi Luo-du and Xiang Jia-ba are 2.57 and 0.42, respectively. Generally, this study provides a well and promising alternative tool to guide the joint operation of hydropower reservoir systems.

Theory of superlocalized magnetic nanoparticle hyperthermia: Rotating versus oscillating fields

The main idea of magnetic hyperthermia is to increase locally the temperature of the human body by means of injected superparamagnetic nanoparticles. They absorb energy from a time-dependent external magnetic field and transfer it into their environment. In the so-called superlocalization, the combination of an applied oscillating and a static magnetic field gradient provides even more focused heating since for large enough static field the dissipation is considerably reduced. Similar effect was found in the deterministic study of the rotating field combined with a static field gradient. Here we study theoretically the influence of thermal effects on superlocalization and on heating efficiency. We demonstrate that when time-dependent steady state motions of the magnetization vector are present in the zero temperature limit, then deterministic and stochastic results are very similar to each other. We also show that when steady state motions are absent, the superlocalization is severely reduced by thermal effects. Our most important finding is that in the low frequency range (ω→0) suitable for hyperthermia, the oscillating applied field is shown to result in two times larger intrinsic loss power and specific absorption rate then the rotating one with identical superlocalization ability which has importance in technical realization.

Homogenization and Correctors for Stochastic Hyperbolic Equations in Domains with Periodically Distributed Holes

The goal of this paper is to present new results on homogenization and correctors for stochastic linear hyperbolic equations in periodically perforated domains with homogeneous Neumann conditions on the holes. The main tools are the periodic unfolding method, energy estimates, probabilistic and deterministic compactness results. The findings of this paper are stochastic counterparts of the celebrated work [D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains, Port. Math. (N.S.) 63 (2006) 467–496]. The convergence of the solution of the original problem to a homogenized problem with Dirichlet condition has been shown in suitable topologies. Homogenization and convergence of the associated energies results recover the work in [M. Mohammed and M. Sango, Homogenization of Neumann problem for hyperbolic stochastic partial differential equations in perforated domains, Asymptot. Anal. 97 (2016) 301–327]. In addition to that, we obtain corrector results.

Stochastic long-term reliability of water distribution networks using Monte Carlo simulation

ABSTRACT In this paper, a new method is developed to consider the effect of pipe roughness, diameter and nodal demand uncertainty on the overall reliability of the Water Distribution networks (WDNs) throughout the day as well as the planning horizon. For this purpose, probabilistic series for each of the mentioned parameters is generated by Monte Carlo Simulation (MCS). Network Pressure Reliability Index (NPRI) is then used to evaluate the overall reliability of the system. The study is performed on the benchmark Two-loop sample network and a real-world one. The comparison of deterministic and stochastic results reveal that the stochastic method tends to capture subtleties missed by deterministic method such as probability of failing the reliability in various locations at the same time. Also, the stochastic method seems to have an undoubted advantage in prediction of undesirable results prior to deterministic method, making it an essential component in long-term planning.

Life cycle cost comparison of strengthening a steel bridge using post-installed shear connectors with bridge reconstruction

The growth of the world population increases traffic loads on infrastructures. Due to considerable number of low-capacity steel bridges, transportation agencies need to strengthen or rebuild them as two possible scenarios. As a novel means of strengthening low-capacity steel bridges, post-installed shear connectors lack economic analysis determining the user and agency costs. To this end, this paper focuses on the life cycle cost comparison of strengthening steel bridges using post-installed shear connectors with bridge reconstruction. Moreover, a steel bridge in Lakeport, Texas, that was strengthened using the aforementioned method is presented in the case study. One of the main contributions of this study is determining the life cycle cost of post-installed shear connectors, which provides important managerial insights to transportation agencies interested in deciding about rebuilding or strengthening steel bridges. The deterministic analysis results indicate that bridge strengthening is more beneficial for all stakeholders than bridge reconstruction. Furthermore, the results depict that user cost is the dominant contributor to total life-cycle costs. Considering the stochastic nature of LCCA elements, the probabilistic analysis results show the same results as deterministic analysis. Finally, the sensitivity analysis suggests that the discount rate is the most influential parameter on the life cycle cost.

A data-driven methodology for enhanced measurement and verification of energy efficiency savings in commercial buildings

Methods to obtain accurate estimations of the savings generated by building energy efficiency interventions are a topic of great importance, and considered to be one of the keys to increase capital investments in energy conservation strategies worldwide. In this study, a novel data-driven methodology is proposed for the measurement and verification of energy efficiency savings, with special focus on commercial buildings and facilities. The presented approach involves building use characterization by means of a clustering technique that allows to extract typical consumption profile patterns. These are then used, in combination with an innovative technique to evaluate the building’s weather dependency, to design a model able to provide accurate dynamic estimations of the achieved energy savings. The method was tested on synthetic datasets generated using the building energy simulation software EnergyPlus, as well as on monitoring data from real-world buildings. The results obtained with the proposed methodology were compared with the ones provided by applying the time-of-week-and-temperature (TOWT) model, showing up to 10% CV(RMSE) improvement, depending on the case in analysis. Furthermore, a comparison with the deterministic results provided by EnergyPlus showed that the median estimated savings error was always lower than 3% of the total reporting period consumption, with similar accuracy retained even when reducing the total training data available.