Function Of State Research Articles

Current research on exoskeletal lower limb rehabilitation robots

Stroke is characterized by a high incidence rate, and walking is one of the essential human functions. Lower limb rehabilitation robots can offer safe and effective walking training to patients with walking impairments caused by conditions such as neural injuries, aiding in their recovery or assisting in walking. For the needs of patients themselves, restoring their physical state and motor function as much as possible is the primary purpose of rehabilitation, and rehabilitation efficiency is an important factor affecting the quality of life of patients after surgery. Research on exoskeleton robots varies both domestically and internationally, each with its own unique characteristics and features. This paper outlines the design of lower limb rehabilitation robots based on gait analysis and control methods. It also provides an overview of the current state of research on lower limb exoskeleton robots in terms of degrees of freedom, actuation methods, and clinical applications. Furthermore, it offers insights into future directions for research on lower limb exoskeleton robots.

Wojna na Ukrainie jako czynnik państwotwórczego rozwoju Unii Europejskiej

The aim of the article is to analyze the impact of the war in Ukraine on European integration. In particular, bellicist theories will be analyzed. I pose the following research questions: Has the security threat resulting from Russian imperialism prompted the European Union to develop its own defense capabilities? Did it stimulate the development of state functions of this organization, e.g. centralization or federalization aimed at guaranteeing the security of member states, especially those located in the east of the EU? I am also trying to verify the reasons why the state-building of the EU encounters difficulties in the situation of the war in Ukraine. The study was conducted during the first two years of the full-scale war in Ukraine (2022–2023).

On the question of the concept of external functions in Ukraine and Hungary

The main goal of any state, as a socio-legal entity, is to ensure, protect, regulate, and guarantee social, public, and individual interests. And that’s why all attention is focused on the regulation of socially important spheres. Such directions in the theory of the state and law of Ukraine and the state-legal theory of Hungary traditionally have the name - functions of the state, which according to different definitions and approaches of both Ukrainian and Hungarian specialists can be interpreted as the main directions of activity. Although this definition is not the only one. Today, in the scientific literature, you can find different opinions about what functions are, what are the constituent elements, and what are the functions, according to which criteria to classify them. The doctrine of the functions of the modern state is traditionally considered as an integral part of state and general theoretical jurisprudence, because nowadays the questions of the functions of the state, the necessity of which relates to the transformation of the role of the state in society, are becoming increasingly relevant. The functioning of the state is a rather complex and dynamic process that requires theoretical understanding. This causes considerable effort and serious disagreement among scientists. In the process of research, it is relevant to consider the functions of the state in the philosophical-legal system of the conceptual provisions of the state-legal theory. Find out what are the different definitions of the function of the state and how they relate to each other. But the main thesis of this article is the issue of specifically external functions, which should be understood by this, which is their vocation. Their study is of particular importance at the time of revision of existing mechanisms under the influence of globalization fluctuations. But this direction is extremely important for Ukraine, which is at the stage of acute renewal of social spheres of life, including the state and legal sphere. In general, this scientific article attempts to demonstrate the different points of view of Ukrainian and Hungarian specialists for the expansion of scientific research on the issue of defining the concept of external functions, and thus to contribute to the general scientific base on the part of Ukrainian scientists.

Complex-valued Wigner entropy of a quantum state

It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space that extends to negative Wigner functions and then advocate the merits of defining a complex-valued entropy associated with any Wigner function. This quantity, which we call the complex Wigner entropy, is defined via the analytic continuation of Shannon’s differential entropy of the Wigner function in the complex plane. We show that the complex Wigner entropy enjoys interesting properties, especially its real and imaginary parts are both invariant under Gaussian unitaries (displacements, rotations, and squeezing in phase space). Its real part is physically relevant when considering the evolution of the Wigner function under a Gaussian convolution, while its imaginary part is simply proportional to the negative volume of the Wigner function. Finally, we define the complex-valued Fisher information of any Wigner function, which is linked (via an extended de Bruijn’s identity) to the time derivative of the complex Wigner entropy when the state undergoes Gaussian additive noise. Overall, it is anticipated that the complex plane yields a proper framework for analyzing the entropic properties of quasiprobability distributions in phase space.

Dietary menhaden fish oil supplementation suppresses lipopolysaccharide-induced neuroinflammation and cognitive impairment in diabetic rats

Context Menhaden fish oil (FO) is widely recognized for inhibiting neuroinflammatory responses and preserving brain function. Nevertheless, the mechanisms of FO influencing brain cognitive function in diabetic states remain unclear. Objective This study examines the potential role of FO in suppressing LPS-induced neuroinflammation and cognitive impairment in diabetic animals (DA). Materials and methods Thirty male Wistar rats were divided into 5 groups: i) DA received LPS induction (DA-LPS); ii) DA received LPS induction and 1 g/kg FO (DA-LPS-1FO); iii) DA received LPS induction and 3 g/kg FO (DA-LPS-3FO); iv) animals received normal saline and 3 g/kg FO (NS-3FO) and v) control animals received normal saline (CTRL). Y-maze test was used to measure cognitive performance, while brain samples were collected for inflammatory markers and morphological analysis. Results DA received LPS induction, and 1 or 3 g/kg FO significantly inhibited hyperglycaemia and brain inflammation, as evidenced by lowered levels of pro-inflammatory mediators. Additionally, both DA-LPS-1FO and DA-LPS-3FO groups exhibited a notable reduction in neuronal damage and glial cell migration compared to the other groups. These results were correlated with the increasing number of entries and time spent in the novel arm of the Y-maze test. Discussion and conclusion This study indicates that supplementation of menhaden FO inhibits the LPS signaling pathway and protects against neuroinflammation, consequently maintaining cognitive performance in diabetic animals. Thus, the current study suggested that fish oil may be effective as a supporting therapy option for diabetes to avoid diabetes-cognitive impairment.

Regularity of the Optimal Sets for a Class of Integral Shape Functionals

We prove the first regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} is obtained as the integral of a cost function j(u, x) depending on the solution u of a certain PDE problem on Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}. The main feature of these functionals is that the minimality of a domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} cannot be translated into a variational problem for a single (real or vector valued) state function. In this paper we focus on the case of affine cost functions j(u,x)=-g(x)u+Q(x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j(u,x)=-g(x)u+Q(x)$$\\end{document}, where u is the solution of the PDE -Δu=f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\Delta u=f$$\\end{document} with Dirichlet boundary conditions. We obtain the Lipschitz continuity and the non-degeneracy of the optimal u from the inwards/outwards optimality of Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} and then we use the stability of Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} with respect to variations with smooth vector fields in order to study the blow-up limits of the state function u. By performing a triple consecutive blow-up, we prove the existence of blow-up sequences converging to homogeneous stable solution of the one-phase Bernoulli problem and according to the blow-up limits, we decompose ∂Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Omega $$\\end{document} into a singular and a regular part. In order to estimate the Hausdorff dimension of the singular set of ∂Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Omega $$\\end{document} we give a new formulation of the notion of stability for the one-phase problem, which is preserved under blow-up limits and allows to develop a dimension reduction principle. Finally, by combining a higher order Boundary Harnack principle and a viscosity approach, we prove C∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^\\infty $$\\end{document} regularity of the regular part of the free boundary when the data are smooth.

Injection of anomalous-Hall current into a load circuit

The anomalous-Hall current injection is studied in a Hall device contacted to a lateral load circuit. This anomalous-Hall current is generated inside a Co75Gd25 ferrimagnetic Hall bar and injected into a lateral load circuit contacted at the edges. The current, the voltage, and the power are measured as a function of the magnetization states, the load resistance Rl, and the temperature. It is shown that (1) the resistance associated with the anomalous-Hall current flowing inside the Hall bar is that of the portion of the ferrimagnet located between the lateral contacts, (2) the role of the non-uniformity of the current due to the lateral contacts is small, (3) the maximum power efficiency of the current injection into the load circuit corresponds to the condition of the resistance matching of the two sub-circuits, and (4) this maximum power efficiency is of the order of the square of the anomalous-Hall angle. These observations are in agreement with recent predictions based on a non-equilibrium variational approach.

Analysis of the impact of introspective therapy on the psychological state and family functioning of cervical cancer patients with anxiety.

Analysis of the impact of introspective therapy on the psychological state and family functioning of cervical cancer patients with anxiety.

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: I. Existence

The Kelvin–Planck statement of the second law of thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy. Beginning with a Kelvin–Planck statement of the Second Law, we show that entropy and temperature—in particular, existence of functions that relate the local specific entropy and thermodynamic temperature to the local state in a material body—emerge immediately and simultaneously as consequences of the Hahn–Banach theorem. The existence of such functions of state requires no stipulation that their domains be restricted to equilibrium states. Further properties, including uniqueness, are addressed in a companion paper.

Integrative Probabilistic Design of River Jetties by 3D Numerical Models of Transport Phenomena: The Case Study of Kabakoz River Jetties

Various methods are employed to investigate the effects of coastal structures in coastal areas on marine environments and transport phenomena. These methods can be categorized into physical models and numerical simulations. Due to the lack of long-term wave height data in Türkiye, numerical models are utilized to estimate wave heights generated by wind based on long-term measured wind speeds. These wave heights generated in deep sea conditions can be transported to the coast by wave transformation and interactions between coastal structures and waves, turbulence, currents induced by wind and breaking waves, coastal sediment transport rates, and changes in the coastline can be successfully predicted with the assistance of numerical models. In the scope of this study, the new “Integrative Probabilistic Design Approach of River Jetties” was developed. 3D numerical models were used for the optimum design, considering the sediment transport near the jetties and aiming to protect the coastal environment in the long term. 3D numerical modeling has been conducted to investigate the transport phenomena occurring at the outlet of the Kabakoz River in the Şile District of İstanbul Province to acquire the optimum layout and design of the coastal structures. The study presents the “Integrative Probabilistic Design Approach” for coastal protection structures by wind and wave climate, wave transformation, coastal sediment transport, shoreline change, and coastal structure probabilistic design sub-models. Monte Carlo Simulation of Hudson Limit State function conducts probabilistic design for the jetties. The greatest advantage of probabilistic design (Monte Carlo Simulation) is the prediction of uncertainties, such as wave height changes under design conditions. Following the completion of the construction of groins, the effect of probabilistic design on both design and coastal morphology can be evaluated precisely. In conclusion, in the study area, 146,237.55 m3 of sediment is transported annually from west to east and 221,043.49 m3 from east to west. In the absence of coastal structures, sediment transport from east to west is approximately 1.5 times greater than from west to east. The annual net coastal sediment transport from east to west is approximately 74,805.94 m3, while the total transport is estimated to be 367,281.04 m3. The coastline is expected to reach sediment balance within approximately two years. In this study, the coastal structure of a jetty is designed from an innovative probabilistic design perspective. The aim is to ensure the reliability of the structure and, at the same time, protect the morphology of the coastline where the structure will be constructed. The region’s wind and wave climate were initially determined using Hydrotam 3D software. Following this procedure, the length of the jetty is predicted considering the closure depth. The model parameters were calibrated from coastline morphology using satellite images and Google Earth over the past twenty years. These parameters are defined to Hydrotam 3D as input data; a trial-and-error model application procedure calibrates the coastline’s accumulation and erosion. Finally, the probabilistic design is conducted with Monte Carlo Simulation using the Hudson Equation as the limit state function. Det Norske Veritas developed a design code for marine structures in 1992, where the target reliability is 10-3 for structures with less serious failure consequences. This reliability level validated the Level IV model presented in this paper. The class of failure depends on the possibility of timely warning, and these standards can be revised by the model presented to address the effects of climate change on the design of maritime structures.

Open-Circuit Voltage Variation in LiCoO2 Battery Cycled in Different States of Charge Regions

Open-Circuit Voltage Variation in LiCoO2 Battery Cycled in Different States of Charge Regions

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: II Properties

In a companion article it was shown in a certain precise sense that, for any thermodynamical theory that respects the Kelvin–Planck second law, the Hahn–Banach theorem immediately ensures the existence of a pair of continuous functions of the local material state—a specific entropy (entropy per mass) and a thermodynamic temperature—that together satisfy the Clausius–Duhem inequality for every process. There was no requirement that the local states considered be states of equilibrium. This article addresses questions about properties of the entropy and thermodynamic temperature functions so obtained: To what extent do such temperature functions provide a faithful reflection of “hotness”? In precisely which Kelvin–Planck theories is such a temperature function essentially unique, and, among those theories, for which is the entropy function also essentially unique? What is a thermometer for a Kelvin–Planck theory, and, for the theory, what properties does the existence of a thermometer confer? In all of these questions, the Hahn–Banach Theorem again plays a crucial role.

Optimum embedment depths for CFST column-to-foundation connections: Analytical and reliability-based approach

In the present study, the pullout capacity models were developed to derive analytical expressions for the minimum required depths of embedment for conventional and two recently published schemes of connection for circular and square concrete-filled steel tubular (CFST) columns. The models were developed by equating the pullout strength of the tube with the pullout capacity of the reinforced concrete (RC) footing. The pullout capacity of the RC footing was a function of the strength of cement grout, footing concrete, and RC footing reinforcement. The analytical expressions derived for the minimum required depths of embedment were utilized to deduce limit state functions. These limit state functions were then employed for the reliability calculations by means of the Monte Carlo Simulation (MCS) technique. The reliability calculations provide optimum embedment depths for CFST columns for the given reliability level. It was shown for the required reliability index of 3.0, the requirements of nominal embedment depth for the second column-to-foundation connecting scheme for circular and square CFST columns are 37.3% and 45.2% less than their corresponding first schemes of connection. This outcome proves the superiority of the second scheme (as a result of mechanical interlocking) over the first scheme. A few parametric studies were also conducted to obtain results of practical value.

Multi-Debris Capture by Tethered Space Net Robot via Redeployment and Assembly

This paper presents an advanced multiple pieces of debris capture method for the tethered space net robot. A novel capture strategy that integrates redeployment and self-assembly techniques is introduced. With this strategy, the net robot self-assembles to close the net pocket and quickly maneuvers to nearby target debris. Upon reaching its target, the robot redeploys the net for debris capture. Central to this approach is the development of a capturing model that accurately describes the state function of the deployed net and incorporates an effective dragging method to counteract debris bouncing. To enable this multiple pieces of debris capture, an attitude consensus controller and a capture controller are designed using a finite-time scheme and terminal sliding mode, respectively. Numerical simulations reveal limitations in capturing multiple pieces of debris by existing design of tethered space net robots, where debris has the propensity to bounce out of a fully deployed net during multicapture attempts. The proposed strategy effectively mitigates these challenges, minimizing debris bounce and ensuring dependable multiple pieces of debris capture. Overall, the findings offer valuable insights to enhance the efficiency of active space debris removal missions.

The right to freedom of speech: theoretical and legal aspect

The article defines the right to freedom as a vital role in the existence of humanity, as it allows citizens to take an active part in the country's political life and shape public opinion. The author notes that the right to freedom of speech has ancient historical origins. Documents were analyzed in which the principle of freedom of speech was declared, in particular the Great Charter of Freedoms (1215), Bill of Rights (1689), Declaration of Independence (1776), Declaration of the Rights of Man and Citizen (1789), Universal Declaration of Human Rights (1948), International Covenant on Civil and Political Rights (1966) and other acts. It is emphasized that these documents became the basis for developing the right to freedom of speech in modern democratic countries and provided an opportunity to freely express one's opinions without being persecuted by the authorities. The article pays special attention to domestic regulation of the right to freedom of speech. The author notes that freedom of speech is one of the critical components of human and citizen rights in many legal systems. The theoretical aspect of this issue includes the analysis of different approaches and concepts to understanding the essence and scope of this subjective legal right. Philosophical foundations and legal methods for understanding "freedom of speech” are described. It was determined that the right to freedom of speech is not absolute and may be limited. The work lists the circumstances under which the outlined right may be limited. The author emphasizes that possible restrictions must be legal, necessary in a democratic society, and comply with the principle of proportionality. The article summarizes that freedom of speech is historically an essential human right, which forms the basis of the legal status of an individual. Without it, the functioning of a democratic state is impossible at all. But at the same time, it should be taken into account that freedom of speech is not only a right but also a responsibility that rests on those who use this right. Ensuring its adequate protection requires a combination of international standards, national legislation, and constant adaptation to modern realities.

Impact of blue-shifted effective joint density of electronic states on the photoluminescence of nanostructured silicon

Light emission from nanostructured silicon has triggered tremendous research interest for three decades. Yet, the exact mechanism of photoluminescence from silicon-based nano-systems is still not completely understood. It is generally believed that quantum confinement and surface chemistry play a combined role in determining the luminescence characteristics of nano silicon. In this work, we show that the evolution of electron-hole effective joint density of states, resulting from the relaxation of k-selection rule, can account for the much-observed temperature dependent shift of the luminescence spectra of nanostructured silicon. Deconvolution of the emission characteristics reveals three distinct radiative recombination channels those can be attributed to band-to-band, band-to-trap and trap-to-trap transitions. At temperatures below ∼200 K, the peak due to band-to-band transition exhibit a nearly linear blue shift with increasing temperature while at higher temperatures, this trend is reversed. The rate of variation of emission peak energy with temperature is also found to be dependent on the effective crystallite size. These results are explained in terms of shift in the effective joint density of state function of photogenerated electron-hole pairs. The shift provides experimental evidence of the pseudo-direct transitions in the quantum-confined nanostructure of silicon.

Conformal field theory approach to parton fractional quantum Hall trial wave functions

We show that all lowest Landau-level projected and unprojected chiral parton type fractional quantum Hall ground and edge-state trial wave functions, which take the form of products of integer quantum Hall wave functions, can be expressed as conformal field theory (CFT) correlation functions, where we can associate a chiral algebra to each parton state such that the CFT defined by the algebra is the “smallest” such CFT that can generate the corresponding ground and edge-state trial wave functions (assuming that the corresponding chiral algebra does indeed define a physically “sensible” CFT). A field-theoretic generalization of Laughlin's plasma analogy, known as generalized screening, is formulated for these states. If this holds, along with an additional assumption, we argue that the inner products of edge-state trial wave functions, for parton states where the “densest” trial wave function is unique, can be expressed as matrix elements of an exponentiated local action operator of the CFT, generalizing the result of Dubail [], which implies the equality between edge-state and entanglement level counting to state counting in the corresponding CFT. We numerically test this result in the case of the unprojected ν=2/5 composite fermion state and the bosonic ν=1ϕ22 parton state. We discuss how Read's arguments [] still apply, implying that conformal blocks of the CFT defined by the corresponding chiral algebra are valid quasihole trial wave functions, with the adiabatic braiding statistics given by the monodromy of these functions, assuming the existence of a quasiparticle trapping Hamiltonian. Generalizations of these constructions are discussed, with particular attention given to simple current constructions. It is shown that all chiral composite fermion wave functions can be expressed as CFT correlation functions without explicit symmetrization or antisymmetrization and that the ground, edge, and certain quasihole trial wave functions of the ϕnm parton states can be expressed as the conformal blocks of the U(1)⊗SU(n)m WZW models. Finally, we discuss the relation of the ϕ2k series with the Read-Rezayi series, where several examples of quasihole braiding statistics calculations are given. Published by the American Physical Society 2024

The mechanistic origins of heterogeneous void growth during ductile failure

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth.

Efficient reliability assessment of slope stability with insightful sensitivity analysis concerning the safety factor

The limit state functions (LSFs) of slope stability are nonlinear, implicit, or derived from numerical simulations, and additional surrogate models are usually used for its reliability problems. Alternatively, an efficient numerical procedure using a variant of the HLRF-BFGS algorithm is proposed to address this issue without additional surrogate models. This proposed procedure simultaneously conducts reliability assessment and sensitivity analysis concerning the safety factor by suggested calculations of partial derivatives using the finite difference method (FDM). Two highly nonlinear numerical examples are presented to validate its convergence and to investigate the step length of the FDM. Results show that the proposed procedure can get considerable accuracy while the HLRF algorithm cannot converge, and its required iterations are about 30% and 81% less than those of the limited step-size iteration algorithm. In addition, a step length not greater than 0.1 is suggested after investigations. Application to a classical two-layered slope is illustrated. Reliability results show that the proposed procedure can get the same accuracy as those of surrogate models after only 5 iterative steps. Sensitivity results show that the cohesion of the upper soil is the only sensitivity factor, and the most possible potential slide surface lies in the upper soil.

Reliability analysis of rolling bearings considering failure mode correlations

AbstractAs an essential mechanical component, a rolling bearing can exhibit multiple failure modes that may occur independently or in correlation with one another. A reliability analysis method that meticulously accounts for the interdependencies among various bearing failure modes is presented in this paper. The examination of wear and fatigue failure mechanisms in rolling bearings is carried out using the Physics of Failure (PoF) approach. By considering the influence of uncertain variables, the limit state functions for individual failure modes are formulated through the application of stress‐strength interference theory. In the context of wear failure, the limit state function is derived using working clearance as the characteristic quantity. On the other hand, the limit state function for fatigue failure is constructed with a focus on fatigue damage accumulation. The Copula function is used to characterize the relationship between wear failure and fatigue failure, and a reliability calculation model for rolling bearings is developed, considering the correlation between these failure modes. Ultimately, the proposed method is utilized to assess the reliability of bearings under two different sets of test conditions. The feasibility of this method is confirmed through test data, demonstrating its effectiveness in predicting bearing reliability. Through the application of this method, engineers can optimize bearing size parameters, select appropriate initial clearances, and enhance the reliability design of bearing.