Linear Rule Research Articles

A linear state feedback switching rule for global stabilization of switched nonlinear systems about a nonequilibrium point

A switched equilibrium of a switched system of two subsystems is a such a point where the vector fields of the two subsystems point strictly towards one another. Using the concept of stable convex combination that was developed by Wicks et al. (1998) for linear homogeneous systems, Bolzern and Spinelli (2004) offered a design of a state feedback switching rule that is capable to stabilize a linear nonhomogeneous switched system to any switched equilibrium. The state feedback switching rule of Bolzern–Spinelli gives a nonlinear (quadratic) switching threshold passing through the switched equilibrium. In this paper we prove that the switching threshold (i.e. the associated switching rule) can be chosen linear, if each of the subsystems of the switched system under consideration is globally asymptotically stable.

Adaptive Distributionally Robust Optimization

We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions, and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high-quality solutions for medical appointment scheduling and inventory management problems. The electronic companion is available at https://doi.org/10.1287/mnsc.2017.2952 . This paper was accepted by Noah Gans, optimization.

A plain linear rule for fatigue analysis under natural loading considering the coupled fatigue and corrosion effect

Fatigue under variable amplitude loading is currently assessed by applying the Palmgren-Miner linear rule in structural standards. However, this linear rule is inadequate in natural scenarios with coupled fatigue and corrosion effects, because the coupled corrosion-fatigue process synergistically accelerates deterioration. In view of the absence of specifications for the coupled fatigue-corrosion effect in structural standards, the objective here is to develop a simple and practical correction factor that will ensure a conservative linear summation of damage, taking the corrosion-fatigue effect into account. The theoretical consistency and the feasibility of the new adapted rule are tested in a case study.

Bearings-Only Tracking Using Augmented Ensemble Kalman Filter

Tracking targets with bearings-only measurement is a great challenge caused by poor observability and highly nonlinear estimation. In this brief, a novel augmented ensemble Kalman filter (AEnKF) is presented to address this bearings-only tracking problem. Different from the conventional ensemble Kalman filter (EnKF), the AEnKF overcomes the limitation of the linear measurement update rule in the linear minimum mean-square error (LMMSE) framework. The AEnKF utilizes a nonlinear transform of the measurement, called uncorrelated conversion (UC), to augment the measurement space. This conversion serves as a pseudomeasurement and is uncorrelated with the original measurement statistically. Unlike other UC filters based on the Gaussian assumption in the existing literature, the AEnKF does not impose any assumption on the probability density of the measurement by using generalized orthogonal polynomials to construct the UCs in a systematic way. The simulation results show that the AEnKF outperforms the conventional EnKF and other UC filters in the bearings-only tracking problem.

Block invariance and reversibility of one dimensional linear cellular automata

Consider a one-dimensional, binary cellular automaton f (the CA rule), where its n nodes are updated according to a deterministic block update (blocks that group all the nodes and such that its order is given by the order of the blocks from left to right and nodes inside a block are updated synchronously). A CA rule is block invariant over a family F of block updates if its set of periodic points does not change, whatever the block update of F is considered. In this work, we study the block invariance of linear CA rules by means of the property of reversibility of the automaton because such a property implies that every configuration has a unique predecessor, so, it is periodic. Specifically, we extend the study of reversibility done for the Wolfram elementary CA rules 90 and 150 as well as, we analyze the reversibility of linear rules with neighbourhood radius 2 by using matrix algebra techniques.

AllerCatPro-prediction of protein allergenicity potential from the protein sequence.

MotivationDue to the risk of inducing an immediate Type I (IgE-mediated) allergic response, proteins intended for use in consumer products must be investigated for their allergenic potential before introduction into the marketplace. The FAO/WHO guidelines for computational assessment of allergenic potential of proteins based on short peptide hits and linear sequence window identity thresholds misclassify many proteins as allergens.ResultsWe developed AllerCatPro which predicts the allergenic potential of proteins based on similarity of their 3D protein structure as well as their amino acid sequence compared with a data set of known protein allergens comprising of 4180 unique allergenic protein sequences derived from the union of the major databases Food Allergy Research and Resource Program, Comprehensive Protein Allergen Resource, WHO/International Union of Immunological Societies, UniProtKB and Allergome. We extended the hexamer hit rule by removing peptides with high probability of random occurrence measured by sequence entropy as well as requiring 3 or more hexamer hits consistent with natural linear epitope patterns in known allergens. This is complemented with a Gluten-like repeat pattern detection. We also switched from a linear sequence window similarity to a B-cell epitope-like 3D surface similarity window which became possible through extensive 3D structure modeling covering the majority (74%) of allergens. In case no structure similarity is found, the decision workflow reverts to the old linear sequence window rule. The overall accuracy of AllerCatPro is 84% compared with other current methods which range from 51 to 73%. Both the FAO/WHO rules and AllerCatPro achieve highest sensitivity but AllerCatPro provides a 37-fold increase in specificity.Availability and implementation https://allercatpro.bii.a-star.edu.sg/ Supplementary information Supplementary data are available at Bioinformatics online.

Theoretical Considerations on the Optimal Performance of Sub-100 Nanometer Top-Gated Graphene Field-Effect Transistors

The operation and performance of top-gated sub-100 nanometer graphene channel field-effect transistors were investigated. The device model is designed for graphene with a narrow energy band gap epitaxially grown on the SiC substrate. The issue of graphene-metallic lead coupling is appropriately taken into account. By assuming the graphene-metal physisorption contact, a self-consistent calculation reproduces two regions of high carrier density at the ends of the graphene channels underneath the metallic leads according to the charge transferred effect between the metallic lead surface and graphene. The charge carrier densities in these source and drain regions, however, are not pinned, but vary with respect to the drain and gate voltages. It is shown that, in general, the graphene channel supports the ambipolar characteristics for all device samples, but for the samples with the channels shorter than 40 nm, the current-voltage characteristic takes the exponential law. Particularly, the current saturation with a rather small output conductance of 126 S/m was observed in a sufficiently large range of drain voltage due to the dominance of the thermionic emission and conventional tunneling mechanisms to the band-to-band tunneling. A rough assessment of the device performance was also carried out. It reveals an extremely high cutoff frequency in the order of $$10^3\hbox { GHz}$$ and a linear scaling rule for transistors with the channel length longer than 40 nm. The behaviour and magnitude of these quantities are consistent with an experimental study of sub-100 nm devices fabricated using the self-alignment technique.

Linear Voting Rules

How should a society choose between two social alternatives if participation in the decision process is voluntary and costly, and monetary transfers are not feasible? Assuming symmetric independent private values, we show that it is utilitarian‐optimal to use a linear voting rule: votes get alternative‐dependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Any combination of weights and threshold can be optimal. A standard quorum rule can be optimal only when it yields the same outcome as a linear rule. A linear rule is called upper linear if the default is upset at every election result that meets the threshold exactly. We develop a perturbation method to characterize equilibria of voting rules in the case of small participation costs and show that leaving participation voluntary increases welfare for any two‐sided upper linear rule that is optimal under compulsory participation.

Nonlinear Damage Accumulation Rule for Solder Life Prediction Under Combined Temperature Profile With Varying Amplitude

Due to a mismatch of the coefficient of thermal expansion, electronic solder joints experience cyclic shear strain, which ultimately leads to fatigue failure. Traditional predictions of solder joint thermal fatigue life that use the experimental data or the physics-of-failure model often assume a regular profile. For complex temperature profiles, the linear accumulation rule is typically used to integrate the superposition effect. However, the linear rule was proved not applicable to most of the complex loading or temperature conditions. Based on the damage curve theory and the fatigue crack propagation theory, a novel nonlinear accumulation rule has been deduced for solder joint life predictions under irregular profiles, which were composed of two standard temperature cycles and may be experienced by phased-mission system. Four groups of experiments were conducted for ball grid array package solder joints with different dimensions and materials to determine parameters of the proposed nonlinear accumulation rule. The finite-element simulation method was used to extend this rule to more general cases for application. Compared to Miner’s linear accumulation rule, prediction of solder joint thermal fatigue life via the proposed nonlinear accumulation rule is closer to the accelerated life test results of real-world electronic solder joints under a combined temperature profile.

A new semi-analytical approach for obtaining crack-tip stress distributions under variable-amplitude loading

Near threshold fatigue crack response is extremely sensitive to load history. It is associated with the influence of near-tip stress on instantaneous resistance of crack tip surface layers to failure under atmospheric conditions. The paper deals with computational aspects of stress and strain distributions at the crack tip. A new approach is proposed to obtain near-tip stress under variable amplitude loading. The method considers a combination of standard rules for determining local strains (Linear rule, Neuber rule, ESED method, etc.) and well-known in Finite Element Analysis (FEA) return mapping algorithm in context of nonlinear mixed hardening material model. Iterative procedure based on Newton-Raphson method is proposed to calculate plastic variables and near-tip stress at each load step. The calculated results obtained by new model are validated with the traditional approach in case of Al2024-T3 alloy for constant amplitude loading after tensile/comprehensive overloads.

A Collective Investment Problem in a Stochastic Volatility Environment: The Impact of Sharing Rules

It is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors' well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

Robust energy storage allocation for transmission grid integrated by multiple wind farms

Since optimal planning for energy storage sizing and locating is critical to meet the requirement of total wind power absorption, a robust optimization theory based energy storage allocation model for transmission grid with multiple wind farms integrated is proposed in this paper. The model fully considers the transmission capacity limitation, and uses linear decision rule to optimize the allocation of the reserve capacity of the adjustable units and energy storage devices to cope with the fluctuation of wind power, which makes full use of the regulation capacity in the system. Some statistical information of wind power, such as expectation and interval, is used to describe the uncertainty of wind power. The uncertainty model is transformed into a deterministic model by using the duality optimization theory, which provides convenience for engineering application. The Garver’s 6-bus transmission system model is used for example analysis, which shows that the proposed method can effectively solve the energy storage planning problem for uncertain wind power integrated power systems.

Creep damage and life assessment of thick cylindrical pressure vessels with variable thickness made of 304L austenitic stainless steel

Using first-order shear deformation theory (FSDT), a semi-analytical solution is employed to analyze creep damage and remaining life assessment of 304L austenitic stainless steel thick (304L ASS) cylindrical pressure vessels with variable thickness subjected to the temperature gradient and internal non-uniform pressure. Damages are obtained in thick cylinder using Robinson\'s linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The thermo-elastic creep response of the material is described by Norton\'s law. The novelty of the present work is that it seeks to investigate creep damage and life assessment of the vessels with variable thickness made of 304L ASS using LMP based on first-order shear deformation theory. A numerical solution using finite element method (FEM) is also presented and good agreement is found. It is shown that temperature gradient and non-uniform pressure have significant influences on the creep damages and remaining life of the vessel.

Creep-ratcheting-fatigue life prediction of bainitic 2.25Cr1MoV steel

Ratcheting fatigue behavior of bainitic 2.25Cr1MoV forged steel was investigated at 455 oC with various hold periods at peak and valley stress. The incorporation of peak stress holding widened stress-strain hysteresis loop, and this enlargement was more significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and creep damage became dominant at long hold period, which was closely related to shortened fatigue lives with stress holding. The linear damage summation rule was used for fatigue life prediction, and it gave satisfactory predictions for peak holding mode. A new model was proposed by introducing stress ratio to consider the influence of asymmetric cycling, and estimates for peak/valley holding were greatly improved.

Single Snapshot Super-Resolution DOA Estimation for Arbitrary Array Geometries

We address the problem of search-free direction of arrival (DOA) estimation for sensor arrays of arbitrary geometry under the challenging conditions of a single snapshot and coherent sources. We extend a method of searchfree super-resolution beamforming, originally applicable only for uniform linear arrays, to arrays of arbitrary geometry. The infinite dimensional primal atomic norm minimization problem in continuous angle domain is converted to a dual problem. By exploiting periodicity, the dual function is then represented with a trigonometric polynomial using a truncated Fourier series. A linear rule of thumb is derived for selecting the minimum number of Fourier coefficients required for accurate polynomial representation, based on the distance of the farthest sensor from a reference point. The dual problem is then expressed as a semidefinite program and solved efficiently. Finally, the searchfree DOA estimates are obtained through polynomial rooting, and source amplitudes are recovered through least squares. Simulations using circular and random planar arrays show perfect DOA estimation in noise-free cases.

Ion-irradiation hardening and microstructural evolution in F82H and ferritic alloys

A reduced activation martensitic steel (F82H), Fe−8Cr ferrite model steel (8CrFS) and pure iron (Fe) were irradiated with 6.4 MeV Fe3+ ions at 300 °C to a displacement damage of 30 dpa at a nominal depth of 600 nm. Nano-indentation tests were performed at room temperature in continuous stiffness measurement (CSM) mode before and after the irradiation. Nix-Gao model was used to extract the nano-hardness of specimens and irradiation hardening (ΔH) was measured. Irradiation hardening was observed in all materials with F82H lowest (ΔH = 0.85 GPa) and pure iron highest (ΔH = 4.03 GPa). Transmission electron microscopy (TEM) observations indicated that dislocation loops dominated the damage microstructure after ion-irradiation. Both the average diameter and number density of dislocation loops were obtained. The correlation between microstructure and irradiation hardening was established based on dispersed barrier hardening (DBH) model. The obstacle strength factors of <100> and 1/2 <111> loops were assigned to be 0.54 and 0.17 with an assumption of linear rule.

Bath Gas Mixture Effects on Multichannel Reactions: Insights and Representations for Systems beyond Single-Channel Reactions.

Nearly all studies of and available data for pressure-dependent reactions focus on pure bath gases. Of the comparatively fewer studies on bath gas mixtures, important to combustion and planetary atmospheres, nearly all focus on single-channel reactions. The present study explores, and seeks reliable representations of, bath gas mixture effects on multichannel reactions. Analytical and numerical solutions of the master equation here reveal several unique manifestations of mixture effects for multichannel reactions, including behavior completely opposite to trends observed for single-channel reactions. The most common way of evaluating mixture rate constants from data for pure components, the classic linear mixture rule, is found to yield errors exceeding a factor of ∼10. A new linear mixture rule based on the reduced pressure, instead of the absolute pressure, is found to be accurate within ∼30% for rate constants (and ∼50% for the branching ratio). A new nonlinear mixture rule that additionally incorporates analytically derived activity coefficients is found to be accurate within ∼10% for rate constants and branching ratios. These new mixture rules are therefore recommended for use in fundamental and applied chemical kinetics investigations of reacting mixtures, including reacting flow codes and experimental interpretations of third-body efficiencies.

Master S-N Curve-Based Fatigue Life Assessment of Steel Bridges Using Finite Element Model and Field Monitoring Data

The accuracy of fatigue life assessment for the welded joint in a steel bridge is largely dependent on an appropriate [Formula: see text]-[Formula: see text] curve. In this paper, a master [Formula: see text]-[Formula: see text] curve-based fatigue life assessment approach for the welded joint with an open-rib in orthotropic steel bridge deck is proposed based on the finite element model (FEM) and field monitoring data from structural health monitoring (SHM) system. The case studies on fatigue life assessment by use of finite element analysis (FEA) for constant-amplitude cyclic loading mode and field monitoring data under variable-amplitude cyclic loading mode are addressed. In the case of FEA, the distribution of structural stress at fatigue-prone weld toe is achieved using 4-node shell element model and then transformed into equivalent structural stress by fracture mechanics theory. The fatigue life of the welded joint is estimated with a single master [Formula: see text]-[Formula: see text] curve in the form of equivalent structural stress range versus the cycles to failure. In the case of monitoring data-based fatigue life assessment, the daily history of structural stress at diaphragm to U-rib is derived from the raw strain data measured by the instrumented fiber Bragg grating (FBG) sensors and transformed into equivalent structural stress. The fatigue life of the investigated welded joint is calculated by cyclic counting method and Palmgren–Miner linear damage cumulative rule. The master [Formula: see text]-[Formula: see text] curve method provides an effective fatigue life assessment process, especially when the nominal stress is hard to be defined. A single master [Formula: see text]-[Formula: see text] curve will facilitate to solve the difficulty in choosing a proper [Formula: see text]-[Formula: see text] curve which is required in the traditional fatigue life assessment methods.

Quantification of Viscosity for Solvents−Heavy Oil/Bitumen Systems in the Presence of Water at High Pressures and Elevated Temperatures

In this study, a new and pragmatic methodology has been developed to accurately predict the viscosity for light solvents (i.e., methane, ethane, propane, n-butane, n-pentane, N2, and CO2)–heavy oil/bitumen/water systems as a function of pressure in the temperature range of 287.9–463.4 K. The LV and ALV (L is the oleic phase, V is the vapor phase, and A is the aqueous phase) phase equilibria of the aforementioned systems are calculated using the Peng–Robinson equation of state (PR EOS) with modified alpha functions and binary interaction parameters (BIPs). The six widely used mixing rules for predicting viscosity of solvents−heavy oil/bitumen systems pertaining to vapor–liquid equilibria are compared and evaluated, while the linear mixing rule is used for hydrocarbons−water mixtures. Plus, effective density is for the first time successfully introduced into the volume-based mixing rules. The volume-based power law, weight-based power law, and weight-based Cragoe’s mixing rules are found to well reproduce t...

Reduced late mismatch negativity and auditory sustained potential to rule-based patterns in schizophrenia.

Complex rule-based auditory processing is abnormal in individuals with long-term schizophrenia (SZ), as demonstrated by reduced mismatch negativity (MMN) to deviants in rule-based patterns and reduced auditory sustained potential (ASP) that appears when grouping tones together. Together, this suggests deficits later in the auditory processing hierarchy in Sz. Here, MMN and ASP were elicited by deviations from a complex zig-zag pitch pattern that cannot be predicted by simple linear rules. Twenty-seven SZ and 26 matched healthy controls (HC) participated. Frequent groups of patterns contained eight tones that zig-zagged in a two-up one-down pitch-based paradigm. There were two deviant patterns: the final tone was either higher in pitch than expected (creating a jump in pitch) or was repeated. Simple MMN to pitch-deviants among repetitive tones was measured for comparison. Sz exhibited a smaller pitch MMN compared to HC as expected. HC produced a late MMN in response to the repeat and jump-deviant and a larger ASP to the standard group of tones, all of which were significantly blunted in SZ. In Sz, the amplitude of the late complex MMN was related to neuropsychological functioning, whereas ASP was not. ASP and late MMN did not significantly correlate in HC or in Sz, suggesting that they are not dependent on one another and may originate within distinct processing streams. Together, this suggests multiple deficits later in the auditory sensory-perceptual hierarchy in Sz, with impairments evident in both segmentation and deviance detection abilities.