Linear Rule Research Articles

Modeling and solving for vibration and buckling of circular functionally graded dielectric plates reinforced by graphene platelets considering complex conditions

The vibration and bucking behaviors of circular functionally graded (FG) dielectric plates reinforced by graphene platelets (GPL) under external electric fields are studied at the presence of many complex factors such as dielectric effect, pre-stress, gradient slope, imperfect bonding between GPL and matrix material, interface electron tunneling and Maxwell–Wagner-Sillars (MWS) polarization. Based on the effective medium theory and linear rule of mixtures, material properties of the GPL reinforced composites (GPLRC) are calculated. Dynamic differential equations of the circular FG-GPLRC dielectric plates are numerically solved by the differential quadrature method, and natural frequencies and critical loads are obtained. Trans-scale analyses for the influences of the volume fraction, geometric size, gradient distributed pattern and gradient slope on the percolation threshold, permittivity and the vibration or buckling characteristics are provided. Furthermore, variations of the natural frequencies and critical loads with electric field parameters, the pre-stress and thickness of the interphase layer are also discussed. Results show that the natural frequencies and critical loads of the plates can be changed artificially and effectively by adjusting the external electric field, pre-stress and the parameters of GPL. The larger the diameter to thickness ratio of GPL, the bigger the equivalent permittivity and the smaller the percolation threshold. When the volume fractions of GPL are less than the threshold, the mechanical properties dominate the vibration and buckling. However, when the volume fractions are bigger than the threshold, the electrical properties have significant influences. Therefore, higher macro mechanical properties can be obtained by changing the microstructure of the materials.

Reliable Frequency Regulation Through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency deviation trajectories in a functional uncertainty set that encodes applicable legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem nonconvex. Methodology/results: By exploiting a total unimodularity property of the uncertainty set and an exact linear decision rule reformulation, we prove that this nonconvex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. Managerial implications: We find that the prevailing penalties for nondelivery of promised regulation power are too low to incentivize vehicle owners to honor the delivery guarantees given to grid operators. Funding: This work was supported by the Institut Vedecom. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0154 .

Comparative dynamics analysis of the environmental policy efficacy in a nonlinear Cournot duopoly with differentiated goods and emission charges

The price and the exchanged quantity volatility observed in real-world markets may be explained, according to the existing empirical literature, in terms of the endogenous fluctuations generated by the presence of nonlinearities. We then replace with a sigmoid adaptive best response mechanism the linear partial adjustment best response rule considered in Mamada and Perrings (2020), where the effect produced by quadratic emission charges on the dynamics of a Cournot duopoly model with homogeneous goods was investigated. Moreover, the sigmoid nonlinearity, in addition to being well suited to describe the bounded output variations caused by physical, historical and institutional constraints, makes the model able to generate interesting, non-divergent dynamic outcomes, despite the linearity of the demand function and of marginal costs. Additionally, following the suggestion in Mamada and Perrings (2020), we deal with the more general case of differentiated products. Beyond analytically studying the stability of the unique steady state, coinciding with the Nash equilibrium, and the effect produced by the main parameters on the stability region, we perform two comparative dynamics investigations which allow to evaluate the environmental policy efficacy when the Nash equilibrium is not stable and thus the standard comparative statics technique does not fit for the purpose. In particular, the former analysis, which is based on a comparison of emissions for different levels of charges, shows that, also in case the Nash equilibrium is not stable, the considered environmental policy may be effective both with complements and with substitutes. The latter investigation, consisting in a comparison of emissions along non-stationary trajectories and along the equilibrium path, in the proposed experiments highlights that emissions are larger along non-stationary trajectories. This gives us the opportunity to show how to act on the level of the asymptotes of the sigmoid adjustment mechanism to reduce output variations, reaching at one time a complete stabilization of the system and limiting pollution.

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.

Diffuse low-grade glioma: What is the optimal linear measure to assess tumor growth?

Radiological follow-up of diffuse low-grade gliomas (LGGs) growth is challenging. Approximative visual assessment still predominates over objective quantification due to the complexity of the pathology. The infiltrating character, diffuse borders and presence of surgical cavities demand LGG-based linear measurement rules to efficiently and precisely assess LGG evolution over time. We compared optimized 1D, 2D, and 3D linear measurements with manual volume segmentation as a reference to assess LGG tumor growth in 36 patients with LGG (340 magnetic resonance imaging scans), using the clinically important mean tumor diameter (MTD) and the velocity diameter expansion (VDE). LGG-specific progression thresholds were established using the high-grade gliomas-based RECIST, Macdonald, and RANO criteria, comparing the sensitivity to identify progression/non-progression for each linear method compared to the ground truth established by the manual segmentation. 3D linear volume approximation correlated strongly with manually segmented volume. It also showed the highest sensitivity for progression detection. The MTD showed a comparable result, whereas the VDE highlighted that caution is warranted in the case of small tumors with multiple residues. Novel LGG-specific progression thresholds, or the critical change in estimated tumor volume, were increased for the 3D (from 40% to 52%) and 2D methods (from 25% to 33%) and decreased for the 1D method (from 20% to 16%). Using the 3D method allowed a ~5-minute time gain. While manual volumetric assessment remains the gold standard for calculating growth rate, the 3D linear method is the best time-efficient standardized alternative for radiological evaluation of LGGs in routine use.

Multi-Stage Decision Rules for Power Generation & Storage Investments With Performance Guarantees

We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the optimized LDRs guarantee operational and carbon policy feasibility of the resulting dynamic investment plan even when the planning uncertainty distribution is ambiguous. Second, the optimized LDRs internalize the tolerance of the system planner towards the stochasticity (variance) of uncertain investment outcomes. They can eventually produce a quasi-deterministic investment plan, which is insensitive to uncertainty (as in deterministic planning) but robust to its realizations (as in stochastic planning). Last, we certify the performance of the optimized LDRs with the bound on their sub-optimality due to their linear functional form. Using this bound, we guarantee that the preference of LDRs over less restrictive – yet poorly scalable – scenario-based optimization does not lead to financial losses exceeding this bound. We use a testbed of the U.S. Southeast power system to reveal the trade-offs between the cost, stochasticity, and feasibility of LDR-based investments. We also conclude that the LDR sub-optimality depends on the amount of uncertainty and the tightness of chance constraints on operational, investment and policy variables.

Fatigue behavior of a nodular cast iron subjected to a variable amplitude strain-based load spectrum applied in bench tests of an Off-highway axle

Nodular cast irons are commonly adopted in off-highway applications, owing to the possibility to shape complex components and to guarantee good mechanical properties. In the fatigue strength assessment of axles made of nodular cast irons, engineers have to deal with external loads that turn into local strain spectra at the fatigue crack initiation zones, which are usually located in areas weakened by notched geometrical details. Moreover, off-highway axles are subjected to variable amplitude load histories during their service life; during the design phase, the field load histories are usually applied to the axles in the form of simplified bench load spectra. In this paper, the mechanical properties of EN-GJS-500-7 have been investigated through static tensile tests and strain-controlled fatigue tests performed on specimens with machined surface extracted from an axle. Furthermore, a local strain-based spectrum has been derived by means of strain gauges which have been applied at the failure location of the axle during the bench tests. Finally, the damage index to failure relevant to the simplified bench load spectrum has been calculated by adopting Miner's linear damage rule and the Smith, Watson and Topper mean stress corrected life equation.

Prediction of papillary thyroid cancer recurrence according to preoperative data

To create a formalized method for predicting papillary thyroid cancer recurrence after hemithyroidectomy based on preoperative data. At this stage of the study, we selected 101 patients with papillary thyroid cancer who underwent surgical treatment in 2017-2023. Recurrence was observed in in 47 patients. Fifty-four patients had no recurrence within 5 years after surgical treatment, i.e. these patients underwent surgery in 2017-2018. To find prediction rules, we used original classification method based on searching for subsets of variables and piecewise linear rules separating classes in pairs with subsequent voting of such rules to make a decision. The exam was carried out using a training sample (101 cases) and sliding control method (10 tests on 10 random cases). On the training sample, sensitivity of predictive algorithm was 91%, specificity 78% and error rate 13%. The aggregated result of 10 trials using sliding control method revealed sensitivity of predictive algorithm 86%, specificity 75% and error rate 15%. This result is close to overall sample and confirms the effectiveness of this method for predicting recurrence. The pilot experiments revealed the patterns in data for potential prediction of recurrence based on preoperative indicators. Further study of this problem may be valuable for decision-making and adjustments in the management of patients with papillary thyroid cancer.

Constitutive modelling and damage prediction of AlSi10Mg alloy manufactured by SLM technology with emphasis on ratcheting in LCF regime

The present work has been aimed at developing an improved cyclic plasticity model in the framework of Ohno-Wang kinematic hardening formulation and evaluating the performance of the model with reference to the critical experimental investigation. LCF test specimens of the AlSi10Mg aluminium alloy have been fabricated through selective laser melting technology. The material shows strain-range dependent variation of modulus of elasticity under symmetric strain-controlled loading. The modulus of elasticity decreases with increasing strain amplitude. Stress–strain responses have been critically examined under multistep uniaxial ratcheting in the LCF regime with incremental mean stress and stress amplitude. Damage calculation considering ratcheting and LCF mechanisms as independent gives unconservative predictions. The linear damage accumulation rule taking the largest contribution of both is bringing much more accurate estimates. The proposed model incorporates effects of mean stress and stress amplitude under uniaxial multistep ratcheting in the LCF regime. All fatigue tests in the LCF regime have been simulated using the proposed improved model. Evolution of strain-range dependent elastic modulus has been incorporated in the formulation of the improved model through the memory history dependent parameter. The ratcheting parameter is newly formulated in this present work to account for the effects of accumulated mean plastic strain on the opening of stress strain hysteresis loops that results in a better prediction of the behaviour of cyclic plastic deformation. The proposed model has been validated by comparing simulated results with experimental observations and reference published simulation results.

Investigating laypeople’s short- and long-term forecasts of COVID-19 infection cycles

How do laypeople anticipate the severity of the COVID-19 pandemic in the short and long term? The evolution of COVID-19 infection cases is characterized by wave-shaped cycles, and we examine how individuals make forecasts for this type of time series. Over 42 weeks, we ran forecasting experiments and elicited weekly judgments from the general public to analyze their forecasting behavior (Study 1). We find that laypeople often tend to dampen trends when generating judgmental forecasts, but the degree to which this happens depends on the evolution of the cyclic time series data. The observed forecasting behavior reveals evidence of an optimism bias in that people do not expect the number of infection cases to grow at the observed rate while believing that infection rates would drop at an even faster rate than they are. Also, our results suggest that laypeople’s forecasting judgments are affected by the magnitude of the present wave relative to the previously observed ones. Further, we provide evidence that laypeople rely on a cognitive heuristic for generating long-term forecasts. People tend to rely on a linear discounting rule in that they lower their long-term forecasts proportionally to the interval of the forecast horizon, i.e., from tomorrow to 6 months and from 6 months to 1 year. We also find that this linear discounting rule can change to an exponential one in reaction to externally generated optimistic information signals such as vaccine approval. Furthermore, we replicated the major findings of Study 1 in a more controlled setting with a hypothetical pandemic scenario and artificially generated time series (Study 2). Overall, the current research contributes to the judgmental forecasting literature and provides practical implications for decision-makers in the pandemic.

A Decision Rule Approach for Two-Stage Data-Driven Distributionally Robust Optimization Problems with Random Recourse

We study two-stage stochastic optimization problems with random recourse, where the coefficients of the adaptive decisions involve uncertain parameters. To deal with the infinite-dimensional recourse decisions, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. We develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. Applying known ideas, the resulting optimization problem can be reformulated as an exact copositive program that admits semidefinite programming approximations. We design an iterative decomposition algorithm, which converges under some regularity conditions, to reduce the runtime needed to solve this program. Through numerical examples for various known operations management applications, we demonstrate that our method produces significantly better solutions than the traditional sample-average approximation scheme especially when the data are limited. For the problem instances for which only the recourse cost coefficients are random, our method exhibits slightly inferior out-of-sample performance but shorter runtimes compared with a competing approach. History: Accepted by Nicola Secomandi, Area Editor for Stochastic Models & Reinforcement Learning. Funding: This work was supported by the National Science Foundation [Grants 2342505 and 2343869]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0306 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0306 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Computationally efficient simulation methodology for railway repair welding: Cyclic plasticity, phase transformations and multi-phase homogenization

The in-situ railway repair welding process consists of multiple weld passes, which makes it significantly different from other rail welding processes. In this study, finite element simulations of repair welding are performed to predict the resulting microstructure and residual stresses. To accurately simulate the material behavior, the modeling includes phase transformation kinetics, cyclic hardening plasticity, transformation induced plasticity, and multi-phase homogenization. More specifically, four different homogenization methods are investigated: isostrain, isostress, self-consistent and linear mixture rule. The performance of the material modeling is demonstrated by simulating multiple weld passes using a classical three-bar welding experiment. Based on the results, the self-consistent method and linear mixture rule are used in a 3D full-scale railhead repair weld simulation, in which the former generates a more realistic mechanical response. The immense computational cost associated with 3D full-scale, full-detail multi-pass welding simulations is addressed by exploring different model reduction schemes. From this study, a 2D generalized plane strain model, extended with out-of-plane axial and bending stiffness, is found to replicate the full-scale model at a mere fraction of the computational cost. Finally, the longitudinal residual stress distribution obtained from the reduced model is shown to correlate well with experimental measurements.

Creep–Fatigue Life Estimation of Gr.91 Steel and Its Welded Joints

A series of creep–fatigue tests of Gr.91 steel were performed at 600 °C. Fatigue life was reduced by tensile strain holding. The minimum life reduction factor was approximately 0.3. The creep–fatigue life could not be estimated properly via the conventional linear summation rule of the fatigue damage and creep damage. Since this material is considered to have a large creep–fatigue interaction, it was proposed that the creep–fatigue life should be estimated using the improved linear summation rule of the fatigue damage, the creep damage and the creep–fatigue interaction damage. In the future, it will be necessary to clarify the creep–fatigue interaction mechanism and define its damage value. On the other hand, a series of creep–fatigue tests for Gr.91 steel welded joints were also performed in the strain range of 0.5% at 600 °C. Again, the fatigue life was shortened by the tensile strain holding. The minimum fatigue life reduction factor was approximately 0.2. All the test pieces fractured in the fine-grained HAZ of the welded joints. The creep–fatigue life could not be estimated properly using the linear summation rule of the fatigue damage and creep damage in the HAZ. One possible reason was thought to be the effects of the elastic follow-up phenomena peculiar to welded joints. The creep strain of the HAZ might increase due to the transfer of the elastic strain from both the base metal and the weld metal, according to the elastic follow-up phenomena during strain holding. In the future, it will be important to quantitatively estimate the effects of the elastic follow-up phenomena.

Crack growth in high strength mooring line steel under variable amplitude loading

Mooring lines are of key importance for the safe and reliable operation of numerous floating offshore structures. Due to the constantly changing wind and wave conditions acting on such structures, any fatigue crack growth in a mooring line will occur under cyclic loading of distinctly variable amplitude. This paper considers a long-term load history for mooring lines on a North Sea offshore platform. For fatigue testing purposes, a characteristic load sequence representing the actual load history in a condensed and simplified form is developed and presented. Fatigue crack growth rate test results for a grade R4 high strength mooring chain steel subjected to this variable amplitude load sequence is furthermore presented, including tests performed in air as well as under free corrosion conditions in artificial seawater. Based on comparison testing performed under variable- and constant amplitude conditions, the validity of a linear damage rule hypothesis for stable crack growth under the characteristic load sequence is investigated. This damage rule converts the load spectrum to an equivalent constant load range, making it a potentially useful tool for estimating fatigue crack growth in mooring chains when test data for a representative characteristic load sequence are unavailable. Results from the comparison testing are used to show that under stable fatigue crack growth conditions, while subjected to the characteristic load sequence developed for this offshore platform, the linear damage rule can be a reasonable assumption.

Disclosure and pricing of attributes

AbstractA monopolist sells an object characterized by multiple attributes. A buyer can be one of many types, differing in their willingness to pay for each attribute. The seller can provide arbitrary attribute information in the form of a statistical experiment. To screen different types, the seller offers a menu of options that specify information prices, experiments, and object prices.I characterize revenue‐maximizing menus. All experiments belong to a class of linear disclosure rules. An optimal menu may be nondiscriminatory. The analysis highlights the importance of demand microstructure and the benefits of information control in trade settings.

Variational Quantum Linear Solver-based Combination Rules in Dempster–Shafer Theory

Dempster–Shafer Theory (DST), as a method of handling uncertain information, is widely used in decision-making and information fusion. But the issue of exponential computational complexity limits its real-time application. Since quantum computers with its natural parallel computing capability can theoretically achieve speedup, an HHL-based algorithm for implementing DST operations on quantum circuits has been proposed. However, the algorithm is impossible to be implemented with high accuracy due to the limited performance of quantum computers in the current noisy intermediate-scale quantum (NISQ) era. In response to that, we utilize an up-to-date scheme Variational Quantum Linear Solver (VQLS) to conduct DST operations by solving the linear system. Besides, VQLS further reveals the structural consistency of DST with quantum computation, which enables faster circuit configuration and computation. In this paper, we first realize the transformation in belief functions by VQLS and then extends it to a methods of implementing combination rules. Simulated under a realistic classification task, the feasibility and accuracy of the proposed VQLS-based method are verified. The new VQLS-based method proposed is able to achieve combination rules at a lower error level with fewer quantum resources, which is more suitable for the NISQ era.

Fatigue life prediction of rolling bearings based on damage accumulation considering residual stresses

The determination of the fatigue life of rolling bearings is recommended to be conducted using the standard calculation models defined in ISO 281. These models yield reliable results for rotating applications. The standard models are continuously refined to align with advancements in bearing production processes and material improvements. However, when dealing with rolling bearings exposed to complex load conditions including oscillatory movements, as seen in rotor blade bearings in wind turbines, a validated calculation model has yet to be established. In the domain of structural mechanics, fatigue life evaluation for steel components is based on S-N curves. Variable operational loads are treated as load collective, and the load cycle to failure N under given operational conditions is determined through the application of the linear damage rule. This paper introduces a novel model that integrates the linear damage rule with established conventional bearing theories. Within one internal stress cycle, all rolling contacts are regarded as an internal load collective. To evaluate the internal load collective, the stress state at each rolling contact is assessed based on the S-N curve determined in alternating torsional loads. The core rationale behind the selection of an S-N curve lies in the stress criterion τo based on Lundberg-Palmgren theory, which is incorporated in the new model. This paper includes a comprehensive step-by-step procedure for applying the new model, utilizing the cylindrical roller bearing NU 1006 as a reference. The results of this study indicate a favorable agreement between the fatigue life obtained using the new model and those determined according to ISO 281. Furthermore, a new approach is introduced to analytically account for residual stress - es when measured values are available. In this study, by applying this new approach, the results were observed to be in close agreement with the test results. Based on this investigation, it can be confirmed that the new model has the potential to provide reliable results without necessitating the bearing life exponent as well as the correction factors often required in conventional calculation models.

Multistage Adaptive Robust Binary Optimization: Uncertainty Set Lifting versus Partitioning through Breakpoints Optimization

Two methods for multistage adaptive robust binary optimization are investigated in this work. These methods referred to as binary decision rule and finite adaptability inherently share similarities in dividing the uncertainty set into subsets. In the binary decision rule method, the uncertainty is lifted using indicator functions which result in a nonconvex lifted uncertainty set. The linear decision rule is further applied to a convexified version of the lifted uncertainty set. In the finite adaptability method, the uncertainty set is divided into partitions and a constant decision is applied for each partition. In both methods, breakpoints are utilized either to define the indicator functions in the lifting method or to partition the uncertainty set in the finite adaptability method. In this work, we propose variable breakpoint location optimization for both methods. Extensive computational study on an illustrating example and a larger size case study is conducted. The performance of binary decision rule and finite adaptability methods under fixed and variable breakpoint approaches is compared.

The Conceptual Flaws of Decentralized Automated Market Making

Decentralized exchanges (DEXs) are an essential component of the nascent decentralized finance (DeFi) ecosystem. The most common DEXs are so-called automated market makers (AMMs): smart contracts that pool liquidity and process trades as atomic swaps of tokens. AMMs price transactions with a deterministic liquidity invariance rule that only uses the AMM’s token deposits as inputs and that has no precedent in traditional finance. Yet, in the context of transparent and open blockchain operations, any liquidity invariance pricing function allows so-called sandwich attacks (akin to front running) that increase the cost of trading and threaten the long-term viability of the DeFi ecosystem. Invariance pricing is also not regret free. Linear pricing rules have similar problems except for uniform pricing, which has regret-free prices and limits sandwich attack profits but which invites excessive order splitting. Comparing trading costs using a model of liquidity provision, constant product pricing is often cheaper except when the variance of the underlying asset is small or when the order is large. This paper was accepted by Will Cong, Special Section of Management Science: Blockchains and Crypto Economics. Funding: A. Park received financial support from the Global Risk Institute and the Social Sciences and Humanities Research Council of Canada [Grant 435-2017-0647]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2021.02802 .

Hydrophobic Matching Dictates over the Linear Rule of Mixtures in Binary Lipid Membranes.

Biological membranes feature heterogeneous mixtures of lipids with different head and tail characteristics. Their biophysical properties are dictated by the intimate interaction among different constituent lipids. Previous studies suggest that the membrane area-per-lipid (APL) deviates from the linear rule of mixtures (LRM) for binary lipid membranes, but the underlying mechanism remains elusive. Our molecular dynamics (MD) simulations of binary lipid membranes consisting of lipids with different tail characteristics reveal a competitive mechanism whereby lipids tend to deform each other to minimize the hydrophobic mismatch between their tails. Depending on the relative tail lengths and saturation levels, this may result in an either positive or negative deviation of APL from the LRM. As lipid packing plays an essential role in membrane fusion and peptide-membrane binding, our findings may help guide the selection of lipids for the effective rational design of nanoliposomes and membrane-targeting peptides.