Lower Bound Model Research Articles

Sparsified simultaneous confidence intervals for high-dimensional linear models

AbstractStatistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. Currently, the inference of the model and the inference of the coefficients are separately sought. A critical question remains unsettled; that is, is it possible to embed the inference of the model into the simultaneous inference of the coefficients? If so, then how to properly design a simultaneous inference tool with desired properties? To this end, we propose a notion of simultaneous confidence intervals called the sparsified simultaneous confidence intervals (SSCI). Our intervals are sparse in the sense that some of the intervals’ upper and lower bounds are shrunken to zero (i.e., [0, 0]), indicating the unimportance of the corresponding covariates. These covariates should be excluded from the final model. The rest of the intervals, either containing zero (e.g., $$[-1,1]$$ [ - 1 , 1 ] or [0, 1]) or not containing zero (e.g., [2, 3]), indicate the plausible and significant covariates, respectively. The SSCI intuitively suggests a lower-bound model with significant covariates only and an upper-bound model with plausible and significant covariates. The proposed method can be coupled with various selection procedures, making it ideal for comparing their uncertainty. For the proposed method, we establish desirable asymptotic properties, develop intuitive graphical tools for visualization, and justify its superior performance through simulation and real data analysis.

A bi-objective model for scheduling green investments in two-stage supply chains

Investing in green technologies to increase sustainability in supply chains has become a common practice for two reasons: the first is directly related to the defense of the environment and people’s health to smooth the emissions of pollutants; the second is the increasing consumer awareness of green products. Despite the higher costs of producing with green technologies and processes, there is also a higher markup on the price of products which rewards the former costs. This study proposes a mathematical model for scheduling green investments over time in a two-stage supply chain to minimize the impact of production on the environment and the economic costs deriving from the investment. The resulting bi-objective model has nonlinear constraints and is solved using a commercial solver. Given its complexity, we propose an upper-bound heuristic and a lower-bound model to reduce the optimality gap attained at a given time limit. Tests on synthetic instances have been conducted, and an example demonstrates the applicability and efficacy of the proposed model.

Logistics UAV Air Route Network Capacity Evaluation Method Based on Traffic Flow Allocation

A bi-level optimization model for the logistics UAV air route network capacity evaluation based on traffic flow allocation is designed in order to meet the future trend of large-scale and normalized operation of logistics UAVs. The maximum sorties of logistics UAVs that can be served by the air route network are the upper-bound model objective, namely, the maximum flow of the logistics UAV air route network. The impedance function is constructed by considering safety and efficiency factors, and the lower-bound model objective function with the minimum logistics UAV air route network impedance value. An improved particle swarm optimization(PSO) algorithm is combined with the method of the successive algorithm(MSA) for solving the bi-level optimization model. To verify the effectiveness of the proposed model and algorithm, a simplified logistics UAV air route network is built. The results show that the proposed algorithm obtains reliable results after 26 iterations, and most segments capacity utilization rate is more than 70%. Parametric analysis of safe separation and algorithm population size shows that the capacity of logistics UAV air route network decreases with the increase of safe separation and the decreasing trend is gradually slowed down, and the optimal algorithm population size corresponding to different safe separations also varies. Based on the study described above, a logistics UAV air route network based on actual geographic information data is constructed, and the experimental results demonstrate that the suggested technique could be used to a specific scale of logistics UAV route network capacity evaluation and had validity.

Disturbance Modeling and Prediction of Closed-Loop Micro-Actuator Stroke Usage in Dual-Stage Hard Disk Drives

Abstract This letter presents a method to model the disturbance environment of a dual-stage hard disk drive (HDD), which is then used to predict the actuator stroke usage (i.e., the range of actuator displacement used) of a closed-loop track-following controller. In particular, a data-driven disturbance modeling approach is proposed and the stochastic interpretation of the H2 norm is used to systematically estimate the micro-actuator (PZT) stroke usage of the HDD controller. Upper- and lower-bound models of the frequency response of the external disturbance environment are used to provide a range of possible stroke usage, which involves a data-driven calibration process. The accuracy of the prediction model is validated in experiments with a controller that differs from the controllers in the calibration data set.

Lower Bound Capacity of Strip Footings on Rock Masses with Two Discontinuity Sets

This paper presents a lower bound model for predicting the rock strip footing bearing capacity. The model is based on strip footings on rock masses with two sets of ubiquitous, closed discontinuities. The model considers explicitly the strength of the intact rock and the discontinuities, as well as the number and orientation of the discontinuities. The validation of the model is presented. The parametric study of footings on rock masses with two discontinuity sets having the same strength is performed, and the results are reported graphically in detail. The bearing capacity is controlled primarily by the rock structures (number of discontinuity sets and orientation) and the discontinuity strength, and it is controlled by the intact rock strength for a very limited number of cases. The minimum bearing capacity factor is independent of the intact rock friction angle, but it is a linear function of discontinuity cohesion. The bearing capacity factor is also presented in terms of its ratio to UCS; the ratio for the maximum bearing capacity is rather insignificantly affected by intact rock friction angle, and not linearly correlated to discontinuity cohesion. The bearing capacity factor for rock masses with low discontinuity strengths tends to be more sensitive to any variation in discontinuity orientation. There are some exceptions to the above points, suggesting that there would always be some rock mass conditions leading to unexpected rock footing bearing capacities and therefore good characterization processes of rock masses would always be essential. The practical significant of this study is briefly discussed.

Polycrystalline simulations of in-reactor deformation of recrystallized Zircaloy-4 tubes: Fast Fourier Transform computations and mean-field self-consistent model

Fuel cladding and structural components made of zirconium alloys, used in light and heavy water nuclear reactors, exhibit, during normal operation, significant in-reactor deformation. Fast Fourier Transform (FFT) simulations have been conducted on large grain aggregates to simulate the in-reactor behavior of recrystallized Zircaloy-4. Original constitutive equations have been proposed to account, at the microscopic scale, for thermal creep, irradiation creep and irradiation induced growth. The evolution of irradiation defects with irradiation is taken into account, especially to deduce the local growth strain. A good description of the in-reactor behavior is obtained with irradiation defects evolution consistent with Transmission Electron Microscopy observations. The FFT simulations are compared to a self-consistent model. A good agreement is obtained when the behavior is linear (irradiation creep and growth) while the nonlinear response (thermal creep) is underestimated by the self-consistent model. The FFT simulations are also compared to the lower-bound model which neglects the interactions between grains. The lower-bound model underestimates the growth strain proving the importance of using an accurate polycrystalline model to predict the growth strain from the knowledge of the irradiation defect evolution.

Undrained bearing capacity of irregular T-bar by the lower bound method in clay

The lower bound method is employed to investigate the ultimate bearing capacity of the irregular T-bar in uniform soil. The stress field is constructed to illustrate the evolution of the soil flow mechanisms and considering the frictional influence. Simultaneously finite element analyses and two special conditions are also employed to verify the reasonability of the lower bound model. The general expressions of the bearing capacity factors for two types of irregular T-bars are presented, which have reference value for similar ocean structures. The main results are shown as follows: ①The friction coefficients significantly influence the bearing capacity factor with increasing aspect ratio. ② The rigid zones are presented at the front and rear of the elliptical probe and progressively decrease with increasing ξ (probe aspect ratios) and reducing ω (friction factor), until disappearing at a larger aspect ratio following a smooth interface. ③ For ξ > 1, the degree of streamlining of the elliptical probe easily results in an attached flow mechanism to the probe surface and a decreasing rigid zone with increasing ξ in the high strength soil. ④ Compared with the CPT test, the advantage of the diamond T-bar is without the need for overburden stress correction in the full flow mechanism. ⑤ The large aspect ratio of the irregular T-bar tries to determine the interface friction factor based on the bearing factor equation.

An Approximation Algorithm for Unrelated Parallel Machine Scheduling Under TOU Electricity Tariffs

In an era of sustainable development, considerable emphasis has been put onto energy saving, environment friendly, and social welfare as well as productivity in the manufacturing sector. In this work, an unrelated parallel manufacturing setting with time-of-use (TOU) electricity price is explored, with an aim to reduce the electricity cost and increase productivity simultaneously. A nonlinear mathematical programming model is formulated to exploit the special structure of the scheduling problem, where the quadratic constraints are reformulated as second-order-cone (SOC) constraints, and several tailored cutting planes are introduced to further tighten the feasible region of the problem. Then, the original scheduling problem is transformed into several single-machine scheduling problems with TOU electricity price, which could be relaxed as a single-objective programming problem, and it could be solved rapidly via commercial solvers, such as CPLEX. Based on the optimal solution of the relaxed problem, an approximate algorithm is proposed, where a special rounding technique is employed to assign jobs to the unrelated parallel machines in a local search manner. Furthermore, a lower bound model is constructed by eliminating the nonpreemption constraint, and an iteration-based algorithm is devised to obtain the optimal solution of the lower bound problem. Meanwhile, a dispatch rule-based approach is proposed to provide an upper bound of the scheduling problem with TOU constraint. In the numerical analysis section, the proposed approximate algorithm is validated through extensive testing on various scales of instances, different emphasis on productivity and electricity price, and under two typical TOU electricity pricing policies. It is observed that the gap between the proposed approximate algorithm and CPLEX is mostly within 4%, and the lower/upper bound methods could obtain a relaxed/feasible solution within 0.01 s.

Modelling shear strength of compacted soils

Compacted soils constitute most engineering projects such as earth dams, embankments, pavements, and engineered slopes because of their high shear strength and low compressibility. The shear strength of compacted soils is a key soil parameter in the design of earth structures but it is seldom determined correctly due to their unsaturated state. The shear strength of compacted soils can be better evaluated under the framework of unsaturated soil mechanics. Saturated and unsaturated tests were conducted on compacted specimens using conventional direct shear apparatus under constant water content condition. Tests were conducted at different water contents and net normal stresses. The main objective of this study is to develop a shear strength model for compacted soils. Initial matric suction was measured before the test using the filter paper method. The two-stress state variables together with the extended Mohr-Coulomb failure criterion for unsaturated soils were used to obtain a lower bound model of the shear strength. The model was demonstrated using published data.

Predicting viscoplastic anisotropy in the upper mantle: a comparison between experiments and polycrystal plasticity models

Viscoplastic deformation of mantle rocks produces crystal preferred orientations (CPO or texture) of olivine and, by consequence, an anisotropic mechanical response for subsequent deformation events. Olivine polycrystals deformed experimentally in torsion and then in extension normal to the previous shear plane have extensional strengths ∼2 times higher than the torsional ones. Implementation of this viscoplastic anisotropy in geodynamic codes depends nevertheless on the predictions of polycrystal plasticity models, since the full range of orientation relations between applied stresses and the broad range of texture types observed in upper mantle rocks may only be tested numerically. Here, we compare instantaneous viscoplastic responses of olivine polycrystals predicted by tangent and second-order viscoplastic self-consistent (VPSC) and stress equilibrium-based models to experimental data. These polycrystal plasticity models, in which only dislocation glide is considered to accommodate strain, reproduce qualitatively the viscoplastic anisotropy observed in the laboratory, but overestimate its magnitude for rocks with strong textures. The lower bound model better approaches the laboratory results, suggesting that the discrepancy between laboratory and numerical experiments arises from the models forcing strain compatibility in olivine polycrystals that can only deform by dislocation creep. The experimental data is indeed well reproduced by the second-order VPSC model modified to include additional isotropic deformation mechanisms, which accommodate the deformation components that cannot be produced by dislocation glide but do not produce plastic spin. These results corroborate that other processes in addition to dislocation glide contribute significantly to viscoplastic deformation under laboratory conditions, reducing the magnitude of anisotropy. In nature, coarser grain sizes probably result in lower activity of these additional deformation processes. We therefore propose that standard and modified second-order VPSC models provide a good prediction of the possible range of texture-induced viscoplastic anisotropy in upper mantle domains deforming by dislocation creep.

Test and lower bound modeling of keyed shear connections in RC shear walls

This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests showed that connections with larger key indentations failed by complete key cut-off. In contrast, connections with smaller key indentations were more prone to suffer local crushing failure at the key corners. The local key corner crushing has an effect on the load-displacement response, which is relatively more ductile. In addition to the tests, the paper also presents lower bound modeling of the load carrying capacity of the connections. The main purpose of the lower bound model is to supplement an already published upper bound model of the same problem and thereby provide a more complete theoretical basis for practical design. The two models display the same overall tendencies although identical results are not possible to obtain, due to differences in the basic assumptions usually made for upper and lower bound analysis of connections. It is found that the test results, consistent with the extremum theorems of plasticity, are all lying within the gap between the upper and the lower bound solution. The obtained results finally lead to a discussion of how the two models can be used in practice. The primary merit of the upper bound model lies in its simplicity (a closed-form equation). On the other hand, the lower bound model provides safe results, but is more complicated to apply. It is therefore argued that the upper bound model may be used in cases, where calibration with tests has been carried out. The lower bound model should be applied in situations, where the design deviates significantly from the configurations of the available tests.

A model-driven approach for predicting and analysing the execution efficiency of multi-core processing

Techniques for predicting the efficiency of multi-core processing associated with a set of tasks with varied CPU and main memory requirements are introduced. Prediction of CPU and memory availability is important in the context of making process assignment, load balancing, and scheduling decisions in distributed systems. Given a set of tasks each with varied CPU and main memory requirements, and a multi-core system (which generally has fewer cores than the number of tasks), we provide upper- and lower-bound models (formulas) for the efficiency with which the tasks are executed. In addition, a model for average CPU availability is introduced from the empirical study for applications that require a single predicted value instead of bounds. To facilitate scientific and controlled empirical evaluation, real-world benchmark programs with dynamic behaviour (CPU and memory requirements change in a short interval of time) are employed on UNIX systems that are parameterised by their CPU usage factor and memory requirement.

A model-driven approach for predicting and analysing the execution efficiency of multi-core processing

Techniques for predicting the efficiency of multi-core processing associated with a set of tasks with varied CPU and main memory requirements are introduced. Prediction of CPU and memory availability is important in the context of making process assignment, load balancing, and scheduling decisions in distributed systems. Given a set of tasks each with varied CPU and main memory requirements, and a multi-core system (which generally has fewer cores than the number of tasks), we provide upper- and lower-bound models (formulas) for the efficiency with which the tasks are executed. In addition, a model for average CPU availability is introduced from the empirical study for applications that require a single predicted value instead of bounds. To facilitate scientific and controlled empirical evaluation, real-world benchmark programs with dynamic behaviour (CPU and memory requirements change in a short interval of time) are employed on UNIX systems that are parameterised by their CPU usage factor and memory requirement.

Cost efficiency in data envelopment analysis under the law of one price

To impose the law of one price (LoOP) restrictions, which state that all firms face the same input prices, Kuosmanen, Cherchye, and Sipiläinen (2006) developed the top-down and bottom-up approaches to maximizing the industry-level cost efficiency. However, the optimal input shadow prices generated by the above approaches need not be unique, which influences the distribution of the efficiency indices at the individual firm level. To solve this problem, in this paper, we developed a pair of two-level mathematical programming models to calculate the upper and lower bounds of cost efficiency for each firm in the case of non-unique LoOP prices while keeping the industry cost efficiency optimal. Furthermore, a base-enumerating algorithm is proposed to solve the lower bound models of the cost efficiency measure, which are bi-level linear programs and NP-hard problems. Lastly, a numerical example is used to demonstrate the proposed approach.

A Theory of Network Equivalence – Part II: Multiterminal Channels

A technique for bounding the capacities of networks of independent channels is introduced. Parts I and II treat point-to-point and multiterminal channels, respectively. Bounds are derived using a new tool called a bounding model. Channel 1 is an upper (lower) bounding model for channel 2 if replacing channel 2 by channel 1 in any network yields a new network whose capacity region is a superset (subset) of the capacity region of the original network. This paper derives bounding models from noiseless links, with lower bounding models corresponding to points in the channel's capacity region and upper bounding models corresponding to points in a new channel characterization called an emulation region. Replacing all channels in a network by their noiseless upper (lower) bounding models yields a network of lossless links whose capacity region is a superset (subset) of the capacity region for the original network. This converts a general (often stochastic) network into a network coding instance, enabling the application of tools and results derived in that domain. A channel's upper and lower bounding models differ when the channel can carry more information in some networks than in others. Bounding the difference between upper and lower bounding models bounds both the accuracy of the technique and the price of separating source-network coding from channel coding.

Allowable Shears for Plastered Straw-Bale Walls

AbstractAlthough straw-bale construction originated in the midwestern United States in the late 1800s, the engineering of plastered straw-bale walls to resist in-plane lateral loads is a modern development. Relevant experimental studies are reviewed and allowable shears are developed for use in design for wind and seismic loading. Clay, soil-cement, lime, lime-cement, and cement plasters having various thicknesses and reinforced with welded steel wire mesh, woven steel wire mesh, or polypropylene mesh are considered. Experimental values are adjusted on the basis of moment-curvature analysis results to account for lower-bound model code material strengths, plaster thicknesses, and mesh reinforcement. A conventional model for shear strength is used to provide a preliminary assessment of true shear strength. The resulting design values and associated detailing requirements are summarized in a format suitable for implementation in model code provisions for straw-bale construction.

Scalable Capacity Bounding Models for Wireless Networks

The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (respectively, lower) bounding models, which can be used to calculate the outer (respectively, inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed to decompose wireless networks into decoupled multiple-access channels and broadcast channels. The upper bounding model, consisting of only point-to-point bit pipes, is constructed by first extending the one-shot upper bounding models developed by Calmon et al. and then integrating them with network equivalence tools. The lower bounding model, consisting of both point-to-point and point-to-points bit pipes, is constructed based on a two-step update of the lower bounding models to incorporate the broadcast nature of wireless transmission. The main advantages of the proposed methods are their simplicity and the fact that they can be extended easily to large networks with a complexity that grows linearly with the number of nodes. It is demonstrated that the resulting upper and lower bounds can approach the capacity in some setups.

Transport of Gases in Glassy Polymers under Transient Conditions: Limit-Behavior Investigations of Dual-Mode Sorption Theory

Considerable interest had been focused during 1950–1980 on the pure gas isothermal sorption–diffusion modeling in glassy polymers. In particular, the theory of dual-mode sorption has been developed during this period. It postulates that two concurrent sorption modes occur in the microheterogeneous medium. On the basis of this theory, rather complete and successful models have been roposed. In this paper, a short review of dual-mode-sorption models is first given. By considering a general expression of the sorption mode, the conventional models (partial immobilization model and immobilization model) become one limit-behavior model: the time-lag upper-bound model. Another limit-behavior model, the time-lag lower-bound model called the dual-diffusion model, is particularly investigated and compared to conventional models in this paper. It is shown that the steady-state permeability is independent of the molecule exchange rate, while the time-lag prediction depends on it. Furthermore, the time-lag lower-bound model provides, in general, a better agreement with experiments. In this respect, the dual-diffusion model is considered as a simple and efficient dual-mode-sorption theory approach.

Simple lower bound limit analysis homogenization model for in- and out-of-plane loaded masonry walls

A simple homogenized equilibrated and admissible model for the limit analysis of masonry walls in- and out-of-plane loaded is presented. A rectangular running bond elementary cell (RVE) is discretized by means of a few constant stress triangular elements (CST) and interfaces. Non linearity is concentrated on brick–brick interfaces and joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength. When dealing with the flexural behavior, a Kirchhoff–Love homogenized model is derived, subdividing the REV into several layers along the thickness and in discretizing each layer analogously to the in-plane case. When dealing with the in-plane behavior, a linear programming problem with very few variables is obtained, which can be handled even manually for some cases of technical interest. The lower bound model proposed is validated at a cell level through literature kinematic models, to show that the lower bound approach provides almost identical results with respect to upper bound approaches, meaning that the actual solution is well approximated. Homogenized masonry behavior is then implemented at a structural level in consolidated FE limit analysis codes for the evaluation of collapse loads and failure mechanisms of real scale masonry structures.

A Lower Bound Model for Multiple Record Systems Estimation with Heterogeneous Catchability

This work considers the estimation of the size N of a closed population using incomplete lists of its members. Capture histories are constructed by establishing the presence or the absence of each individual in all the lists available. Models for data featuring a heterogeneous catchability and list dependencies are considered. A log-linear model leading to a lower bound for the population size is derived for a known set of list dependencies and a latent catchability variable with an arbitrary distribution. This generalizes Chao’s lower bound to models with interactions. The proposed model can be used to carry out a search for important list interactions. It also provides diagnostic information about the nature of the underlying heterogeneity. Indeed, it is shown that the Poisson maximum likelihood estimator of N under a dichotomous latent class model does not exist for a particular set of LB models. Several distributions for the heterogeneous catchability are considered; they allow to investigate the sensitivity of the population size estimate to the model for the heterogeneous catchability.