Linear Rule Research Articles

Intelligent Control Method for Loss Distribution Balance of High-Power Photovoltaic Grid-Connected Inverters.

Aiming at the problem that the loss distribution balance control effect of high-power photovoltaic grid-connected inverter is poor due to the complex loss factors, this paper proposes a loss distribution analysis and balance intelligent control method for high-power photovoltaic grid-connected inverter. The topology structure of high-power photovoltaic grid-connected inverter is constructed and the overall control scheme is designed. The loss of inductance, resonant frequency, harmonic attenuation, and damping resistance in the circuit of PV grid-connected inverter is analyzed, respectively. On this basis, a two-stage loss control model of high-power PV grid-connected inverter is constructed, and the generalized linear decision rule is adopted to schedule PV power supply and fluctuating load. A two-stage loss control model for high-power photovoltaic grid-connected inverter was established and the optimal loss control value was obtained. Experimental results show that the proposed method can accurately suppress voltage and current losses of grid-connected photovoltaic inverters and has strong resonance resistance and robustness.

Crack initiation and evolution in glass/epoxy laminates under two-stage block loadings

In this work, the transverse crack initiation, propagation, and the crack density evolution in cross-ply laminates are analysed under two-stage block loadings. A theoretical formulation for the cracking probability under variable amplitude blocks is obtained based on the linear damage accumulation rule, often adopted in crack density prediction models from the literature. The comparison between the experimental results and the predictions for the cracking probability and the crack density evolution validate, from the phenomenological point of view, the adequacy of the linear damage accumulation rule for crack initiation under block loadings. Investigations of the damage evolution at the micro-scale are also presented, providing a mechanistic support to this approach.

Density functional study of electronic, elastic and optical properties of [formula omitted] (x=0, 0.25, 0.50, 0.75, 1) alloys

In this study, the structural, electronic, elastic and optical properties of GaAs, GaN and their ternary alloys GaAs1−xNx (x = 0.25, 0.50, 0.75) are investigated within density functional theory utilizing WIEN2K package. The calculations are performed using the exchange-correlation energy functional from Wu-Cohen GGA for the structural and elastic properties and (mBJ –LDA) functional for the electronic and optical properties. The results show the calculated lattice constants as a function of x are in the best agreement with Vegard's linear rule. In the case of electronic properties, the electronic band structures are calculated and the results show GaAs1−xNx alloys are direct band gap semiconductors with a reduction in the band gap for N concentration x = 0.25 and x = 0.50. The results also show that the minimum band gap for the considered alloys occurs for N concentrations x = 0.25. Regarding the optical properties, the imaginary and real parts of dielectric function within the random phase approximation are investigated. The major points in the imaginary part of dielectric function are identified according to the electronic band structure calculations for each concentration. Furthermore, the elastic properties of considered alloys are investigated and the elastic constants, the bulk modulus, the shear modulus, the Young's modulus, the anisotropy factor and Poisson's ratio are calculated.

Evaluation of uncoupled ductile damage models for fracture prediction in incremental sheet metal forming

The formability limit in a typical incremental sheet forming (ISF) far exceeds the conventional estimate assuming necking failure. The material subjected to incremental forming fails by fracture. Although damage models have been used to correlate the failure in incremental forming, a detailed understanding of the failure mechanism spanning strain paths is not clear yet. In this work, three parts with varied shapes (hybrid five lobe, pyramid and variable wall angle conical frustum (VWACF)) were developed using ISF to cover a range of possible strain paths. The failure is predicted using established uncoupled phenomenological damage models. Damage models were calibrated for AA1050 aluminium sheet by the method of inverse approach using carefully designed tensile tests and FE simulations. Three different damage models were implemented as user subroutine in commercial software code, ABAQUS/Explicit and the results predicted were compared. The linear damage accumulation used to develop fracture locus under monotonic loading could not predict the failure limit in a benchmark single groove test. Therefore a non linear damage accumulation rule (NLDA) is implemented to simulate ISF. The parameters of the NLDA were calibrated from the single groove test. The fracture forming limits during ISF was established using circular grid analysis near the failure zone of the formed part. A good agreement can be found between the experimental observations and numerical predictions for fracture location and part height. It was observed that the overall predictive capability of Hosford Coulomb (HC) damage model is better among three damage models investigated for the given range of loading conditions. However all the three models under-predicted the experimental fracture strain measured in ISF. The possible explanation for the discrepancy is explored.

Machine Learning for Physicochemical Property Prediction of Complex Hydrocarbon Mixtures

Machine learning has proven effective for predicting properties of pure compounds from molecular structures, but properties of mixtures, in particular oil fractions, are rarely dealt with. At best, the bulk properties are estimated based on pure compound properties, linear mixing rules, and a reconstructed composition of the feedstock. As the detailed composition of such mixtures is rarely well determined and often approximated by lumps, the accuracy of the estimated bulk properties can be improved. In this work, we demonstrate for a naphtha case study our bulk property estimation method. First, a detailed PIONA composition is delumped into a molecule-level composition, and a machine learning-based approach is used to predict properties of those molecules, which are further combined in another deep neural network for the prediction of bulk properties. The latter machine learning models are trained on mixture properties using vectors that represent the mixture. The first vector is a linear combination of the molecular representation vectors and the representation of the molecular geometries that make up the mixture. The second vector applies linear mixing rules on boiling temperatures, critical temperatures, liquid densities, and vapor pressures that are predicted with machine learning. The last vector consists of a learned distillation curve. We show that an integrated machine learning approach that starts from the molecular structures in the mixture offers significant improvements in predicting mixture properties over existing approaches applied in industry and academia.

Optimization of Numerical Methods for Transforming UTM Plane Coordinates to Lambert Plane Coordinates

The rapid transformation from UTM (Universal Transverse Mecator) projection to Lambert projection helps to realize timely merging, inversion, and analysis of high-frequency partitioned remote sensing images. In this study, the transformation error and the efficiency of the linear rule approximation method, the improved linear rule approximation method, the hyperbolic transformation method, and the conformal transformation method were compared in transforming the coordinates of sample points on WGS84 (The World Geodetic System 1984)-UTM zonal projections to WGS84-Lambert projection coordinates. The effect of the grid aspect ratio on the coordinate transformation error of the conformal transformation method was examined. In addition, the conformal transformation method-based error spatial pattern of the sample points was analyzed. The results show that the conformal transformation method can better balance error and efficiency than other numerical methods. The error of the conformal transformation method is less affected by grid size. The maximum x-error is less than 0.36 m and the maximum y-error is less than 1.22 m when the grid size reaches 300 km × 300 km. The x- and y-error values decrease when square grids are used; namely, setting the grid aspect ratio close to 1 helps to weaken the effect of increasing grid area on the error. The dispersion of the error distribution and the maximum error of sample points both decrease relative to their minimum distance to the grid edge and stabilize at a minimum distance equal to 70 km. This study can support the rapid integration of massive remote sensing data over large areas.

Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective

In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this end, a solution scheme based on a blending of three popular robust optimization techniques is proposed. For disjoint bilinear optimization problems with a polyhedral feasible region and a general convex feasible region, we show that, under mild regularity conditions, the convex relaxations of the original bilinear formulation and its two-stage robust reformulation obtained from a reformulation-linearization-based technique and linear decision rules, respectively, are equivalent. For generic bilinear optimization problems, the convex relaxations from the reformulation-linearization-based technique are generally tighter than the one from linear decision rules. Numerical experiments on bimatrix games, synthetic disjoint bilinear problem instances, and convex maximization problems demonstrate the efficiency and effectiveness of the proposed solution scheme. Summary of Contribution: Computing solutions for disjoint bilinear optimization problems are of much interest in real-life applications, yet they are, in general, computationally intractable. This paper proposes a computationally tractable approximation as well as a convergent algorithm to the optimal values of such problems. Extensive computational experiments on (i) (constrained) bimatrix games, (ii) synthetic disjoint bilinear problems, and (iii) convex maximization problems are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

Control, cost, and confidence: Perseverance and procrastination in the face of failure

We study effort provision and the development of the belief that effort matters over time: a student is uncertain whether she has control over success through her effort or whether success is determined by her innate ability, which she also does not know. In each period, what she can learn about her control and her ability depends on the level of effort she exerts. The student's optimal effort policy in this two-dimensional bandit problem takes the form of a linear belief cutoff rule and typically features repeated switching of the effort level. Moreover, we define perseverance and procrastination as indices for the student's behavior over time and analyze how they are affected by control, cost, and confidence. Finally, we relate our results to findings in educational psychology and discuss policies to foster perseverance and to lower procrastination.

Fluid limits for shortest job first with aging

We investigate fluid scaling of single-server queues operating under a version of shortest job first (SJF) where the priority level undergoes aging. That is, a job’s priority level is initialized by its size and varies smoothly in time according to an ordinary differential equation. Linear and exponential aging rules are special cases of this model. This policy can be regarded as an interpolation between FIFO and SJF. We use the measure-valued Skorokhod map to characterize the fluid model and establish convergence under fluid scale. We treat in detail examples of linear and exponential aging rules and provide a performance criterion based on our main result.

Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization

In “Dual Approach for Two-Stage Robust Nonlinear Optimization,” de Ruiter, Zhen, and den Hertog study adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables. They reformulate the original adjustable robust nonlinear problem with a polyhedral uncertainty set into an equivalent adjustable robust linear problem, for which all existing approaches for adjustable robust linear problems can be used. The reformulation is obtained by first dualizing over the adjustable variables and then over the uncertain parameters. The polyhedral structure of the uncertainty set then appears in the linear constraints of the dualized problem, and the nonlinear functions of the adjustable variables in the original problem appear in the uncertainty set of the dualized problem. The authors show how to recover linear decision rules to the original primal problem and how to generate bounds on its optimal objective value.

Türkiye’de Para Politikasının Maliyet İtişli Şoklara Tepkisi: Rüzgâra Karşı Bir Duruş mu?

In Turkey, monetary policy responds to cost shocks rather than the inflation gap and output gap. To clarify this policy, we estimate the linear and non-linear Taylor rule using the Thresold GMM for 2006:01-2020:07. The linear model estimates that the policy rate responds significantly to the inflation gap and the real effective exchange rate. The non-linear model captures that monetary policy differs in regimes where imported goods and input prices are set as high and low. In a high price regime, monetary policy also reacts to cost-push shocks. The response of monetary policy to the exchange rate implicitly leads to "a leaning against the wind".

Distributionally robust optimization for fire station location under uncertainties

Emergency fire service (EFS) systems provide rescue operations for emergencies and accidents. If properly designed, they can decrease property loss and mortality. This paper proposes a distributionally robust model (DRM) for optimizing the location of fire stations, the number of fire trucks, and demand assignment for long term planning in an EFS system. This is achieved by minimizing the worst-case expected total cost, including fire station construction cost, purchase cost for fire trucks, transportation cost, and penalty cost for not providing adequate service. The ambiguity in demands and travel durations distributions are captured through moment information and mean absolute deviation. A cutting plane method is used to solve the problem. Due to fact that it is computationally intensive for larger problems, two approximate methods are introduced; one that uses linear decision rules (LDRs), and another that adopts three-point approximations of the distributions. The results show that the heuristic method is especially useful for solving large instances of DRM. Extensive numerical experiments are conducted to analyze the model’s performance with respect to different parameters. Finally, data obtained from Hefei (China) demonstrates the practical applicability and value of the model in designing an EFS system in a large metropolitan setting.

Dynamic optimization with side information

We develop a tractable and flexible data-driven approach for incorporating side information into multi-stage stochastic programming. The proposed framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration result for a class of supervised machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information. We also describe a general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of multi-stage and single-stage examples in inventory management, finance, and shipment planning, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.

A modified fatigue damage model considering loading sequence effect

A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect.

A model for balance responsible distribution systems with energy storage to achieve coordinated load shifting and uncertainty mitigation

An operation model is established in this paper to fully utilize the flexibility of energy storage to reduce the operation costs of balance responsible distribution systems, which are responsible for their energy balance. Depending on whether uncertainties in outputs of renewable energy sources are involved, energy storage operation is classified into load shifting and uncertainty mitigation. Such classification enables separate analysis of the two types of energy storage operation and also facilitates their coordination to achieve optimal overall costs. To handle the computational difficulty that is brought by temporal sequences of uncertainties and track uncertainties that are mitigated by energy storage, linear decision rules are adopted to model the process of uncertainty mitigation. As a flexible device, energy storage is distinct because using its flexibility influences its state of charge and eliminating such influence is essential for recovering its flexibility. Based on these features of energy storage, keys of using energy storage to mitigate uncertainties in balance responsible distribution systems are revealed, which are aggregating uncertainties from different times and thus letting them offset each other. Through case studies, it is shown that uncertainties are better mitigated when they are better aggregated, and the aggregation level of uncertainties is limited by energy storage parameters including its maximum charging and discharging power and its capacity. Besides, it is demonstrated that the cooperation between the two kinds of energy storage operation, i.e., load shifting and uncertainty mitigation, achieves better outcomes because of more efficient use of energy storage flexibility in some cases, but it is also possible that they compete for the limited flexibility of energy storage and thus need to be coordinated in other cases.

The Cross-Scale Life Prediction for the High-Speed Train Gearbox Shell Based on the Three-Interval Method

The gearbox shell is a key component of class A of high-speed trains. In engineering applications, the fatigue life prediction of the gearbox shell is a critical issue to be addressed. It is not feasible to obtain fatigue life results for the gearbox shell experimentally because of its long design life, lack of actual failure data, complex structure, high test cost, and material dispersion. Therefore, the cross-scale method was introduced to accurately predict the fatigue life of the gearbox shell. In this study, the entire gearbox shell is divided into two scales of “material structure.” Firstly, the S-N curve is plotted within the material layer, based on the data from the rotating bending fatigue test. Secondly, the finite element model of the gearbox shell is established within the structural layer via the simulation platform. The characteristics and random vibration of the established model are analyzed and presented. Additionally, the first ten-order frequency of modal analysis and power spectral density responses of the gearbox are obtained. The fatigue life of the gearbox shell and the safe running distance of the train are calculated by using the three-interval method and the linear cumulative damage rule, respectively, by combining the fatigue analysis from the material layer with the simulation analysis from the structure layer. Finally, to illustrate the application of the proposed method, a group of small-scale test examples is provided. The proposed method can be used in fatigue life prediction more effectively than the single finite element simulation method.

Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks.

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.

Distributionally Robust Joint Chance-Constrained Dispatch for Electricity–Gas–Heat Integrated Energy System Considering Wind Uncertainty

With the increasing penetration of wind power, the uncertainty associated with it brings more challenges to the operation of the integrated energy system (IES), especially the power subsystem. However, the typical strategies to deal with wind power uncertainty have poor performance in balancing economy and robustness. Therefore, this paper proposes a distributionally robust joint chance-constrained dispatch (DR-JCCD) model to coordinate the economy and robustness of the IES with uncertain wind power. The optimization dispatch model is formulated as a two-stage problem to minimize both the day-ahead and the real-time operation costs. Moreover, the ambiguity set is generated using Wasserstein distance, and the joint chance constraints are used to ensure that the safety constraints (e.g., ramping limit and transmission limit) can be satisfied jointly under the worst-case probability distribution of wind power. The model is remodeled as a mixed-integer tractable programming issue, which can be solved efficiently by ready-made solvers using linear decision rules and linearization methods. Case studies on an electricity–gas–heat regional integrated system, which includes a modified IEEE 24-bus system, 20 natural gas-nodes, and 6 heat-node system, are investigated for verification. Numerical simulation results demonstrate that the proposed DR-JCCD approach effectively coordinates the economy and robustness of IES and can offer operators a reasonable energy management scheme with an acceptable risk level.

Convex Maximization via Adjustable Robust Optimization

Maximizing a convex function over convex constraints is an NP-hard problem in general. We prove that such a problem can be reformulated as an adjustable robust optimization (ARO) problem in which each adjustable variable corresponds to a unique constraint of the original problem. We use ARO techniques to obtain approximate solutions to the convex maximization problem. In order to demonstrate the complete approximation scheme, we distinguish the cases in which we have just one nonlinear constraint and multiple linear constraints. Concerning the first case, we give three examples in which one can analytically eliminate the adjustable variable and approximately solve the resulting static robust optimization problem efficiently. More specifically, we show that the norm constrained log-sum-exp (geometric) maximization problem can be approximated by (convex) exponential cone optimization techniques. Concerning the second case of multiple linear constraints, the equivalent ARO problem can be represented as an adjustable robust linear optimization problem. Using linear decision rules then returns a safe approximation of the constraints. The resulting problem is a convex optimization problem, and solving this problem gives an upper bound on the global optimum value of the original problem. By using the optimal linear decision rule, we obtain a lower bound solution as well. We derive the approximation problems explicitly for quadratic maximization, geometric maximization, and sum-of-max-linear-terms maximization problems with multiple linear constraints. Numerical experiments show that, contrary to the state-of-the-art solvers, we can approximate large-scale problems swiftly with tight bounds. In several cases, we have equal upper and lower bounds, which concludes that we have global optimality guarantees in these cases.Summary of Contribution: Maximizing a convex function over a convex set is a hard optimization problem. We reformulate this problem as an optimization problem under uncertainty, which allows us to transfer the hardness of this problem from its nonconvexity to the uncertainty of the new problem. The equivalent uncertain optimization problem can be relaxed tightly by using adjustable robust optimization techniques. In addition to building a new bridge between convex maximization and robust optimization, this approach also gives us strong algorithms that improve the state-of-the-art optimization solvers both in solution time and quality for various convex maximization problems.

Enhancing mechanical properties of metallic materials by architecting gradient structures

Here, two types of gradient structures (GS), i.e. gradient dislocation structure (GDS) and gradient grain structure (GGS) are successfully constructed . Results indicate that the relationship between the strength and ductility of the samples with GDS and GGS is referred to as an inverse linear rule, which is in stark contrast to and superior to the banana-shaped strength-ductility trade-off dilemma in monolithic materials. In low-strength (σy ∼400–550 MPa) range, plausible strength-ductility-toughness synergies can be achieved by both the GDS and GGS, however, in high-strength (σy ∼550–750 MPa) range, much better strength-ductility-toughness combinations are presented by the GGS than those by the GDS. For the GGS, the formation of strong 〈110〉 fibre texture in the tensile direction is beneficial for enhancing the high strength-ductility-toughness synergy.