Linear Rule Research Articles

An approach for fatigue damage estimation under broadband non-Gaussian random loadings based on the Johnson transformation model

Estimating fatigue damage of marine structures using spectral methods under broadband random loadings is a complex and challenging task. In the presence of non-Gaussian loading, the spectral method typically employs the Hermite polynomial model (HPM) to address the non-Gaussianity. However, the applicability of HPM is limited in certain non-Gaussian cases due to the requirement of monotonicity. This paper adopts the Johnson transformation model (JTM) instead of HPM and integrates it with the non-Gaussian TB method (Ding and Chen, 2015) to overcome the constraints in broadband non-Gaussian fatigue estimation. To verify the performance of the new approach, this paper analyses the transformation accuracy of the two models. Additionally, taking the time-domain fatigue damage obtained by the rainflow counting method and the linear damage accumulation rule as a benchmark, this paper compares the fatigue damage estimates obtained from the spectral methods. The comparative assessment encompasses various spectra, S-N curves, and non-Gaussian characteristics. The results indicate the performance of JTM within the non-Gaussian TB method is comparable to HPM in most cases and even surpasses it in hardening non-Gaussian cases. Given the broader applicability of JTM across ranges of skewness and kurtosis, it emerges a superior option for the non-Gaussian TB method in estimating broadband non-Gaussian fatigue damage. Furthermore, the limitations of the proposed approach are discussed.

Time-dependent reliability analysis for structures under multilevel loads based on fatigue damage theory

This paper proposes an efficient method to evaluate the time-dependent fatigue reliability of structures under complex multilevel loads using a finite set of fatigue test data obtained under single-level loading conditions. The method preserves the simplicity of linear damage accumulation theory while considering the interactions among multiple load levels and the influence of load sequence on reliability. Leveraging the linear damage rule, a cumulative damage probability model was established under single-level constant amplitude loading. This model incorporates a fatigue life degradation function to characterize the cumulative damage effect of load cycles and corrects the fatigue reliability curve under single-level constant amplitude loading. By employing the principle of fatigue damage equivalence, the method determines the damage equivalence at the load switching point using the damage curve method, enabling the conversion of equivalent reliability under multilevel loads. The proposed method was validated by combining the test data obtained under three working conditions, including two-level loads loading, load blocks loading, and changing loads loading. The results demonstrate that the proposed method can accurately and efficiently evaluate the time-dependent fatigue reliability under different types of multilevel loads, using only a limited set of fatigue life data under single constant amplitude loads.

Strain-Based damage model for ductile tearing simulation under combined tensile and shear modes

This paper proposes a strain-based damage model to simulate ductile tearing under combined tensile and shear modes. For tensile mode, the multiaxial fracture strain model depending only on the stress triaxiality is used, determined by analysing smooth bar tensile test and fracture toughness test data. For shear mode, a simple constant fracture strain model is used, determined by analysing smooth bar torsion test and torsion fracture test using a deep surface cracked cylinder specimen. The proposed damage model is applied to simulate circumferential surface cracked pipe made of SUS 304 under combined bending and torsion. Comparison with full-scale surface cracked pipe test data suggests that the use of the combined tensile and shear damage model with the linear interaction rule gives good and conservative prediction results.

Connection strength analysis and prediction of external swaging based on tube deformation measurement

Fittings have extensive use in the aerospace, automotive, and other industries as they serve as sealing and connecting components for tube systems. External Swaging (ES) forming creates a permanent joint through plastic deformation of the metal. This technique is not dependent on the tube's wall thickness and offers benefits such as high-pressure resistance and effective sealing. Using the forming process of a 10 mm Ti-3Al-2.5 V tube with an adapted 21-6-9 fitting as an illustration, a three-dimensional finite element model for the entire assembly was developed. The model consists of the tube, fitting, elastic clamp, and crimping tool. The formation mechanism and joint strength of external swaging are analyzed by numerical simulation and experimental testing. The results show that during the extrusion process, the tangential contact between the extrusion tool and the elastic clamps converts external radial loads into circumferential loads, resulting in circumferential strains in the tube. Circumferential strain creates an arched sealing area between the tube and fitting contact surfaces, providing sealing and joint strength. The joint strength of 10.60 kN was determined through finite element simulation. The load required for forming is determined by analysis to be 80.13 kN. and the relationship between squeeze load, crimp volume and joint strength is clarified. The study revealed that the height of the arch area aligns with the connection strength's change rule concerning extrusion load, fitting the two found that when the external extrusion load changes, the two are linear rule of changing. Based on this, a method is suggested for forecasting the strength of a joint by measuring the height of the arch in the tube after forming.

Target-oriented robust satisficing models for the single machine scheduling problems with release time

In this paper, we investigate single machine scheduling problems with release times and random processing times, where the release times can be either deterministic or random. The objective is to determine a scheduling sequence that exhibits strong out-of-sample performance. To achieve this, we employ target-oriented robust satisficing models to obtain the scheduling sequence. For the scheduling problem with deterministic release times, we derive an equivalent mixed-integer linear program and an approximate reformulation to address cases involving a large number of jobs. For the scheduling problem with random release times, we first demonstrate the challenges associated with providing an equivalent reformulation. To overcome this intractability, we propose an approximate reformulation based on the linear decision rule. Numerical experiments are conducted to demonstrate the superiority of our solutions through comparisons with several benchmarks. Furthermore, the numerical results demonstrate that a relatively higher target should be chosen if the worst-case performance is valued, otherwise, the decision-maker should set a relatively lower target to obtain better average performance.

Multistage adaptive distributionally robust optimization for the medical supplies distribution problem with uncertain demand in humanitarian aid

Production, inventory, distribution, and dispensing of relief resources are critical operational functions in humanitarian aid. To design an efficient humanitarian relief network, it is beneficial to study these operational functions in an integrated way. Accounting for the demand uncertainty of medical supplies, we propose a multistage adaptive distributionally robust model for the medical supplies distribution network design that considers simultaneously the issues of production, inventory, distribution and dispensing of medical resources, as well as the life-loss due to the delays in treatment. The objective is to dynamically match the supply and demand of medical supplies so as to minimize the total cost consisting of the production cost, holding cost, dispensing cost, and life-loss cost related to the unmet demand. We also introduce a safety-stock and production capacity model to efficiently predetermine the initial supply of medical supplies and maximum available production abilities under the given demand information. To obtain tractable formulations, we approximate the developed models using an enhanced linear decision rule (ELDR) and a simplified ELDR (SELDR), respectively. Using a set of real-world COVID-19 data, we show that (i) both the ELDR and SELDR can yield feasible solutions extremely close to the optimal solution of the multistage adaptive distributionally robust model, whereas the SELDR is about one order of magnitude faster than the ELDR; and (ii) accounting for the safety-stock and production capacity model yields significant improvements of the obtained solution, which can also inform the decision-maker about at least how many initial supply of vaccines and the maximum available production abilities should be set to counter the risk of demand uncertainty. We also analyze the impact of some model parameters to gain managerial implications.

Distributionally Robust Optimization of Photovoltaic Power With Lifted Linear Decision Rule for Distribution System Voltage Regulation

Distributionally Robust Optimization of Photovoltaic Power With Lifted Linear Decision Rule for Distribution System Voltage Regulation

Joint flexibility-risk managed distributed energy trading considering network constraints and uncertainty

This paper addresses the operational challenges in distribution systems caused by the integration of fluctuating renewable energy sources and rising peak loads from widespread electrification. We propose a new distributed energy coordination framework that facilitates seamless interoperation between peer-to-peer (P2P) energy trading and the operation of distributed flexibility resources. This framework ensures network constraints are respected while promoting Energy Trading Consistency (ETC). Our approach utilizes a two-stage dynamic energy and flexibility sharing mechanism. It achieves energy efficiency through demand-management and P2P energy trading in the day-ahead (DA) stage, followed by adjustments of flexible resources and flexibility sharing through a receding-horizon feedback mechanism inspired by model predictive control (MPC) in the real-time (RT) stage. High-risk scenarios and computational overhead are managed by employing conditional value-at-risk (CVaR) measures, as well as approximation of constraints through dual robust reformulation and linear decision rules. To uphold the autonomy and privacy of prosumers, we propose distributed algorithms based on the fast consensus alternating direction method of multipliers (ADMM). Numerical results demonstrate that our framework achieves a 20% reduction in social cost while providing a coherent and interactive P2P energy trading environment, facilitating reliable network operation under high penetration of renewable energy sources without third-party intervention.

Learning Fair Policies for Multi-Stage Selection Problems from Observational Data

We consider the problem of learning fair policies for multi-stage selection problems from observational data. This problem arises in several high-stakes domains such as company hiring, loan approval, or bail decisions where outcomes (e.g., career success, loan repayment, recidivism) are only observed for those selected. We propose a multi-stage framework that can be augmented with various fairness constraints, such as demographic parity or equal opportunity. This problem is a highly intractable infinite chance-constrained program involving the unknown joint distribution of covariates and outcomes. Motivated by the potential impact of selection decisions on people’s lives and livelihoods, we propose to focus on interpretable linear selection rules. Leveraging tools from causal inference and sample average approximation, we obtain an asymptotically consistent solution to this selection problem by solving a mixed binary conic optimization problem, which can be solved using standard off-the-shelf solvers. We conduct extensive computational experiments on a variety of datasets adapted from the UCI repository on which we show that our proposed approaches can achieve an 11.6% improvement in precision and a 38% reduction in the measure of unfairness compared to the existing selection policy.

Estimating the optimal duration of random loading as part of machine part durability research

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

Neural network based fatigue lifetime prediction of metals subjected to block loading

Fatigue lifetime predictions for variable amplitude loading are primarily based on the linear damage accumulation rule of Palmgren–Miner, which does not account for load sequence effects. Various nonlinear models have been developed, but their generalization capability is limited. Although neural network models have been used for prediction of the lifetime of metals subjected to constant amplitude loading, random loading and two-level block loading sequences before, they have never been used for multi-level block loading to the authors knowledge. The primary goal of this study is the development of neural network models for fatigue life estimation of metals subjected to block loading. To achieve this, a sufficient amount of qualitative data is required. Therefore a large number of rotating bending fatigue experiments with constant amplitude and block loading sequences are carried out. This new data is combined with data gathered from literature, leading to the most extensive open-access collection of variable amplitude fatigue data published to date. Neural network models are trained with the developed dataset and compared to four cumulative damage models including the linear Palmgren–Miner rule and three non-linear models. It is concluded that the neural network model for multi-level block loading outperforms all of the considered analytical models.

Optimizing bike rebalancing strategies in free-floating bike-sharing systems: An enhanced distributionally robust approach

Bike-sharing systems are important components of urban transportation systems that facilitate short-distance travel. In recent years, free-floating bike-sharing systems have become popular. However, a major problem in such systems is the increasing number of idle bikes due to their spatial dispersion, which leads to a loss of demand and difficulty in bike rebalancing. To overcome these drawbacks, operators reserve parking areas, and laborers are incorporated into the bike rebalancing operation. We propose a novel dynamic bike rebalancing strategy based on trucks and laborers for free-floating bike-sharing systems. This strategy combines bike collection by laborers and bike transportation by trucks for rebalancing operations. In addition, we consider broken bike detection by laborers and user dynamics in two extension models. Because of the demand uncertainty in bike-sharing systems, we employ an enhanced distributionally robust optimization (EDRO) approach to protect against uncertainty. A target-level constraint is added to the general distributionally robust optimization (DRO) model to further improve the out-of-sample performance. An adaptive robust strategy is also employed to avoid overly conservative solutions. Furthermore, a linear decision rule is adopted to reformulate the EDRO model into a mixed-integer programming model, which guarantees computational tractability. The results of numerical experiments show that the EDRO model outperforms other benchmark models on a series of measures. Moreover, we verify the value of laborers in dynamic rebalancing operations and explore the effect of different bike supply levels and several other parameters on the value of laborers. We also test how the target-level parameter affects the model performance.

Creep-fatigue life estimation of circumferential welds in thermal high energy piping systems

ABSTRACT To prevent accidents in high energy piping systems of thermal power plants, it may be important to accurately estimate the creep-fatigue life of circumferential piping welds. The main failure mode in the damage cases was Type IV damage which was creep-dominated damage occured at the fine-grained HAZ(FGHAZ). The damege mode is considered to change from longitudinal failure at the base metal to circumferential Type IV failure when the ratio of axial stress to hoop stress exceeds a certain value. The allowable thermal expansion stress in the design, the stress relaxation property of the material, and the creep rupture strength of welded joints are investigated, as factors affecting creep damage of circumferential piping welds. Fundamental creep-fatigue tests were perfomed using cross-weld specimens and their lives were estimated by a linear damage summation rule. In the life estimation, it seems necessary to consider elastic follow-up phenomena where strain transfers to the HAZ.

A sample robust optimal bidding model for a virtual power plant

In many energy markets, the trade amount of electricity must be committed to before the actual supply. This study explores one consecutive operational challenge for a virtual power plant—the optimal bidding for highly uncertain distributed energy resources in a day-ahead electricity market. The optimal bidding problem is formulated as a scenario-based multi-stage stochastic optimization model. However, the scenario-tree approach raises two consequent issues—scenario overfitting and massive computation cost. This study addresses the issues by deploying a sample robust optimization approach with linear decision rules. A tractable robust counterpart is derived from the model where the uncertainty appears in a nonlinear objective and constraints. By applying the decision rules to the balancing policy, the original model can be reduced to a two-stage stochastic mixed-integer programming model and then efficiently solved by adopting a dual decomposition method combined with heuristics. Based on real-world business data, a numerical experiment is conducted with several benchmark models. The results verify the superior performance of our proposed approach based on increased out-of-sample profits and decreased overestimation of in-sample profits.

Mixed-Material Feedstocks for Cold Spray Additive Manufacturing of Metal–Polymer Composites

High-performance polymers such as poly(ether ether ketone) (PEEK) are appealing as composite components for a wide variety of industrial and medical applications due to their excellent thermomechanical properties. However, conventional PEEK metallization methods can often lead to poor quality control, low deposition rate, and high cost. Cold spray is a promising potential alternative to produce polymer–metal composites rapidly and inexpensively due to its relatively mild operating conditions and high throughput. In this study, we investigated the deposition characteristics of metal–polymer composite feedstock, composed of PEEK powder and copper flake in varying ratios, onto a PEEK substrate. Copper-PEEK powder blends were prepared by both hand-mixing and cryogenic milling (cryomilling), which predominantly creates composite particles with micron-scale copper domains coating PEEK particle surfaces. This process non-monotonically affects the relative dominance and length scales of the multiple contributing deposition mechanisms present in mixed-material cold spray. In low-pressure cold spray, deposits showed significant changes in deposition efficiency and composition as a result of milling, with improvements in these characteristics most dramatic at lower Cu fractions. Deposits of a cryomilled blend of nominally 30 vol.% copper in PEEK exhibited minimal porosity under scanning electron microscopy, complete retention of powder composition, and the highest deposition efficiency among all samples tested. Notably, neither neat PEEK nor neat Cu meaningfully deposited at the same mild conditions as this 30 vol.% Cu blend, indicating a synergistic departure from linear mixing rules driven by the relative balance of local deposition interactions (e.g., hard–soft, soft–soft, etc.). Intentional powder and process design toward optimizing this balance may facilitate cold spray metallization applications.

Robust CARA Optimization

Decision making under uncertainty involves both ambiguity and risk. In “Robust CARA Optimization,” Chen and Sim have developed innovative optimization models designed for ambiguity-averse decision makers whose risk preference is consistent with constant absolute risk aversion (CARA). The research delves into maximizing the worst-case expected exponential utility amid uncertainties from independent factors with ambiguous marginals. To enhance computational feasibility, the authors developed a series of approximations: starting with tractable concave functions in affinely perturbed cases, advancing to concave piecewise affinely perturbed scenarios, and culminating in novel multi-deflected linear decision rules for adaptive optimization. This comprehensive framework extends to a multi-period consumption model, ultimately forming an exponential conic optimization problem efficiently solvable with existing solvers. Practical applications demonstrated in project and multiperiod inventory management highlight the models’ potential to surpass existing stochastic optimization methods, especially under high risk aversion.

Two-stage chance-constrained programming based on Gaussian mixture model and piecewise linear decision rule for refinery optimization

The two-stage chance-constrained program (CCP) is studied for a refinery optimization problem. In stage-I, the refinery decision-makers determine the type and quantity of crude oil procurement under operational uncertainties to maximize the expected profit under all possibilities. In stage-II, process unit flowrates are adjusted based on the realized uncertainties and available crude oil, while introducing probabilistic constraints to manage the off-spec risk. To solve such a two-stage optimization problem, we propose a novel approach using Gaussian mixture model (GMM) to characterize uncertainties, and piecewise linear decision rule for stage-II operations. Comparing to the conventional scenario-based mixed-integer linear program (MILP), our new approach offers three advantages. First, it leverages a well-developed global optimization scheme for joint CCP to avoid scenario generation and potential bias. Second, the data-driven GMM enables CCP to handle uncertainties with general distributions. Third, the stage-II variables are parameterized via Gaussian component induced piecewise linear decision rule to strike an excellent trade-off between optimality and computational time. A simplified refinery plant, consisting of distillation, cracker, reformer, isomerization, and desulfurization units, is used as a test bed to demonstrate the superiority of the proposed optimization method in solution time, probabilistic feasibility, and optimality over the large-scale scenario-based MILP.

Hook's law scaled broken-bond model for surface energy: From metals to ceramics

Innovative surfaces via lattice engineering are crucial challenges and critical to enhance the mechanical and functional properties of advanced materials. Here, a universal linear scaling rule in terms of key property parameters (KPPs) is proposed to estimate the modifications of local lattice strain (LLS) caused by the surface, in which the bulk modulus (B), the B/G ratio, and the bond energy are utilized to describe the KPPs of the BCC and FCC, the isotropic HCP, and the polarized A2B2O7-type Pyrochlore, individually. The modified broken-bond model by the Hook's law is addressed to predict the elastic-energy-corrected surface energy efficiently and precisely, which is capable to deal with the complex of geometry, chemistry, charge states of clean surface and are verified and validated in 28 metals and ceramics. While the LLS of metals is caused by the improved bond length, the ceramics one is yielded by the reduced one of polarized surface.

ReLiCADA: Reservoir Computing Using Linear Cellular Automata design algorithm

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models’ hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude.

Forecasting Post-Epidemic Air Passenger Flow Among Hub Cities in China Based on PLS and GA-SVR Model

For stakeholders and companies involved in civil aviation to plan and make wise decisions, accurate estimates of air passenger flow are necessary. The conclusions drawn from this model serve as an invaluable resource for pertinent choices. The top hub cities in mainland China's air travel network are predicted using a variable weight combination model that combines PLS and GA-SVR. According to the test results, the model developed in this study improves prediction accuracy. This demonstrates how well detailed information about social and economic development can be gleaned from linear development patterns and nonlinear fluctuation rules. Predictions can be made with more accuracy and a better fit as a result. Over the next five years, it is predicted that over 300 million passengers will fly between the top hub cities in mainland China, an increase of 6.51% per year. The growth in passenger traffic varies significantly between different routes. The routes from Beijing to Shanghai and Shanghai to Shenzhen saw the most travellers, while the Beijing-Chengdu route saw the fastest growth in traveller numbers. The study's findings provide useful advice for civil aviation businesses and people involved in their decision-making, fostering growth in the sector during the post-pandemic period.