Piecewise Linear Functions Research Articles

Augmented multi-agent algorithm utilizing intelligent search range detection heuristic to solve assembly line sequencing problem: A case study in the truck industry

Car sequencing is a widely adopted approach to implicitly enhance the short-term balancing of mixed-model assembly lines in practical applications. In this research, we investigate this problem in the context of a real-world case taken from a truck final assembly line. Our study considers cross-ratio constraints that address limitations related to dependent features of the products. Additionally, to manage the distribution of violation errors in cases where predefined congestion level thresholds (soft rules) exist, we propose a piecewise linear penalty function. To tackle these considerations, we formulate a mathematical programming model aimed at minimizing the total weighted penalty incurred from violating both independent and dependent sequencing rules. As the problem falls into the NP-hard category, we develop a multi-start parallel local search algorithm based on multi-agent approach to efficiently solve it. The algorithm is augmented by incorporating a self-adaptive diversification mechanism and a novel intelligent search range detection heuristic. The proposed heuristic enables the searching agents to intelligently explore the solution space rather than relying on a purely random search. The numerical experiments are conducted using 30 real-world instances from three truck assembly lines to validate the quality of the proposed algorithm. The comparison of the results indicates that our algorithm outperforms state-of-the-art algorithms. Furthermore, computational experiments demonstrate the effectiveness of each proposed mechanism in enhancing the algorithm's performance.

Likelihood-based inference for semi-parametric transformation cure models with interval censored data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

Semi-analytical solutions for land subsidence due to groundwater withdrawal

This paper introduces novel semi-analytical models tailored for estimating land subsidence resulting from groundwater extraction in confined aquifers. These models offer high scalability, allowing them to be applied to various well configurations and pumping schedules. Their development involves the numerical integration of two key analytical solutions: the “nucleus of strain” (NoS) (Mindlin and Chen, 1950), which represents a localised zone within the aquifer where a unit change in pore pressure leads to deformation and subsequent surface displacement, and the classic Theis equation (Theis, 1935) for the pore pressure changes induced by a constant-rate well pumping from a laterally unbounded aquifer. These integrations yield surface displacement components, both horizontal and vertical, expressed as functions of two dimensionless spatial–temporal variables, which encompass aquifer depth, thickness, well placement, pumping schedules, and critical hydro-geomechanical parameters like hydraulic conductivity, porosity, vertical compressibility, and water compressibility. Proposed are two distinct modelling approaches: one employing a lookup table (LT) derived from numerical integration results, and the other providing direct closed-form surface displacement solutions by fitting LT data with “hinge models”, which use piecewise-linear functions linked by sigmoidal curves for computational efficiency. In both cases, surface displacement components are estimated by plugging in the dimensionless variables. Conditions of variable pumping from multiple wells can be addressed by applying superposition of solutions. In essence, these semi-analytical models offer swift computational capabilities for understanding and forecasting land subsidence dynamics. Their scalability makes them adaptable to a wide array of well configurations and scheduling scenarios, rendering them valuable for numerous applications. They are particularly significant for providing preliminary estimates of the impacts of groundwater development, conducting “what-if” tests, and performing sensitivity analyses to identify key factors affecting land subsidence risk. This underscores the importance of these models in sustainable groundwater resource management and in mitigating land subsidence and its associated consequences.

The role of posted speed limit on pedestrian and bicycle injury severities: An investigation into systematic and unobserved heterogeneities

The posted speed limit, as a proxy of actual speed, is one of the most fundamental predictors of active travelers’ (pedestrian and bicyclist) injury outcomes when involved in crashes with motor vehicles. Although earlier studies predominantly considered posted speed limit as an exogenous variable and provided highly insightful findings, majorities of them assume the effects of active traveler behavior to remain the same across different posted speed limits, which in turn neglect the heterogeneity in active traveler behaviors on high-speed roads vs. low-speed roads. This study proposes to develop a latent segmentation-based active traveler injury severity model to relax the homogeneity assumption of the posted speed limit by active traveler behavior. Specifically, this study proposes to estimate a latent segmentation-based correlated random parameters generalized ordered logit model to examine active travel injury severity mechanisms. The proposed model accommodates systematic heterogeneity in the effects of posted speed limit, crash year and active traveler group by using a piecewise linear function in injury severity component of the latent segment model. The model is demonstrated by using active traveler crash data from Queensland, Australia, for the years 2015 through 2019. To demonstrate the implications of the estimated models, a number of hypothetical scenario analyses are performed with a specific focus on active traveler behavior and reduction in posted speed limits. The outcomes from the hypothetical scenario analysis highlighted that a 76 % (73 %) reduction in active traveler fatalities can be achieved by converting 50–60 km/hr roadways to 10–40 km/hr roadways in the urban areas (rural areas) of Queensland. The outcomes of the study will allow us to identify effective speed management strategies while targeting those with high-risk behavior.

Efficient Sleep Stage Identification Using Piecewise Linear EEG Signal Reduction: A Novel Algorithm for Sleep Disorder Diagnosis.

Sleep is a vital physiological process for human health, and accurately detecting various sleep states is crucial for diagnosing sleep disorders. This study presents a novel algorithm for identifying sleep stages using EEG signals, which is more efficient and accurate than the state-of-the-art methods. The key innovation lies in employing a piecewise linear data reduction technique called the Halfwave method in the time domain. This method simplifies EEG signals into a piecewise linear form with reduced complexity while preserving sleep stage characteristics. Then, a features vector with six statistical features is built using parameters obtained from the reduced piecewise linear function. We used the MIT-BIH Polysomnographic Database to test our proposed method, which includes more than 80 h of long data from different biomedical signals with six main sleep classes. We used different classifiers and found that the K-Nearest Neighbor classifier performs better in our proposed method. According to experimental findings, the average sensitivity, specificity, and accuracy of the proposed algorithm on the Polysomnographic Database considering eight records is estimated as 94.82%, 96.65%, and 95.73%, respectively. Furthermore, the algorithm shows promise in its computational efficiency, making it suitable for real-time applications such as sleep monitoring devices. Its robust performance across various sleep classes suggests its potential for widespread clinical adoption, making significant advances in the knowledge, detection, and management of sleep problems.

Divisors and curves on logarithmic mapping spaces

We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.

A contact-based constitutive model for the numerical analysis of masonry structures using the distinct element method

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm.

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data.

Overcoming mechanistic limitations of process-based phenological models: A data clustering method for large-scale applications

Process-based phenological models use thermal requirement (TR) defined by planting date, temperature and photoperiod to predict crop developmental stages. The TR value for a specific developmental stage for a given variety is often presumed to be constant regardless of environmental conditions. We calibrated and compared 12 phenological models using 27-year of observation data of one unique rice (Oryza sativa L.) variety ('Shanyou63') from 46 sites in southern China. Our findings indicated that shifts in environmental conditions significantly affected TR values, e.g., standard deviations of TR at physiological maturation ranged from 83 to 167 °C d. Clustering sites together minimized environmental heterogeneity, and thus minimized the differences in TR for different phenological stages. When the increased from 1 to 24, simulation errors for the 12 models showed a significant decrease across all developmental stages, from 1.8 to 1.4 days for tillering, from 5.3 to 3.7 days for jointing, from 5.6 to 3.9 days for booting, from 4.7 to 3.3 days for heading, and from 6.6 to 3.7 days for physiological maturation. Furthermore, our findings indicate that models featuring a three-segment piecewise linear temperature response function provide a more precise prediction. In contrast, models incorporating a Beta temperature response function have not performed well. This difference is attributed to different mechanisms used to describe the response of crop development rate to temperature, particularly at non-optimum temperatures. The impact of the photoperiod response function on prediction accuracy became significant with the expansion of scale. Our results demonstrate that clustering method effectively compensates for the lack of crop adaptation processes in common phenological models, leading to significantly improved phenological prediction accuracy in regions with environmental diversity.

Anomalous diffusion in external-force-affected deterministic systems.

This study investigates the impact of external forces on the movement of particles, specifically focusing on a type of box piecewise linear map that generates normal diffusion akin to Brownian motion. Through numerical methods, the research delves into the effects of two distinct external forces: linear forces linked to the particle's current position and periodic sinusoidal forces related to time. The results uncover anomalous dynamical behavior characterized by nonlinear growth in the ensemble-averaged mean-squared displacement (EAMSD), aging, and ergodicity breaking. Notably, the diffusion pattern of particles under linear external forces resembles an Ehrenfest double urn model, with its asymptotic EAMSD coinciding with the Langevin equationunder linear potential. Meanwhile, particle movement influenced by periodic sinusoidal forces corresponds to an inhomogeneous Markov chain, with its external force amplitude and diffusion coefficient function exhibiting a "multipeak" fractal structure. The study also provides insights into the formation of this structure through the turnstiles dynamics.

Methods for Assessing the Layered Structure of the Geological Environment in the Drilling Process by Analyzing Recorded Phase Geoelectric Signals

Assessment of the current state of the near-surface part of the geological environment and understanding of its layered structure play an important role in various scientific and applied fields. The presented work is devoted to the application of phasometric modifications of geoelectric control methods to solve the problem of the detailed complex study of the underground layers of the environment in the process of drilling operations with the use of special equipment. These studies are based on the analysis of variations in phase parameters and characteristics of an artificially excited multiphase electric field to assess poorly distinguishable details and changes in the layered structure of the medium. The proposed method has increased accuracy, sensitivity and noise proofness of measurements, which allows for extracting detailed information about the heterogeneity, composition and stratification of underground geological formations not only in the zone where the drill makes contact with the medium, but also in the entire control zone. This paper considers practical mathematical models of phase images for basic scenarios of drill penetration between the layers of the near-surface part of the geological medium with different characteristics, obtained by means of approximation apparatus based on continuous piecewise linear functions, and also suggests the use of modern machine learning methods for intelligent analysis of its structure. Studying the phase shifts in electrical signals during drilling highlights their value for understanding the dynamics of soil response to the process. The observed signal changes during the drilling cycle reveal in detail the heterogeneity in soil structure and its response to changes caused by drilling. The stability of phase shifts at the last stages of the process indicates a quasi-equilibrium state. The results make a significant contribution to geotechnical science by offering an improved approach to monitoring a layered structure without the need for deep drilling.

Weight bound constraints in mean-variance models: a robust control theory foundation via machine learning

Using an innovative representation of the weight bound constrained Markowitz's (Portfolio selection. J. Finance, 1952, 7, 77–91) mean-variance model, developed using the support vector data description, a machine learning algorithm introduced by Tax and Duin (Support vector data description. Mach. Learn., 2004, 54, 45–66), we provide an innovative interpretation of the robustness of these bound constraints in terms of robust control theory in the sense of Hansen and Sargent (Robust control and model uncertainty. Am. Econ. Rev., 2001, 91, 60–66). Building on these insights, firstly, we detail the method for quantifying the degree of misspecification in Markowitz's (1952) mean-variance model using its counterpart with weight upper bounds. Additionally, we show that this degree of misspecification is a decreasing piecewise linear function of the bound. Secondly, we empirically investigate two simulation-based methods, inspired by Michaud's (The Markowitz optimization enigma: Is ‘optimized’ optimal? Financ. Anal. J., 1989, 45, 31–42) resampling technique, for choosing the bound. Thirdly, we compare the robustness of the weight upper bound constrained mean-variance model with that of Goldfarb and Iyengar's (Robust portfolio selection problems. Math. Oper. Res., 2003, 28, 1–38) robust maximum return model.

Universal distances for extended persistence

The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with respect to the bottleneck distance as introduced by Cohen–Steiner, Edelsbrunner, and Harer. We address the question of universality, which asks for the largest possible stable distance on extended persistence diagrams, showing that a more discriminative variant of the bottleneck distance is universal. Our result applies more generally to settings where persistence diagrams are considered only up to a certain degree. We achieve our results by establishing a functorial construction and several characteristic properties of relative interlevel set homology, which mirror the classical Eilenberg–Steenrod axioms. Finally, we contrast the bottleneck distance with the interleaving distance of sheaves on the real line by showing that the latter is not intrinsic, let alone universal. This particular result has the further implication that the interleaving distance of Reeb graphs is not intrinsic either.

A Piecewise Linear Approach for Implementing Fractional-Order Multi-Scroll Chaotic Systems on ARMs and FPGAs

This manuscript introduces a piecewise linear decomposition method devoted to a class of fractional-order dynamical systems composed of piecewise linear (PWL) functions. Inspired by the Adomian decomposition method, the proposed technique computes an approximated solution of fractional-order PWL systems using only linear operators and specific constants vectors for each sub-domain of the PWL functions, with no need for the Adomian polynomials. The proposed decomposition method can be applied to fractional-order PWL systems composed of nth PWL functions, where each PWL function may have any number of affine segments. In particular, we demonstrate various examples of how to solve fractional-order systems with 1D 2-scroll, 4-scroll, and 4×4-grid scroll chaotic attractors by applying the proposed approach. From the theoretical and implementation results, we found the proposed approach eliminates the unneeded terms, has a low computational cost, and permits a straightforward physical implementation of multi-scroll chaotic attractors on ARMs and FPGAs digital platforms.

Wearable Alcohol Monitoring Device for the Data-Driven Transcutaneous Alcohol Diffusion Model.

Wearable alcohol monitoring devices demand noninvasive, real-time measurement of blood alcohol content (BAC) reliably and continuously. A few commercial devices are available to determine BAC noninvasively by detecting transcutaneous diffused alcohol. However, they suffer from a lack of accuracy and reliability in the determination of BAC in real time due to the complex scenario of the human skin for transcutaneous alcohol diffusion and numerous factors (e.g., skin thickness, kinetics of alcohol, body weight, age, sex, metabolism rate, etc.). In this work, a transcutaneous alcohol diffusion model has been developed from real-time captured data from human wrists to better understand the kinetics of diffused alcohol from blood to different skin epidermis layers. Such a model will be a footprint to determine a base computational model in larger studies. Eight anonymous volunteers participated in this pilot study. A laboratory-built wearable blood alcohol content (BAC) monitoring device collected all the data to develop this diffusion model. The proton exchange membrane fuel cell (PEMFC) sensor was fabricated and integrated with an nRF51822 microcontroller, LMP91000 miniaturized potentiostat, 2.4 GHz transceiver supporting Bluetooth low energy (BLE), and all the necessary electronic components to build this wearable BAC monitoring device. The %BAC data in real time were collected using this device from these volunteers' wrists and stored in the end device (e.g., smartphone). From the captured data, we demonstrate how the volatile alcohol concentration on the skin varies over time by comparing the alcohol concentration in the initial stage (= 10 min) and later time (= 100 min). We also compare the experimental results with the outputs of three different input profiles: piecewise linear, exponential linear, and Hoerl, to optimize the developed diffusion model. Our results demonstrate that the exponential linear function best fits the experimental data compared to the piecewise linear and Hoerl functions. Moreover, we have studied the impact of skin epidermis thickness within ±20% and demonstrate that a 20% decrease in this thickness results in faster dynamics compared to thicker skin. The model clearly shows how the diffusion front changes within a skin epidermis layer with time. We further verified that 60 min was roughly the time to reach the maximum concentration, Cmax, in the stratum corneum from the transient analysis. Lastly, we found that a more significant time difference between BACmax and Cmax was due to greater alcohol consumption for a fixed absorption time.

Design and analysis of image encryption based on memristor chaotic systems with hidden attractors

Chaotic systems with hidden attractors are important research hotspots in nonlinear science. In recent years, continuous chaotic systems with special equilibrium points have been widely studied, especially continuous chaotic systems without equilibrium points. A four-dimensional chaotic system devoid of equilibrium point is proposed by using a composite cosine piecewise-linear (COS-PWL)function and a memristor model based on the modified Sprott-C system. The dynamical behaviors of the new system are studied through numerical analysis methods. The results reveal it is extremely sensitive to control parameters as well as initial conditions, which make it particularly suitable for application to image encryption algorithms. In light of these findings, a novel image encryption algorithm is introduced. This algorithm integrates the new four-dimensional chaotic system with ribonucleic acid (RNA) coding technology. Furthermore, the simulation results and security analyses validate the rationality of the encryption mechanism and the robustness of the encryption security of the proposed image encryption algorithm.

Thermal buckling analysis of nano composite laminated and sandwich beams based on a refined nonlocal zigzag model

A refined nonlocal zigzag model for thermal buckling analysis of nano composite laminated and sandwich beams is proposed in this study based on a refined zigzag theory and Eringen’s nonlocal theory. Firstly, present model satisfies the stress-free and continuity conditions a priori by introducing the piecewise-linear zigzag functions and a preprocessing, such that the transverse shear correction factors are not needed. In the preprocessing, accurate and continuous transverse shear stresses are obtained with the aid of the general mixed variational principle, which can be solved simultaneously with other stresses in the governing equations. This is quite different from the previous post-processing. Subsequently, thermal buckling problems of nano composite laminated and sandwich beams are analytically solved in simply supported boundary conditions. The degenerated results without small effect indicate that the non-dimensional critical loads and critical temperatures have a good agreement with the 3D elasticity solutions and previous results, which demonstrate the accuracy and reliability of present model. Moreover, it is observed that the small effect of the critical temperatures can be effectively captured by Eringen’s differential constitutive law (EDCL), which shows the small effect decreases the critical temperature by weakening the stiffness of the beam. Finally, the effects of different thermal expansion coefficients, laminations, geometric sizes and beam theories are discussed. The results show that present model is robust in the arbitrary layouts for both of composite and sandwich structures, which may have some referential significance to Micro-Electro-Mechanical Systems (MEMS) sensors and actuators.

Моделирование отклонений показателей качества объекта от нормы

The concept of a norm on the scale of an object's quality indicator in the context of determining the most preferable object or its state is explored. The notions of permissible and maximum permissible deviations from the norm are uti-lized, with maximum permissible deviations defining the boundaries of the indicator scale. The fundamental version of the norm is represented as a segment on the indicator scale that excludes these boundaries. Point and semi-interval norms (“no more”, “no less”) are considered special cases of the interval norm, where the semi-interval norm reflects the alignment of the original interval norm's boundary with the indicator scale's boundary. For certain indicators, devia-tion in one direction from the norm is not only acceptable but also beneficial. An indicator satisfying this condition is termed optimized, while an indicator with undesirable deviations from both ends of the norm is termed neutral. In the model of belonging to the norm, three classes are distinguished: “norm”, “no more” and “no less” than the norm. Piecewise linear and nonlinear membership functions for these classes are proposed. In the nonlinear model, the boundaries of the interval norm are expanded to acceptable limits, leading to the intersection of membership functions of adjacent classes. Classification into these three classes is conducted separately for neutral and optimized indicators. Interpreting deviations from the norm, both unacceptable and acceptable, necessitates introducing two fictitious clas-ses: “worse than the norm” and “better than the norm.” These classes are formed from the “not less than” and “not more than” classes. To calculate the membership function for each class across all indicators, a weighted average func-tion is employed. Aggregated indices of belonging to the classes “norm,” “better than norm,” and “worse than norm” across all indicators are referred to as indices of stability, development, and deterioration of an object, respectively. These indices are used for a comprehensive assessment of the object, termed an indicator of its condition. An example of analyzing deviations from the norm, implemented in the modified SVIR-M selection and ranking system, is provid-ed.

Optimization of a photovoltaic/wind/battery energy-based microgrid in distribution network using machine learning and fuzzy multi-objective improved Kepler optimizer algorithms

In this study, a fuzzy multi-objective framework is performed for optimization of a hybrid microgrid (HMG) including photovoltaic (PV) and wind energy sources linked with battery energy storage (PV/WT/BES) in a 33-bus distribution network to minimize the cost of energy losses, minimizing the voltage oscillations as well as power purchased minimization from the HMG incorporated forecasted data. The variables are microgrid optimal location and capacity of the HMG components in the network which are determined through a multi-objective improved Kepler optimization algorithm (MOIKOA) modeled by Kepler’s laws of planetary motion, piecewise linear chaotic map and using the FDMT. In this study, a machine learning approach using a multilayer perceptron artificial neural network (MLP-ANN) has been used to forecast solar radiation, wind speed, temperature, and load data. The optimization problem is implemented in three optimization scenarios based on real and forecasted data as well as the investigation of the battery's depth of discharge in the HMG optimization in the distribution network and its effects on the different objectives. The results including energy losses, voltage deviations, and purchased power from the HMG have been presented. Also, the MOIKOA superior capability is validated in comparison with the multi-objective conventional Kepler optimization algorithm, multi-objective particle swarm optimization, and multi-objective genetic algorithm in problem-solving. The findings are cleared that microgrid multi-objective optimization in the distribution network considering forecasted data based on the MLP-ANN causes an increase of 3.50%, 2.33%, and 1.98%, respectively, in annual energy losses, voltage deviation, and the purchased power cost from the HMG compared to the real data-based optimization. Also, the outcomes proved that increasing the battery depth of discharge causes the BES to have more participation in the HMG effectiveness on the distribution network objectives and affects the network energy losses and voltage deviation reduction.

From local utility to neural networks

We introduce and analyze two preference-based notions of local linearity in the spirit of Machina (1982). We show how the weaker among the two extends Machina’s local utility analysis, and that the stronger among the two characterizes continuous finite piecewise linear (CFPL) utility functions. We introduce a representation of the decision maker’s preference called the neural-network utility representation that is equivalent to the CFPL representation, in which the decision maker evaluates an alternative through a neural network.