Piecewise Approach Research Articles

Assessing the Impact of Distance Modelling Approaches on Active Travel Predictions

Trip distance is widely considered a key determinant of active travel choice, although distance is handled in choice modelling in various ways. This study examines how linear, categorical, quadratic, and piecewise representations for distance influence mode choice. The piecewise approach demonstrates superior fit and provides more stable elasticity estimates, ranging from -1% to -3%, compared to the broader range of -0.17% to -36% observed in categorical treatments and occasional positive values in quadratic treatments. These results underscore the piecewise model’s advantage in capturing critical behavioural shifts and offering more reliable insights to inform policy.

Electrolyte jet tomography: Three-dimensional microstructure mapping with an electrochemical machine tool and an optical microscope

There is a general separation between the manufacturing processes that add value to materials on the factory floor and the techniques engineers use in the laboratory to evaluate the microstructures and the surface integrity that results. These techniques are often destructive or require a vacuum and are incompatible with production lines. However, this information has intrinsic value and could be exploited to inform production decisions during manufacture. In this study, a novel approach to acquire this information is presented that is underpinned by electrolyte jet machine tool coupled with optical microscopy, which can allow the extraction of both grain-wise partial orientation and morphological information, and crystallographic macro textures in three dimensions. Here, iterative sections are precisely machined into the near surface of a commercially pure titanium alloy using an electrochemical jet and subsequently imaged, allowing the reconstruction of high-fidelity microstructure models rapidly and under ambient conditions. In doing so, new insights into the specific orientation-dependent dissolution mechanisms are offered, and the acquisition of appropriate conditions that result in nanoscale roughness surfaces (avoiding the dominance of pitting and preferential grain removal) is firstly explored. Building on prior work, a piecewise approach is presented to analyse the acquired image stacks to map partial crystal orientations, while different approaches are proposed to account for jet-specific surface artefacts and waviness. This is repeated over 20 layers in an individual specimen and layer-wise orientation maps are used to construct volumetric models of the specimen. These data sets are then explored from the perspective of materials/manufacturing engineers, who may use to this information to effect advancements to materials processing technologies.

Area-Based Hedonic Pricing of Urban Green Amenities in Beijing: A Spatial Piecewise Approach

AbstractThis study explores a spatial piecewise approach for the hedonic valuation of the area of urban green space at different distances from a property, using a rich census dataset collected from Beijing. We explore three novel empirical strategies that improve the identification of the spatial boundary or threshold distance within which green space is capitalised into housing prices. We first delineated a series of concentric circles surrounding each property and measured the area of green space within each doughnut-shaped ring. We next estimated the hedonic price using three methods. The first is a regression spline model combined with a machine learning type of model selection procedure which objectively selects the exact location of the threshold distance that optimises the model’s predictive performance. The second is a novel matching algorithm that minimises covariate imbalance for a continuous treatment variable (i.e., the area of green space) to provide stronger causal evidence on the hedonic prices of green space at different distances. The third is a spatial difference-in-differences approach that further accounts for endogeneity bias associated with unobserved factors. For our dataset, we found that housing prices are more likely to be affected by green space within a 1 km radius.

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

Artificial-Intelligence-Based Hybrid Extended Phase Shift Modulation for the Dual Active Bridge Converter With Full ZVS Range and Optimal Efficiency

Dual active bridge (DAB) converter is the key enabler in many popular applications such as wireless charging, electric vehicle and renewable energy. ZVS range and efficiency are two significant performance indicators for DAB converter. To obtain the desired ZVS and efficiency performance, modulation should be carefully designed. Hybrid modulation considers several single modulation strategies to achieve good comprehensive performance. Conventionally, to design a hybrid modulation, harmonic approach or piecewise approach is used, but they suffer from timeconsuming model building process and inaccuracy. Therefore, an artificial-intelligence-based hybrid extended phase shift (HEPS) modulation is proposed. Generally, the HEPS modulation is developed in an automated fashion, which alleviates cumbersome model building process while keeping high model accuracy. In HEPS modulation, two EPS strategies are considered to realize optimal efficiency with full ZVS operation over entire operating ranges. Specifically, to build data-driven models of ZVS and efficiency performance, extreme gradient boosting (XGBoost), which is a state-of-the-art ensemble learning algorithm, is adopted. Afterwards, particle swarm optimization with state-based adaptive velocity limit (PSO-SAVL) is utilized to select the best EPS strategy and optimize modulation parameters. With 1 kW hardware experiments, the feasibility of HEPS has been verified, achieving optimal efficiency with maximum of 97.1% and full-range ZVS operation.

Ultimately Bounded PID Control for T–S Fuzzy Systems Under FlexRay Communication Protocol

This paper investigates the ultimately bounded proportional-integral-derivative (PID) control problem for a class of discrete-time Takagi-Sugeno fuzzy systems subject to unknown-but-bounded noises and protocol constraints. The signal transmissions from sensors to the remote controller are realized via a communication network, where the FlexRay protocol is employed to flexibly schedule the information exchange. Such FlexRay protocol is characterized by both the time- and event-triggered mechanisms which are conducted in a cyclic manner. By using a piecewise approach, the measurement outputs affected by the FlexRay protocol are established based on a switching model. Then, a fuzzy PID controller is proposed with a concise and realizable structure. To evaluate the performance of the controlled system, a special time-sequence is introduced that accounts for the behavior of the FlexRay protocol. Subsequently, a general framework is obtained to verify the boundedness of the closed-loop system and then the controller gains are designed by minimizing the bound of the concerned variables. In the end, a simulation study is conducted to validate the effectiveness of the developed control scheme.

Superiorization of projection algorithms for linearly constrained inverse radiotherapy treatment planning.

We apply the superiorization methodology to the constrained intensity-modulated radiation therapy (IMRT) treatment planning problem. Superiorization combines a feasibility-seeking projection algorithm with objective function reduction: The underlying projection algorithm is perturbed with gradient descent steps to steer the algorithm towards a solution with a lower objective function value compared to one obtained solely through feasibility-seeking. Within the open-source inverse planning toolkit matRad, we implement a prototypical algorithmic framework for superiorization using the well-established Agmon, Motzkin, and Schoenberg (AMS) feasibility-seeking projection algorithm and common nonlinear dose optimization objective functions. Based on this prototype, we apply superiorization to intensity-modulated radiation therapy treatment planning and compare it with (i) bare feasibility-seeking (i.e., without any objective function) and (ii) nonlinear constrained optimization using first-order derivatives. For these comparisons, we use the TG119 water phantom, the head-and-neck and the prostate patient of the CORT dataset. Bare feasibility-seeking with AMS confirms previous studies, showing it can find solutions that are nearly equivalent to those found by the established piece-wise least-squares optimization approach. The superiorization prototype solved the linearly constrained planning problem with similar dosimetric performance to that of a general-purpose nonlinear constrained optimizer while showing smooth convergence in both constraint proximity and objective function reduction. Superiorization is a useful alternative to constrained optimization in radiotherapy inverse treatment planning. Future extensions with other approaches to feasibility-seeking, e.g., with dose-volume constraints and more sophisticated perturbations, may unlock its full potential for high performant inverse treatment planning.

Dynamical Analysis of Rubella Disease Model in the Context of Fractional Piecewise Derivative: Simulations with Real Statistical Data

Rubella is a viral disease that can lead to severe health complications, especially in pregnant women and their unborn babies. Understanding the dynamics of the Rubella disease model is crucial for developing effective strategies to control its spread. This paper introduces a major innovation by employing a novel piecewise approach that incorporates two different kernels. This innovative approach significantly enhances the accuracy of modeling Rubella disease dynamics. In the first interval, the Caputo operator is employed to address initial conditions, while the Atangana–Baleanu derivative is utilized in the second interval to account for anomalous diffusion processes. A thorough theoretical analysis of the piecewise derivative for the problem is provided, discussing mathematical properties, stability, and convergence. To solve the proposed problem effectively, the piecewise numerical Newton polynomial technique is employed and the numerical scheme for both kernels is established. Through extensive numerical simulations with various fractional orders, the paper demonstrates the approach’s effectiveness and flexibility in modeling the spread of the Rubella virus. Furthermore, to validate the findings, the simulated results are compared with real data obtained from Rubella outbreaks in Uganda and Tanzania, confirming the practical relevance and accuracy of this innovative model.

Regression versus probabilistic approach for operational data – Heat demand of buildings to be connected to a district heating system

The robust design of 5th generation district heating and cooling (5GDHC) systems requires accurate and sufficient operational data on the energy consumption and production of the connected prosumers. Often these data requirements are not met. Historical energy-related data for buildings is sometimes no longer accessible, and if available, often limited in time span and temporal resolution. Also, technical details on the utilization of the energy within the heating, ventillation and air-conditioning (HVAC) system of a building and its relationship with building occupation and outside weather conditions are often difficult to obtain. This lack of data requires careful pre-processing of this data, to ensure a robust 5GDHC system design. To cope with this lack of data, we propose a two-step model. First, techniques of linear regression are used to detect relations with contextual key factors, such as occupation, day of the week, hour of the day and outside temperature. In a second step, a piece-wise stochastic approach is used to generate artificial data for any combination of the key factors, allowing for the detection and regeneration of intermittent behavior that is typical present in the obtained operational data. The advantage of this method is that it takes into consideration the unknowns and randomness of the system’s behavior. It allows for variance within the artificial time series (peaks and gaps), which makes it better suited for the robust design of 5GDHC systems. We applied this model on operational data from 23 buildings in Flanders, Belgium and produced artificial data for these buildings. The model can separate HVAC energy data related to the outdoor weather conditions from non-HVAC related energy data. It can also forecast energy data for other weather conditions and building occupation.

Piecewise: A Non-Isomorphic 3D Manipulation Technique That Factors Upper-Limb Ergonomics

Virtual reality (VR) is gaining popularity as an educational, training, and healthcare tool due to its decreasing cost. Because of the high user variability in terms of ergonomics, 3D manipulation techniques (3DMTs) for 3D user interfaces (3DUIs) must be adjustable for comfort and usability, hence avoiding interactions that only function for the typical user. Given the role of the upper limb (i.e., arm, forearm, and hands) in interacting with virtual objects, research has led to the development of 3DMTs for facilitating isomorphic (i.e., an equal translation of controller movement) and non-isomorphic (i.e., adjusted controller visuals in VR) interactions. Although advances in 3DMTs have been proven to facilitate VR interactions, user variability has not been addressed in terms of ergonomics. This work introduces Piecewise, an upper-limb-customized non-isomorphic 3DMT for 3DUIs that accounts for user variability by incorporating upper-limb ergonomics and comfort range of motion. Our research investigates the effects of upper-limb ergonomics on time completion, skipped objects, percentage of reach, upper-body lean, engagement, and presence levels in comparison to common 3DMTs, such as normal (physical reach), object translation, and reach-bounded non-linear input amplification (RBNLIA). A 20-person within-subjects study revealed that upper-limb ergonomics influence the execution and perception of tasks in virtual reality. The proposed Piecewise approach ranked second behind the RBNLIA method, although all 3DMTs were evaluated as usable, engaging, and favorable in general. The implications of our research are significant because upper-limb ergonomics can affect VR performance for a broader range of users as the technology becomes widely available and adopted for accessibility and inclusive design, providing opportunities to provide additional customizations that can affect the VR user experience.

Comparison of intra- and inter-patient intensity standardization methods for multi-parametric whole-body MRI

Objective. To test and compare different intensity standardization approaches for whole-body multi-parametric MR images, aiming to compensate voxel intensity differences between scans. These differences, common for magnetic resonance imaging, pose problems in image quantification, assessment of changes between a baseline and follow-up scan, and hinder performance of image processing and machine learning algorithms. Approach. In this work, we present a comparison on the accuracy of intensity standardization approaches with increasing complexity, for intra- and inter-patient multi-parametric whole-body MRI. Several approaches were used: z-scoring of the intensities, piecewise linear mapping and deformable mapping of intensity distributions into established reference intensity space. For each method, the impact on standardization algorithm on the use of single image or average population distribution reference; as well as, whole image and region of interest were additionally investigated. All methods were validated on a data set of 18 whole-body anatomical and diffusion-weighted MR scans consisting of baseline and follow-up examinations acquired from advanced prostate cancer patients and healthy volunteers. Main results. The piecewise linear intensity standardisation approach provided the best compromise between standardization accuracy and method stability, with average deviations in intensity profile of 0.011-0.027 and mean absolute difference of 0.29-0.37 standard score (intra-patient) and 0.014-0.056 (inter-patient), depending on the type of used MR modality. Significance. Linear piecewise approaches showed the overall best performance across multiple validation metrics, mostly because of its robustness. The inter-patient standardization proved to perform better when using population average reference image; in contrary to intra-patient approach, where the best results were achieved by standardizing towards a reference image taken as the baseline scan.

Longitudinal and lateral coupling vehicle stability controller designed based on piecewise T-S fuzzy model

Due to tire force coupling and load transfer coupling during the stability control process, the vehicle longitudinal and lateral dynamics shows particularly obvious nonlinear coupling characteristics, which will deteriorate the performance of the stability controller. This paper proposes a Vehicle Stability Controller considering the vehicle longitudinal and lateral coupling characteristics. First, a piecewise guidance method, including the Adaptive Linear Regression Algorithm and Dimensionless Performance Evaluation Weighting Function, is developed to ensure the Takagi-Sugeno fuzzy model piecewise approaches the nonlinear characteristics of the original system and obtains the multiple linear fuzzy subsystems. Then, an H∞ robust controller with dynamic output feedback is used in each fuzzy subsystem based on the identification result of the driving intention, and the Linear Matrix Inequality is applied to obtain the controller gains. Subsequently, the Parallel Distributed Compensation architecture is adopted to integrate the outputs of all fuzzy subsystems, and vehicle stability controller is realized by using a rule-based control distribution strategy. The proposed controller is evaluated by simulations and hardware in the loop tests, and the results demonstrate satisfactory longitudinal following ability and lateral stability.

Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique

<abstract><p>In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number $ {\bf R}_{0}^{s} $ that can predict pathogen extermination and mean persistence. Furthermore, we show that if $ {\bf R}_{0}^{s} > 1 $, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.</p></abstract>

Semi-analytical calculation of pore-related parameters of wire/woven screens

Wire/woven screens have a wide range of applications, from being used as simple mechanical screening device to nanoscreen wicking with nanofluids. The vast number of applications makes important to study these screens with high accuracy, to reduce errors in characterisation and performance predictions. Previous works to date focused either on the study of these screens as a two-dimensional surface (e.g. in ventilation openings as insect-proof screens) or as three-dimensional structures under important assumptions (symmetric mesh, thickness of two times their diameter, linear evolution of the pore area along the thickness). These incomplete modellings introduce errors in applications such as the estimation of permeability of the porous media (two-dimensional porosity is identical for two meshes with the same projected area of pore but different thickness) or computational simulations of ventilation in buildings/greenhouses, where these parameters are imposed as boundary condition. The present investigation shows a method to calculate three-dimensional pore related structural properties semi-analytically for the first time and for any plain square mesh. We found that when sweeping the mesh with a plane parallel to it there are up to six different zones or stretches which can be integrated by a piece-wise approach (here named Discretisation Method). Results demonstrated high accuracy in the calculation of three-dimensional porosity and constriction factor (a parameter that is calculated by integration over the pore volume). Due to the mathematical complexity in the method, a software (AeroScreen v1.0) is available to obtain pore-related structural parameters from diameters, separations and thickness of the screen.

Theoretical Modeling of Piezoelectric Micromachined Ultrasonic Transducers With Honeycomb Structure

In this work, we reported a theoretical model for a novel piezoelectric micromachined ultrasonic transducer (PMUT). The sensing cells with hexagonal transduction diaphragms in the PMUT array are designed and arranged in a bioinspired honeycomb structure. Based on the classical piece-wise approach commonly used for PMUT with circular diaphragm, an enhanced theoretical model is developed. In this model, the deflection of the honeycomb diaphragm is analytically determined by the volume deflection, rather than the path deflection commonly used in the previous models. The hexagonal diaphragm is converted as a circular one, whose radius is derived by correcting the characteristic size of the hexagonal diaphragm multiplied by a correction factor. The calculated parameters by the reported theoretical model of a transduction cell in the PMUT array, such as resonant frequency and static deflection, matched well with the data obtained by finite element analysis and experiment. Special investigations are made on the effects of top electrode coverage and transduction layer thickness towards PMUT’s performance. The reported theoretical model in this work is suitable not only for PMUTs with circular and hexagonal transduction cells, but also for square and other arbitrary shape diaphragms. This enhanced theoretical model provides an interesting insight on design optimizations of PMUT with various transduction cell geometries. [2022-0093]

A novel mathematical model of smoking: an integer and piece-wise fractional approach

A novel mathematical model of smoking: an integer and piece-wise fractional approach

A Compact Modeling Methodology for Experimental Memristive Devices

A methodology to create and develop electrical compact models for memristive devices is presented. It comprises a six-step algorithm that uses experimental data of memristive devices in order to obtain a compact model suitable for circuit-level simulations. The model methodology makes use of the definition of the intrinsic variables of memristive systems, to obtain the state map that describes the system, from which the mathematical expressions of the model are obtained. In order to illustrate the usage of the algorithm, a compact memristive model is developed by using experimental data from a TiO2-based resistive switching (RS) device. The resulting mathematical model is compared to the experimental data by computing the mean absolute percentage error (MAPE) between both, which results in 11%, and reduces to 6% after a piecewise approach. The circuit-level representation is implemented using a SPICE macromodel and a Verilog-A module, from which the memristive behavior is also properly reproduced.

Assessing mixed-integer-based heat pump modeling approaches for model predictive control applications in buildings

Model predictive control can reduce heating systems’ operating costs and energy consumption. This especially applies to heat pumps, whose operation efficiency highly depends on the heating system’s source and sink temperatures. In literature, process models for heat pumps mostly introduce the coefficient of performance as a parameter thus assuming constant supply temperatures. However, supply temperature adjustment is crucial to overcharge buffer storages and hence shift energy to more favorable times, which is the basis of model predictive control concepts. We close this gap by developing two different air-source heat pump modeling approaches using the supply temperature as control variable: a piecewise linear model based on simulation results and a quadratic modeling approach. Both methods are benchmarked with a simplified linear model representing the state of research. The simplified linear model underestimates the cost of storage charging as it neglects the supply temperature’s influence on the coefficient of performance and results in 8.7% higher operating costs and 12.1% higher energy demand than the piecewise linear approach. However, the simplified linear model yields the lowest average computation time compared to the piecewise and quadratic approaches. The quadratic approach results in both lower operating costs (-1.9%) and energy demand (-1.8%), as well as lower computation times than the piecewise approach, consequently representing the best trade-off between performance and computational effort. We recommend future work to apply the method to a ground- or water-source heat pump and to a coupled building energy system to investigate the transferability of our findings.

E iso–Ep correlation of gamma-ray bursts: calibration and cosmological applications

ABSTRACT Gamma-ray bursts (GRBs) are the most explosive phenomena and can be used to study the expansion of Universe. In this paper, we compile a long GRB sample for the Eiso–Ep correlation from Swift and Fermi observations. The sample contains 221 long GRBs with redshifts from 0.03 to 8.20. From the analysis of data in different redshift intervals, we find no statistically significant evidence for the redshift evolution of this correlation. Then we calibrate the correlation in six subsamples and use the calibrated one to constrain cosmological parameters. Employing a piece-wise approach, we study the redshift evolution of dark energy equation of state (EOS), and find that the EOS tends to be oscillating at low redshift, but consistent with −1 at high redshift. It hints at dynamical dark energy at 2σ confidence level at low redshift.

Modeling the crossover behavior of the bacterial infection with the COVID-19 epidemics

To explore the crossover linkage of the bacterial infections resulting from the viral infection, within the host body, a computational framework is developed. It analyzes the additional pathogenic effect of Streptococcus pneumonia, one of the bacteria that can trigger the super-infection mechanism in the COVID-19 syndrome and the physiological effects of innate immunity for the control or eradication of this bacterial infection. The computational framework, in a novel manner, takes into account the action of pro-inflammatory and anti-inflammatory cytokines in response to the function of macrophages. A hypothetical model is created and is transformed to a system of non-dimensional mathematical equations. The dynamics of three main parameters (macrophages sensitivity κ, sensitivity to cytokines η and bacterial sensitivity ϵ), analyzes a “threshold value” termed as the basic reproduction number R0 which is based on a sub-model of the inflammatory state. Piece-wise differentiation approach is used and dynamical analysis for the inflammatory response of macrophages is studied in detail. The results shows that the inflamatory response, with high probability in bacterial super-infection, is concomitant with the COVID-19 infection. The mechanism of action of the anti-inflammatory cytokines is discussed during this research and it is observed that these cytokines do not prevent inflammation chronic, but only reduce its level while increasing the activation threshold of macrophages. The results of the model quantifies the probable deficit of the biological mechanisms linked with the anti-inflammatory cytokines. The numerical results shows that for such mechanisms, a minimal action of the pathogens is strongly amplified, resulting in the “chronicity” of the inflammatory process.