Empirical Model Research Articles

Empirical modeling of hysteresis in a tendon–sheath mechanism on multi-segmented curves

Empirical modeling of hysteresis in a tendon–sheath mechanism on multi-segmented curves

Functional income distribution, effective demand and wealth in Denmark – insights from an empirical stock-flow consistent model

With the important contribution of Marglin and Bhaduri different demand and growth regimes were identified, which inspired a strand of empirical research aiming to uncover the type of growth regime. Most of these studies can be framed into two methodological approaches: (i) a structural, and (ii) an aggregative approach. In this paper, we use a third approach where we exploit the advantages of the stock-flow consistent framework. We argue that using an empirical SFC model retains the advantages of the two more widely used approaches, while adding some novel features: (i) the endogenization of income distribution, which allows for a two-way relationship between demand and income shares, (ii) the consistent incorporation of stock variables in the estimation of the equations of aggregate demand components, and (iii) the inclusion of endogenous labor market dynamics in the analysis. To introduce these features, we build an empirical stock-flow consistent model for Denmark for the period 2005q1–2020q1. Our analysis suggests that demand can neither be categorically defined as wage-led nor profit-led, as the effects of a change in income distribution on the aggregate demand components cancel each other out. Results are more conclusive for capital accumulation, which is found to be profit-led.

Extraction of Bioactive Secondary Metabolites from Citrus Maxima Peel Via Pressurized Hot Water Extractor for the Synthesis of Iron Oxide Nanoparticles

Using bioactive secondary metabolites (BSM) from Citrus maxima peel extract, this work investigated a green method of synthesizing magnetite iron oxide (Fe3O4) nanoparticles (NPs). The BSM acts as a reducing cum stabilizing agent in the process. The optimization of the BSM parameters were conducted through response surface methodology (RSM). The optimal condition obtained in this study for pressurized hot water extractor (PHWE) extraction was temperature of 94.96 °C, solvent-to-solid ratio of 29.7 ml/g and extraction time of 27.6 min. BSM Yield of 49.31 % could be obtained based on this condition. The formation of Fe3O4 NPs were detected using the FTIR analysis with the absorption peaks observed at around 590 and 580 cm−1. X-ray diffraction results matched standard magnetite Fe3O4 patterns with planes at (220), (311), (400), (511) and (440). Field emission scanning electron microscopy (FESEM) results showed that the magnetite Fe3O4 NPs synthesized in this study predominantly appeared in spherical shape. The extraction process's kinetics were examined using various empirical models, including the Elovich’s model, Peleg’s model, Power law and parabolic diffusion model. All applied models were found to be well fitted with the measured data from experiment, with R2 values exceeding 0.9. Notably, the Peleg’s model exhibited the highest R2, the smallest RMSD, and the least significant p-values, indicating its superior performance.

Improving prediction accuracy of laser-induced shock wave velocity prediction using neural networks

The velocity of laser-induced shock waves affects the efficiency and efficacy of laser-based processes. The ability to accurately estimate shock wave velocity is critical for optimizing experimental combinations, creating laser-based systems, and assuring desired results. Traditional approaches to predict shock wave velocity involve empirical equations and analytical models based on simplified assumptions. However, these methods often lack accuracy and fail to capture the complex dynamics of laser-matter interactions. To overcome these limitations, we used a combination of an artificial neural network and a genetic algorithm to predict shock wave velocity. In this method, the neural network structure is dynamically designed. The optimization method does this by modifying the neural network's weights and figuring out the network's structure on our behalf. Based on the findings, our suggested technique worked very well; it surpassed other comparison methods by achieving the lowest average errors in terms of RMSE and MAE, which are 4.38 and 3.74, respectively. Moreover, the analysis has shown that our proposed method has a high level of reliability in predicting impulsive wave velocity using a neural network.

Seismic fragility analysis of buried pipelines under Kahramanmaraş ground motions

This paper aims to evaluate the failure probability of buried pipelines under pulse-like ground motions based on the seismic records detected during the Kahramanmaraş earthquake in Turkey. The incremental dynamic analysis (IDA) method was used to evaluate the vulnerability of continuous and segmented steel pipes, taking into account the corrosion effect in alkaline and near-neutral soil environments.The results show that pulse-like ground motion can significantly impact the fragility of buried pipelines, particularly segment steel pipelines. Moreover, the failure probability of buried pipelines tends to increase with service age, although the rate of failure gradually decreases. Empirical models notably underestimate the failure probability of buried pipelines under pulse-like ground motion, so they should be used cautiously in engineering application. These insights contribute to advancing our understanding of the seismic fragility of buried pipelines.

Computational intelligence for empirical modelling and optimization of methylene blue adsorption phenomena utilizing an activated carbon‐supported [Co(NH3)6]Cl3 complex

AbstractThe study focuses on the efficiency of hexaamminecobalt (III) chloride (HACo, [Co(NH3)6]Cl3) immobilized on activated carbon for removing methylene blue (MB) from water solutions. The primary objective of this study was to assess the sorption performance of HACo immobilized on activated carbon in removing MB from water solutions. Additionally, predictive models were developed to optimize the MB removal percentage. Lastly, the study aimed to determine the optimal conditions for achieving maximum MB removal. Samples were characterized using scanning electron microscopy. Batch sorption experiments were conducted to analyze the impact of MB concentration, adsorbent mass, pH, temperature, and contact time. Predictive models were built using multiple linear regression and neural network techniques, specifically artificial neural networks (ANN) and hybrid ANN–particle swarm optimization (ANN‐PSO). The PSO‐ANN model with a single hidden layer of eight neurons trained using the Levenberg–Marquardt algorithm demonstrated high accuracy in predicting MB removal percentage, with mean absolute percentage error (MAPE) = 0.083788, root mean square error (RMSE) = 0.11441, and R2 = 0.99693. The MB adsorption process followed a mono‐layer with one energy model and a pseudo‐first‐order kinetic model. Optimization using the genetic algorithm revealed that the maximum MB removal percentage of 99.56% is achievable at an MB concentration of 9.36 mg/L, adsorbent mass of 15.72 mg, and temperature of 311.2 K. The study confirms the effectiveness of HACo immobilized on activated carbon for MB removal. The PSO‐ANN predictive model proved superior in accuracy compared to empirical models. Optimization results provide the optimal conditions for maximizing MB removal, offering valuable insights for practical applications.

Experimental and mechanism study on wax deposit dissolution characteristics by light crude oil

During the sequential transportation of waxy crude oil and light oil, the previous formed wax deposits on the pipe wall will dissolve by light oil, which brings risks to the flow safety of the pipeline. This paper adopted a Couette wax deposit dissolution experimental device to systematically study the effects of dissolution duration, oil temperature, rotation speed and wax deposit properties on the dissolution characteristics of wax deposits. It is found that the dissolution of wax deposits is a process that starts quickly and then slows down. Moreover, the wax content of wax deposit also decreased during the dissolution process. The wax deposit dissolution process is mainly divided into five stages such as diffusion of wax molecules from wax deposit to the light oil and from bottom layer deposit to the wax deposit-oil interface, dissolution of wax crystal particles, weakening of wax deposit structural strength, and shear stripping of wax deposits. Finally, an empirical model of wax deposit dissolution was established and the undetermined parameters were fitted based on experimental data. The prediction results have good prediction accuracy with the experimental values.

Pore unit cell network modeling of the thermal conductivity dynamics in unsaturated sandy soils: Unveiling the role of spanning‐wetting phase cluster

AbstractAs the world struggles with climate change and energy crises, understanding the role of soil in the food–water–energy nexus becomes increasingly critical. Accurately estimating the soil thermal conductivity drying curve is essential for assessing the impacts of temperature on soil biota and crop growth, environmental changes due to forest fires and global warming, and for designing geo‐energy extraction techniques such as geothermal energy piles. Existing empirical models often fail to accurately estimate the soil thermal conductivity (TC), particularly in pendular soil moisture regimes where they do not capture sharp changes in TC. This study introduces a novel approach using a pore unit cell network model to more accurately describe the dynamics of TC in variably saturated soils. A quadratic parallel scheme within each soil pore unit cell links the TCs of solid, water, and air to the overall effective conductivity. By modeling air invasion in the pore network model and employing the proposed equation, we determined the unsaturated soil TC based on varying local conductivities. The model effectively captures the significant decrease in conductivity in the pendular saturation regime, associated with the shrinkage of the spanning‐wetting cluster. Quantitative analyses showed a substantial improvement in prediction accuracy compared to existing models, especially under varying moisture conditions. Our findings have significant implications for better characterizing soil thermal and hydraulic properties, which are crucial for resource management in a changing climate and advancing geo‐energy technologies.

Behind the Door: Practical Parameterization of Propagation Parameters for IEEE 802.11ad Use Cases

The integration of the 60 GHz band into the IEEE 802.11 standard has revolutionized indoor wireless services. However, this band presents unique challenges to indoor wireless communication infrastructure, originally designed to handle data traffic in residential and office environments. Estimating 60 GHz signal propagation in indoor settings is particularly complicated due to dynamic contextual factors, making it essential to ensure adequate coverage for all connected devices. Consequently, empirical channel modeling plays a pivotal role in understanding real-world behavior, which is characterized by a complex interplay of stationary and mobile elements. Given the highly directional nature of 60 GHz propagation, this study addresses a seemingly simple but important question: what is the impact of employing highly directive antennas when deviating from the line of sight? To address this question, we conducted an empirical measurement campaign of wireless channels within an office environment. Our assessment focused on power losses and distribution within an angular range while an indoor base station served indoor users, simulating the operation of an IEEE 802.11ad high-speed WLAN at 60 GHz. Additionally, we explored scenarios with and without pedestrian movement in the vicinity of wireless terminals. Our observations reveal the presence of significant antenna lobes even in obstructed links, indicating potential opportunities to use angular combiners or beamformers to enhance link availability and the data rate. This empirical study provides valuable information and channel parameters to simulate 60 GHz millimeter wave (mm-wave) links in indoor environments, paving the way for more efficient and robust wireless communication systems.

Ensemble X-ray variability of optically selected QSOs: dependence on black hole mass and Eddington ratio

ABSTRACT Although flux variability is one of the defining properties of accretion flows on to supermassive black holes, its dependence on physical parameters such as the mass of the compact object and the Eddington ratio remains under discussion. In this paper, we address this issue using the structure function statistic to measure the variability at X-ray wavelengths of a sample of optically selected QSOs with available black hole masses and Eddington ratios. We present a new Bayesian methodology for estimating the structure function tailored to the Poisson nature of the X-ray data. This is applied to 15 548 SDSS DRQ16 QSOs with repeat observations in the XMM–Newton archive and/or the SRG/eROSITA All Sky Survey. The X-ray structure function monotonically increases to time intervals of about 10–15 yrs, consistent with scenarios in which instabilities of the accretion disc contribute to the X-ray variability on long time-scales. Additionally, there is evidence that the amplitude of the stochastic X-ray flux variations rises with decreasing black hole mass and Eddington ratio. This finding imposes stringent constraints on empirical models of Active Galactic Nuclei variability derived from local samples, emphasizing the significance of high-redshift population studies for comprehending the stochastic flux variations in active black holes.

Determination of muscle shape deformations of the tibialis anterior during dynamic contractions using 3D ultrasound.

In this paper, we introduce a novel method for determining 3D deformations of the human tibialis anterior (TA) muscle during dynamic movements using 3D ultrasound. An existing automated 3D ultrasound system is used for data acquisition, which consists of three moveable axes, along which the probe can move. While the subjects perform continuous plantar- and dorsiflexion movements in two different controlled velocities, the ultrasound probe sweeps cyclically from the ankle to the knee along the anterior shin. The ankle joint angle can be determined using reflective motion capture markers. Since we considered the movement direction of the foot, i.e., active or passive TA, four conditions occur: slow active, slow passive, fast active, fast passive. By employing an algorithm which defines ankle joint angle intervals, i.e., intervals of range of motion (ROM), 3D images of the volumes during movement can be reconstructed. We found constant muscle volumes between different muscle lengths, i.e., ROM intervals. The results show an increase in mean cross-sectional area (CSA) for TA muscle shortening. Furthermore, a shift in maximum CSA towards the proximal side of the muscle could be observed for muscle shortening. We found significantly different maximum CSA values between the fast active and all other conditions, which might be caused by higher muscle activation due to the faster velocity. In summary, we present a method for determining muscle volume deformation during dynamic contraction using ultrasound, which will enable future empirical studies and 3D computational models of skeletal muscles.

Rapid Mass Conversion for Environmental Microplastics of Diverse Shapes.

Rivers have been recognized as the primary conveyors of microplastics to the oceans, and seaward transport flux of riverine microplastics is an issue of global attention. However, there is a significant discrepancy in how microplastic concentration is expressed in field occurrence investigations (number concentration) and in mass flux (mass concentration). Of urgent need is to establish efficient conversion models to correlate these two important paradigms. Here, we first established an abundant environmental microplastic dataset and then employed a deep neural residual network (ResNet50) to successfully separate microplastics into fiber, fragment, and pellet shapes with 92.67% accuracy. We also used the circularity (C) parameter to represent the surface shape alteration of pellet-shaped microplastics, which always have a more uneven surface than other shapes. Furthermore, we added thickness information to two-dimensional images, which has been ignored by most prior research because labor-intensive processes were required. Eventually, a set of accurate models for microplastic mass conversion was developed, with absolute estimation errors of 7.1, 3.1, 0.2, and 0.9% for pellet (0.50 ≤ C < 0.75), pellet (0.75 ≤ C ≤ 1.00), fiber, and fragment microplastics, respectively; environmental samples have validated that this set is significantly faster (saves ∼2 h/100 MPs) and less biased (7-fold lower estimation errors) compared to previous empirical models.

Does high-latitude ionospheric electrodynamics exhibit hemispheric mirror symmetry?

Abstract. Ionospheric electrodynamics is a problem of mechanical stress balance mediated by electromagnetic forces. Joule heating (the total rate of frictional heating of thermospheric gases and ionospheric plasma) and ionospheric Hall and Pedersen conductances comprise three of the most basic descriptors of this problem. More than half a century after identification of their central role in ionospheric electrodynamics, several important questions about these quantities, including the degree to which they exhibit hemispheric symmetry under reversal of the sign of dipole tilt and the sign of the y component of the interplanetary magnetic field (so-called “mirror symmetry”), remain unanswered. While global estimates of these key parameters can be obtained by combining existing empirical models, one often encounters some frustrating sources of uncertainty: the measurements from which such models are derived, usually magnetic field and electric field or ion drift measurements, are typically measured separately and do not necessarily align. The models to be combined moreover often use different input parameters, different assumptions about hemispheric symmetry, and/or different coordinate systems. We eliminate these sources of uncertainty in model predictions of electromagnetic work J⋅E (in general not equal to Joule heating ηJ2) and ionospheric conductances by combining two new empirical models of the high-latitude ionospheric electric potential and ionospheric currents that are derived in a mutually consistent fashion: these models do not assume any form of symmetry between the two hemispheres; are based on Apex magnetic coordinates (denoted Apex), spherical harmonics, and the same model input parameters; and are derived exclusively from convection and magnetic field measurements made by the Swarm and CHAMP satellites. The model source code is open source and publicly available. Comparison of high-latitude distributions of electromagnetic work in each hemisphere as functions of dipole tilt and interplanetary magnetic field clock angle indicates that the typical assumption of mirror symmetry is largely justified. Model predictions of ionospheric Hall and Pedersen conductances exhibit a degree of symmetry, but clearly asymmetric responses to dipole tilt and solar wind driving conditions are also identified. The distinction between electromagnetic work and Joule heating allows us to identify where and under what conditions the assumption that the neutral wind corotates with the Earth is not likely to be physically consistent with predicted Hall and Pedersen conductances.

AI based optimal analysis of electro-osmotic peristaltic motion of non-Newtonian fluid with chemical reaction using artificial neural networks and response surface methodology

PurposeThe present work is devoted to investigating the sensitivity analysis of the electroosmotic peristaltic motion of non-Newtonian Casson fluid with the effect of the chemical reaction and magnetohydrodynamics through the porous medium. The main focus is on flow efficiency quantities such as pressure rise per wavelength, frictional forces on the upper wall and frictional forces on the lower wall. This initiative is to bridge the existing gap in the available literature.Design/methodology/approachThe governing equations of the problem are mathematically formulated and subsequently simplified for sensitivity analysis under the assumptions of a long wavelength and a small Reynolds number. The simplified equations take the form of coupled nonlinear differential equations, which are solved using the built-in Matlab routine bvp4c. The response surface methodology and artificial neural networks are used to develop the empirical model for pressure rise per wavelength, frictional forces on the upper wall and frictional forces on the lower wall.FindingsThe empirical model demonstrates an excellent fit with a coefficient of determination reaching 100% for responses, frictional forces on the upper wall and frictional forces on the lower wall and 99.99% for response, for pressure rise per wavelength. It is revealed through the sensitivity analysis that pressure rise per wavelength, frictional forces on the upper wall and frictional forces on the lower wall are most sensitive to the permeability parameter at all levels.Originality/valueThe objective of this study is to use artificial neural networks simulation and analyze the sensitivity of electroosmotic peristaltic motion of non-Newtonian fluid with the effect of chemical reaction.

Enhancement the electrical and linear/nonlinear optical properties of ZnCo2O4 through Al3+doping

In this work, ZnCo2O4 samples doped with Al3+ were prepared by the hydrothermal method. Synchrotron x-ray diffraction, FTIR, SEM and EDX techniques were used to investigate the structure, microstructure, morphology, and composition of ZnCo2-xAlxO4 samples. Rietveld analysis revealed a nearly inverse structure for the undoped ZnCo2O4. The degree of inversion is increased upon increasing the Al3+ doping content. Al ions preferentially occupy the octahedral B-site. The optical band gaps of ZnCo2−xAlxO4 samples are 1.9, 1.8 and 1.91 eV for x = 0, 0.1 and 0.2, respectively. Different empirical models were used to obtain the refractive index of the different samples using their corresponding optical band gaps. The increase in non-linear optical values in the sample with x = 0.1 suggested that this sample could be used in a variety of photonic applications. The effects of frequency and temperature on the dielectric permittivity, impedance and electrical modulus of different samples were explored. All samples exhibited the non-Debye relaxation phenomenon. The relaxation time of each sample is affected with the frequency and temperature. The Cole-Cole curve is employed to reduce uncertainty regarding the electrical characteristics of these ZnCo2−xAlxO4 samples induced by grain boundaries or bulk grain. The substitution of Al3+ ions can regulate the conductivity of the ZnCo2O4 sample.

An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations

We extend current models of the halo occupation distribution (HOD) to include a flexible, empirical framework for the forward modeling of the intrinsic alignment (IA) of galaxies. A primary goal of this work is to produce mock galaxy catalogs for the purpose of validating existing models and methods for the mitigation of IA in weak lensing measurements. This technique can also be used to produce new, simulation-based predictions for IA and galaxy clustering. Our model is probabilistically formulated, and rests upon the assumption that the orientations of galaxies exhibit a correlation with their host dark matter (sub)halo orientation or with their position within the halo. We examine the necessary components and phenomenology of such a model by considering the alignments between (sub)halos in a cosmological dark matter only simulation. We then validate this model for a realistic galaxy population in a set of simulations in the Illustris-TNG suite. We create an HOD mock with Illustris-like correlations using our method, constraining the associated IA model parameters, with the between our model’s correlations and those of Illustris matching as closely as 1.4 and 1.1 for orientation–position and orientation–orientation correlation functions, respectively. By modeling the misalignment between galaxies and their host halo, we show that the 3-dimensional two-point position and orientation correlation functions of simulated (sub)halos and galaxies can be accurately reproduced from quasi-linear scales down to . We also find evidence for environmental influence on IA within a halo. Our publicly-available software provides a key component enabling efficient determination of Bayesian posteriors on IA model parameters using observational measurements of galaxy-orientation correlation functions in the highly nonlinear regime.

Factors affecting the adoption of high technology in vegetable production in Hanoi, Vietnam

High-tech vegetable production is becoming a priority in agricultural development in Vietnam in the context of digital economic development. This study aims at identifying factors involving the adoption of high technology in vegetable production by local farmers in Hanoi. We used the theory of planned behavior and other farmers’ personal, social and economic factors to develop empirical model and hypotheses. Primary data was collected from a survey of 450 vegetable producers in Hanoi using cluster sampling method combined with random selection. Then, binary logit model was used to analyze the impact of influencing factors. Results showed that there were 7 factors having significant influences the decision to apply technology in vegetable production of farmers including attitude on high tech production, access to information, size of farm, member of extension organization, education level, access to credit and perceived behavior control, in which attitude variable was the most influential factor. Main management implications raised included enhancing access to technological information, providing demostration visits, giving more extension services, improving social inclusion and implementing hi- tech training for farmers in vegetable production.

An Unmet goal? A Scale Development and Model test of the role of Inclusive Leadership

AbstractThere is a lack of evidence on whether inclusive leadership (IL) truly fosters inclusion for those in historically marginalized groups. Further, a conceptually up-to-date and practically useful measure of IL is lacking. Thus, in two separate phases, we first present a newly developed measure of IL and then test an empirical model. In Phase 1, results from five demographically diverse samples demonstrate reliability and validity evidence of a 10-item IL scale. In Phase 2, use this scale to examine how IL may support members of historically marginalized groups by fostering (a) interpersonal behaviors that uphold inclusive work environments (allyship, antiracism) and (b) individual experiences of inclusion (workgroup inclusion, authenticity). Path analysis results from a multi-wave study support the influence of IL on these outcomes and also demonstrate support for IL’s indirect effects on outcomes that may be disproportionately high (emotional exhaustion) and low (empowerment) for members of marginalized groups. Moderation analyses reveal many of the hypothesized relationships are similar across groups representing marginalized identities on the bases of race, sex, and the intersection of race and sex. These results add evidence to the importance of IL for fostering inclusive workplaces, especially for those who face the greatest barriers to inclusion.

Effect of 2-hydroxyethylammonium carboxylate protic ionic liquids on the solubility and cytotoxicity of indomethacin

Recently, there is a particular interest to utilize protic ionic liquids (PILs) in drug solubility. This study is exploring the effect of three protic ionic liquids (PILs) based on 2-hydroxyethylammonium carboxylate [2-hydroxyethylammonium acetate (MEAA), 2-hydroxyethylammonium lactate (MEAL), and 2-hydroxyethylammonium propionate (MEAP)] on the solubility of the very poorly soluble drug in water, indomethacin (IMC). The shake flask method was used to measure the experimental solubility of IMC at the different temperatures range (298.15–313.15) K. The results demonstrate significantly enhancment the solubility of IMC in PILs compared to pure water, with an approximate increase of 200 times. The experimental solubility data have been correlated using the empirical models which showed the performance as the order: Modified Apelblat–Jouyban–Acree > Van’t Hoff–Jouyban–Acree > Modified Apelblat equations and also the performance for the Wilson model indicated as the order (absolute relative deviation): 2-hydroxyethylammonium acetate (3.030) > 2-hydroxyethylammonium propionate (3.239) > 2-hydroxyethylammonium lactate (7.665). Then the thermodynamic dissolution properties were obtained by usage of Gibbs and Van’t Hoff equations to investigate the thermodynamic behavior of the IMC in the aqueous solution PILs. Eventually, the cytotoxicity of the co-solvents (PILs) under study was evaluated using a standard MTT assay. The results showed that the cell viability percentage increased in the following order: MEAA < MEAP < MEAL. These findings indicated that these PILs had low to moderate toxicity. It is noteworthy that the functional groups of the anions were not the only determinant factor of the cytotoxicity. Other factors encompassing concentration, exposure time, and cell line characteristics also had significant effects.

Study of wellbore instability in shale formation considering the effect of hydration on strength weakening

Shale formations often contain a high proportion of clay minerals, which, upon contact with drilling fluid, undergo hydration expansion. This leads to wellbore instability, a problem that poses significant challenges globally. This study aims to investigate the variation of mechanical properties of shale with respect to hydration time. We employ an empirical model that relates shale strength parameters to the time of drilling through geological formations. Additionally, we consider both shear failure along the wellbore boundary and shear sliding along bedding planes in the analysis. We establish a predictive model for wellbore instability in shale formations. The model quantitatively analyzes the variation of wellbore collapse pressure with drilling time. The research findings indicate that, when the influence of bedding is considered, both the wellbore collapse pressure and the optimal well trajectory undergo significant changes, in addition, for some wellbore trajectories, the collapse pressure can increase by more than 30%. Therefore, it is essential to account for the influence of bedding in wellbore stability analysis in shale formations. As the bedding dip angle changes, both the numerical values and distribution range of wellbore collapse pressure and the optimal well trajectory change noticeably. Changes in bedding dip direction, however, do not affect the numerical values of collapse pressure but do influence the distribution region of the optimal well trajectory. Thus, in wellbore trajectory design within shale formations, it is crucial to determine the orientation of bedding and adjust the well trajectory accordingly to enhance wellbore stability. Furthermore, shale hydration does not impact the optimal well trajectory for a block, but with prolonged hydration, the minimum drilling fluid density required to maintain wellbore stability gradually increases. This suggests that hydration intensifies the weakening effect on bedding plane strength. The research results are helpful to understand the effect of hydration on shale wellbore stability and ensure shale wellbore stability during drilling cycle.