Constant Stress Model Research Articles

Instability in Computational Models of Vascular Smooth Muscle Cell Contraction

PurposeThrough their contractile and synthetic capacity, vascular smooth muscle cells (VSMCs) can regulate the stiffness and resistance of the circulation. To model the contraction of blood vessels, an active stress component can be added to the (passive) Cauchy stress tensor. Different constitutive formulations have been proposed to describe this active stress component. Notably, however, measuring biomechanical behaviour of contracted blood vessels ex vivo presents several experimental challenges, which complicate the acquisition of comprehensive datasets to inform complex active stress models. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive datasets.MethodsFirst, we prove analytically that a subset of constitutive active stress formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly for large contractile deformations. Second, using experimental literature data, we present two case studies where these formulations are used to capture the contractile response of VSMCs in the presence of (1) limited and (2) extensive contraction data.ResultsWe show how limited contraction data complicates selecting an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours.ConclusionOur data provide a useful reference for selecting an active stress model which balances the trade-off between accuracy and available biomechanical information. Whilst complex physiologically motivated models’ superior accuracy is recommended whenever active biomechanics can be extensively characterised experimentally, a constant 2nd Piola-Kirchhoff active stress model balances well accuracy and applicability with sparse contractile data.

Estimation of the constant-stress model with bathtub-shaped failure rates under progressive type-I interval censoring scheme

This paper investigates constant-stress accelerated life tests interrupted by a progressive type-I interval censoring regime. We provide a model based on the Chen distribution with a constant shape parameter and a log-linear connection between the scale parameter and stress loading. Inferential methods, whether classical or Bayesian, are employed to address model parameters and reliability attributes. Classical methods involve the estimation of model parameters through maximum likelihood and midpoint techniques. Bayesian approximations are achieved via the utilization of the Metropolis–Hastings algorithm, Tierney-Kadane procedure, and importance sampling methods. Furthermore, we engage in a discourse on the estimation of confidence intervals, making references to both asymptotic confidence intervals and credible intervals. To conclude, we furnish a simulation study, a corresponding discussion, and supplement these with an analysis of real data.

Inference of Constant-Stress Model of Fréchet Distribution under a Maximum Ranked Set Sampling with Unequal Samples

Inference of Constant-Stress Model of Fréchet Distribution under a Maximum Ranked Set Sampling with Unequal Samples

Reliability analysis at usual operating settings for Weibull Constant-stress model with improved adaptive Type-Ⅱ progressively censored samples

<abstract><p>An improved adaptive Type-Ⅱ progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor.</p></abstract>

Building the Space Elevator Tether

A simple Earth-based space elevator consists of a cable or tether extending from the surface to well beyond geosynchronous orbit. A climber grips the tether, pulling itself upward and delivering payload to space. For a space elevator to be feasible, the material from which the tether is built must be strong enough that the tether can support itself and any climbers that ascend it. Three such materials exist today and their industrial-scale production seems near at hand. These materials are compared and, based on previous studies, required improvements for each are listed. The material properties, along with the load, determine the shape and mass of the tether. Two example tether shapes are shown: one using the constant stress model and another which takes into account atmospheric winds and orbital debris. Options for tether construction are discussed. These are influenced by the material fabrication process, the way in which materials are combined and arranged in the tether and how much of the fabrication takes place on Earth or in space. Keywords: Space Elevators, Strong Materials, Tether Construction

Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution

Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution

Assessment of the thermal tissue models for the head and neck hyperthermia treatment planning

PurposeTo compare different thermal tissue models for head and neck hyperthermia treatment planning, and to assess the results using predicted and measured applied power data from clinical treatments. MethodsThree commonly used temperature models from literature were analysed: “constant baseline”, “constant thermal stress” and “temperature dependent”. Power and phase data of 93 treatments of 20 head and neck patients treated with the HYPERcollar3D applicator were used. The impact on predicted median temperature T50 inside the target region was analysed with maximum allowed temperature of 44 °C in healthy tissue. The robustness of predicted T50 for the three models against the influence of blood perfusion, thermal conductivity and the assumed hotspot temperature level was analysed. ResultsWe found an average predicted T50 of 41.0 ± 1.3 °C (constant baseline model), 39.9 ± 1.1 °C (constant thermal stress model) and 41.7 ± 1.1 °C (temperature dependent model). The constant thermal stress model resulted in the best agreement between the predicted power (P = 132.7 ± 45.9 W) and the average power measured during the hyperthermia treatments (P = 129.1 ± 83.0 W). ConclusionThe temperature dependent model predicts an unrealistically high T50. The power values for the constant thermal stress model, after scaling simulated maximum temperatures to 44 °C, matched best to the average measured powers. We consider this model to be the most appropriate for temperature predictions using the HYPERcollar3D applicator, however further studies are necessary for developing of robust temperature model for tissues during heat stress.

Constant and cyclic chronic heat stress models differentially influence growth performance, carcass traits and meat quality of broilers

This experiment compared the effects of 2 chronic heat stress (HS) models, constant (coHS), and cyclic (cyHS), on broiler performance, carcass characteristics, and meat quality. A total of 720 male chicks from a Cobb 500 line were placed in 12 environmentally controlled chambers divided into 2 pens of 30 birds. Before the experimental HS models were applied, chamber temperatures were gradually decreased from 32°C at placement to 24°C on d 20. From 20 to 41 d, 4 chambers were set to 35°C (coHS), and 4 chambers were set to 35°C for 12 h and 24°C for the next 12 h (cyHS). Four thermoneutral chambers were maintained at 24°C with half of the birds pair-fed to equalize feed intake (FI) with coHS birds (TN-coPF) and half fed ad-libitum (TN-al). From 20 to 41 d, FI and BW gain (BWG) of cyHS, coHS and TN-coPF birds were decreased (P < 0.001), whereas feed conversion ratio (FCR) was increased (P < 0.001) for coHS and TN-coPF birds compared with TN-al birds. The overall BWG and FCR of coHS birds were lower (P < 0.001) than TN-coPF birds. Both HS models reduced (P < 0.001) carcass weight, pectoralis major yield, total breast meat yield, and increased (P < 0.001) wing yield relative to TN-al birds, with each of these measurements more impacted by coHS than by cyHS. Pair-fed birds had lower (P < 0.001) fat pad and a higher total breast meat yield than coHS birds. They also had the lowest (P < 0.001) pectoralis major ultimate pH and yellowness, and these parameters were lower (P < 0.001) for coHS birds than for TN-al birds. Both HS models reduced (P < 0.001) the incidence of woody breast and white striping. Thus, these data indicate that the detrimental effects of HS cannot be entirely explained by reduced FI and that HS per se affects metabolic pathways associated with muscle and lipid accretion in broilers.

Estimation of Lindley constant-stress model via product of spacing with Type-II censored accelerated life data

Accelerated Life Test has been introduced as a tool to aid in obtaining sufficient failure time data of test units quickly and extrapolating lifetime information under use conditions. When the lifetime of units is distributed by the Lindley model, the estimations for the unknown parameters and the reliability function are established based on two frequentist methods and Bayesian method of estimation using Type-II censored data under constant-stress accelerated life test. In the frequentist methods, besides, the conventional likelihood-based estimation, another competitive method, known as the maximum product of spacing method is proposed for estimating the parameters and the reliability function under normal conditions as an alternative approach to the common likelihood method. In Bayesian estimation, both maximum likelihood and maximum product of spacing-based Bayesian estimates are discussed for unknown parameters as well as the reliability function. Moreover, the approximate confidence intervals and highest posterior density credible intervals of the parameters and reliability function are also obtained. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates. Finally, to demonstrate the proposed methodology, two real-life accelerated life test data are considered to show the applicabilities of the proposed methods.

Analysis for constant-stress model on multicomponent system from generalized inverted exponential distribution with stress dependent parameters

In this paper, inference of multicomponent system is presented under constant-stress accelerated life test. When the lifetime of the components of the multicomponent system follows a generalized inverted exponential distribution (GIED), different from standard extrapolation approach where only the scale parameter depends on the stress conditions, a life-stress model is proposed assuming that both parameters of the GIED are nonconstant and depend on the stress. The model parameters are estimated along with the existence and uniqueness via maximum likelihood method, and the survival function of the multicomponent system is extrapolated at normal use condition. The approximate confidence intervals are further constructed using the asymptotic distribution theory and delta technique. Furthermore, another alternative generalized estimates are also constructed by using proposed pivotal quantities for comparison. In addition, likelihood ratio testing is presented as a complementary by comparing the life-stress models with nonconstant and constant parameters. Finally, simulation studies and a real data example are carried out for illustrations, and the results indicates that the proposed generalized approach is superior to conventional likelihood estimation.

Reliability analysis of log-normal distribution with nonconstant parameters under constant-stress model

Reliability analysis of log-normal distribution with nonconstant parameters under constant-stress model

Inference for constant-stress Weibull competing risks model under generalized progressive hybrid censoring

In this paper, accelerated life test is considered when the latent failure times follow Weibull competing risks models. When both scale and shape parameters are nonconstant and affected by operating stress, inference is discussed for a constant-stress model under a generalized progressive hybrid censoring. Maximum likelihood estimates together with existence and uniqueness are established, and the approximate confidence intervals for unknown parameters are proposed based on the asymptotic theory. Further, when the distributions of failure causes have common shape or scale parameters, associated point and interval estimates are also proposed. In addition, to compare the equivalence of the parameters of different Weibull competing risks, likelihood ratio tests for interested hypotheses are presented for complementary. Finally, extensive numerical studies and a real-life example are provided for illustrations.

Inference for a constant-stress model under progressive type-I interval censored data from the generalized half-normal distribution

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed.

Using a composite flow law to model deformation in the NEEM deep ice core, Greenland – Part 1: The role of grain size and grain size distribution on deformation of the upper 2207 m

Abstract. The effect of grain size on strain rate of ice in the upper 2207 m in the North Greenland Eemian Ice Drilling (NEEM) deep ice core was investigated using a rheological model based on the composite flow law of Goldsby and Kohlstedt (1997, 2001). The grain size was described by both a mean grain size and a grain size distribution, which allowed the strain rate to be calculated using two different model end-members: (i) the microscale constant stress model where each grain deforms by the same stress and (ii) the microscale constant strain rate model where each grain deforms by the same strain rate. The model results predict that grain-size-sensitive flow produces almost all of the deformation in the upper 2207 m of the NEEM ice core, while dislocation creep hardly contributes to deformation. The difference in calculated strain rate between the two model end-members is relatively small. The predicted strain rate in the fine-grained Glacial ice (that is, ice deposited during the last Glacial maximum at depths of 1419 to 2207 m) varies strongly within this depth range and, furthermore, is about 4–5 times higher than in the coarser-grained Holocene ice (0–1419 m). Two peaks in strain rate are predicted at about 1980 and 2100 m depth. The prediction that grain-size-sensitive creep is the fastest process is inconsistent with the microstructures in the Holocene age ice, indicating that the rate of dislocation creep is underestimated in the model. The occurrence of recrystallization processes in the polar ice that did not occur in the experiments may account for this discrepancy. The prediction of the composite flow law model is consistent with microstructures in the Glacial ice, suggesting that fine-grained layers in the Glacial ice may act as internal preferential sliding zones in the Greenland ice sheet.

Bayesian prediction of future observations from weighted exponential distribution constant-stress model based on Type-II hybrid censored data

In this paper, the problem of Bayesian prediction intervals for a future observations from weighted exponential distribution is concerned. Constant-stress partially accelerated life test under Type-II hybrid censoring scheme of the observed data is used. One- and two-sample Bayesian prediction intervals for a future observations based on Type-II hybrid censored data are derived. Markov Chain Monte Carlo (MCMC) technique is used to find Bayesian predictive intervals because one- and two-sample Bayesian predictive survival function cannot be obtained in closed-form. Finally, some numerical results are presented to illustrate all the inferential results developed in this paper.

Regional stochastic ground-motion model for low to moderate seismicity area with variable seismotectonic: application to Peninsular India

A new stochastic ground motion prediction equation (GMPE) for low and diverse seismicity region, i.e., Peninsular India has been derived for a wide range of magnitude (\(M_{w}\) 4–8) and distance (10–500 km). Source, path, and site terms have been determined by comparing the recorded and simulated response spectra using derived values from the literature. Uncertainty has been assessed through simulation by random sampling of the corresponding distribution of all the input parameters. To capture the non-uniform seismicity of Peninsular India, GMPE has been derived using constant stress and variable stress model. The synthetic data has been regressed using linear mixed-effect model algorithm by determining the functional form that is compatible for magnitude and distance scaling. Sensitivity analysis has been used in determining the impact of uncertainty of each input parameter on GMPE standard deviation. Further, new GMPEs have been validated using the recorded ground-motion data.

Estimation of exponential population with nonconstant parameters under constant-stress model

Accelerated life test (ALT) was introduced which provides a feasible and efficient way by testing units at higher-than-use condition. This paper considers inference of constant-stress ALT model for exponential population under a general assumption that both exponential scale and location parameters are nonconstant and follow log-linear life-stress model with stress level. Under progressive Type-II censoring, maximum likelihood and pivotal quantities based point estimates for unknown coefficient parameters are proposed. Confidence interval estimates are also constructed by using asymptotic theory and bootstrap techniques. Simulation study and an illustrative example are provided for illustrative purpose. • Inference for nonconstant exponential parameters is studied in constant-stress model. • Pivotal based method is proposed for parameter estimation. • Bootstrap and asymptotic intervals are investigated. • The proposed methods can be extended to more other cases. • Example for the oil breakdown times of insulating fluid is considered.

A simplified method for predicting burst pressure of type III filament-wound CFRP composite vessels considering the inhomogeneity of fiber packing

The present study proposes a method to predict the burst pressures (BPs) of type III filament winding carbon fiber-reinforced plastic (CFRP) composite pressure vessels considering the inhomogeneity of carbon fiber packing through experimental work and simplified mechanical models reflecting the evolution of local damage in the CFRP layers. Vessels that had different carbon fiber volume fractions (Vfs) were prepared and tested to measure their BPs. The inhomogeneity of carbon fiber packing was evaluated using Weibull probability based on the microscopic observation of CFRP cross-sections in the virgin vessels. Detailed stress analyses of pressurized composite vessels considering the carbon Vf were conducted. Unstable fracture of the hoop layer was demonstrated by a simplified mechanical model combined with the inhomogeneity of the carbon Vf and de-bonding between the fiber and matrix. About 20% difference in the BP was measured between tested vessels with and without glass fiber-reinforced plastic layers over CFRP layers. The proposed method for predicting the BP based on the constant stress model enables consideration of the development of local fiber breaking prior to catastrophic fracture and to quantitatively estimate the change in the BP due to the difference in Vf.

Degradation model analysis of two-component series and parallel systems

ABSTRACTMany high-reliability and long-life products to form a system in series or parallel. Based on the assumption that the degradation process of the performance characteristics is Wiener procession, this article proposes a degradation model of the series and parallel systems. Here, a bivariate constant-stress degradation model is established, assuming Wiener procession and utilizing the copula function to describe the correlation among the performance characteristics. The adoption of an inference function for margins method for estimating the model's parameter ensures the accuracy of the estimation results as well as reduces the difficulties of parameter estimation effectively. In the numerical example research, we estimate the parameters of the degradation models of Gaussian Copula and Frank Copula using the rubidium spectral lamp as an example. Furthermore, we also adopt the Monte Carlo simulation method on the effects of copula function's estimation. We find that the Frank Copula more applicable than Gaussian Copula. For the two-component series and parallel systems composed by the rubidium spectral lamp, we get the reliability curve, the failure probability density curve and the MTBF value of the series system and parallel system. These curves are compared and analysed to achieve the conclusions.

Model development and analysis of the evolution of coal permeability under different boundary conditions

Coal permeability is an important parameter for coalbed methane (CBM) production and CO2-enhanced coalbed methane (ECBM) recovery. Coal permeability is mainly controlled by the structure of the coal. In this study, based on the pore-elasticity principle and the coal matrix-fracture interactions, we developed an analytical coal permeability model and its five forms under the corresponding specific boundary conditions, and four of them are validated by matching the corresponding field data or experimental data. The study presents a discussion of the permeability evolution for the different forms. The results show that the coal permeability under constant volume and constant effective stress conditions are controlled by the matrix sorption deformation and that the coal permeability under uniaxial strain and constant external stress conditions is governed by both the effective stress and the matrix sorption deformation. The constant volume model may be a special form of the constant effective stress model. For the same pressure drawdown, the permeability that is predicted under constant external stress conditions decreases more than that the permeability that is predicted under uniaxial strain conditions, and the permeability change induced by the matrix sorption deformation depended on the values of the internal swelling partition. The boundary conditions are important to the model, and different boundary conditions will lead to different evolutions of coal permeability. The permeability model can only be used to predict the evolution of permeability under the corresponding boundary conditions.