Empirical Nonlinear Model Research Articles

A Comparative Analysis of the Solar Ultraviolet Spectral Irradiance Measured from Earth and Mars: Toward a General Empirical Model for the Study of Planetary Aeronomy

Accurate estimation of the solar vacuum ultraviolet irradiance between 0.1 and 200 nm is critical for the study of planetary aeronomy. Previous empirical models have relied on a limited number of reference spectra, or on multiple data sets with various degrees of uncertainty, and on an empirical selection of solar proxies. Here we propose a novel method for the development of empirical models based on Fourier transform and least-squares fitting of the long-term measurements from the Solar EUV Experiment on the Thermosphere Ionosphere Mesosphere Energetics and Dynamics mission. A Fourier transform analysis is performed to examine a large number of solar proxies, which reveals that the solar radio flux at 10.7 cm and the solar Lyα flux at 121.6 nm are better proxies for solar irradiance below and above ∼120 nm, respectively. Using these two proxies, a nonlinear empirical model is developed through Fourier transform and least-squares fitting of solar irradiance measurements, which can reproduce the solar irradiance with uncertainties of only ∼1%–2% above ∼120 nm, ∼2%–4% within ∼45–120 nm, and ∼4%–8% below ∼45 nm. Comparison with measurements from the Extreme Ultraviolet Monitor on the Mars Atmosphere and Volatile Evolution mission indicates that the solar irradiance at Mars can be predicted with uncertainties of less than ∼8% by geometric extrapolation of the solar irradiance measured from Earth, provided that the measurements from Earth can be calibrated accurately. Our study provides a general method for the development of empirical models using long-term observations in planetary aeronomy.

Combining observed linear basin amplification factors with 1D nonlinear site-response analyses to predict site response for strong ground motions: Application to Wellington, New Zealand

This study develops a method for estimating site amplification that combines instrumentally observed site-specific amplification factors with adjustment factors from nonlinear site-response analyses. This approach provides estimates of site response for large-strain motions based on observations and sophisticated nonlinear modeling. A database of weak-to-moderate intensity ground motions recorded in three basins of Wellington, New Zealand is used to study the observed site amplification. A subset of nine strong-motion stations was selected to perform nonlinear site-response analyses with scaled strong ground motions to assess the influence of nonlinearity on site amplification factors and demonstrate the approach. Different shear-wave velocity ( VS) profiles, constitutive models, and modeling approaches (e.g. one-dimensional (1D) site-response analyses vs empirical [Formula: see text]-based approaches) are used to quantify the sensitivity and modeling uncertainty in the nonlinear site-response analyses. It was found that for soft sites subjected to strong ground motions, there may be a decrease in spectral acceleration amplification factors for periods up to approximately 2 s, relative to the expected linear site response. For longer periods, there is little to no amplification from the effects of soil nonlinearity. However, at stiffer sites, which generally experience less basin amplification in observations, there may be moderate amplification at longer periods when nonlinearity is considered due to softening of the soil profile. Empirical ground-motion models were found to under-represent the observed amplification between basin sites and the nearby reference site, especially at intermediate to long periods, corresponding to resonant frequencies of these basin sites. In addition, the empirical nonlinear site amplification models ([Formula: see text]-based) were found to deviate from nonlinear analyses at large strains, where such models are poorly constrained due to such a limited number of observations.

High-amplitude effect on Richtmyer–Meshkov instability at a single-mode heavy–light interface

An experimental study is conducted to explore the high-amplitude effect on Richtmyer–Meshkov instability (RMI) at a single-mode heavy–light interface. A wide range of scaled initial amplitude (ka0, where k and a0 are perturbation wavenumber and initial amplitude, respectively) is considered. Qualitatively, nonstandard (standard) indirect phase inversion occurs in experiments with high (low and moderate) ka0. The nonstandard indirect phase inversion exhibits a complex process, and the interface mixing width does not reduce to near zero. Quantitatively, the linear model poorly (accurately) predicts the post-phase-inversion linear amplitude growth rate when ka0 is high (low and moderate). Additionally, a representative theoretical reduction factor fortuitously evaluates the high-amplitude effect on the post-phase-inversion linear amplitude growth rate well. The high-amplitude effect significantly alters the nonlinear evolution law, which differs from the case of RMI at a light–heavy interface. None of the considered nonlinear models can accurately predict the amplitude evolution under all ka0 conditions, regardless of whether their expressions are related to ka0 or not. Based on the current experimental results, an empirical nonlinear model is proposed to describe RMI at a single-mode heavy–light interface across a wide range of ka0 conditions.

Experimental study on Richtmyer–Meshkov instability at a light–heavy interface over a wide range of Atwood numbers

Richtmyer–Meshkov instability (RMI) at a light–heavy single-mode interface over a wide range of post-shock Atwood numbers $A_1$ is studied systematically through elaborate experiments. The interface generation and $A_1$ variation are achieved by the soap-film technology and gas-layer scheme, respectively. Qualitatively, the nonlinear interface evolution features, including spike, bubble and roll-up structures, are more significant in RMI with higher $A_1$ . Quantitatively, both the impulsive model and an analytical linear model perform well in predicting the linear growth rate under a wide range of $A_1$ conditions. For the weakly nonlinear stage, the significant spike acceleration occurring when $A_1$ is high, which is observed experimentally for the first time, results in the evolution law of RMI with high $A_1$ being different from the counterpart with low or intermediate $A_1$ . None of the considered nonlinear models is found to be applicable for RMI under all $A_1$ conditions, and the predictive capabilities of these models are analysed and summarized. Based on the present experimental results, an empirical nonlinear model is proposed for RMI over a wide range of $A_1$ . Further, modal analysis shows that in RMI with high (low or intermediate) $A_1$ , high-order harmonics evolve rapidly (slowly) and cannot (can) be ignored. Accordingly, for RMI with high (low or intermediate) $A_1$ , the modal model proposed by Zhang & Sohn (Phys. Fluids, vol. 9, 1997, pp. 1106–1124) is less (more) accurate than the one proposed by Vandenboomgaerde et al. (Phys. Fluids, vol. 14, 2002, pp. 1111–1122), since the former ignores perturbation solutions higher than fourth order (the latter retains only terms with the highest power in time).

Direct parameter extraction method of EEHEMT nonlinear model for InP HEMT

AbstractA direct parameter extraction method of EEHEMT nonlinear empirical model is proposed in this paper. An improved DC model is also presented by considering the channel length modulation parameter () as a function of gate‐to‐source voltage. Model verification is carried out by comparison of measured and simulated current–voltage characteristics and S‐parameters. Good agreement is obtained between the measured and modeled results for 2 × 15 μm gatewidth (number of gate fingers × gatewidth) 70‐nm gatelength InP high electron mobility transistors (HEMT). An increased accuracy in modeling the I–V and RF characteristics is also obtained in the proposed model, compared with the conventional one.

Modeling hydraulic fracture fluid efficiency in tight gas reservoirs using non-linear regression and a back-propagation neural network

ABSTRACT This study introduces a back-propagation (BP) neural network model and a regression model for estimating the fracture fluid efficiency based on a data set consisting of 1261 staged and ramped simulation runs of tight gas reservoirs subjected to hydraulic fracturing treatment. Data were generated using a 3-D commercial simulator which is a versatile software portfolio that models many well configurations, proppant placement, and fracture geometries. The BP network inputs consist of shear rate/fracture conductivity ratio, the injection rate, reservoir permeability, formation closure stress, reservoir thickness, effective viscosity, and fracture height. The neural network model was able to generate satisfactory estimates of the fracture fluid efficiency for the training dataset, and for the blind testing data. An average error of approximately 2.5% was obtained for the training set, and an average error of 3% was obtained for the testing set. An empirical non-linear regression model has been constructed based on dimensionless groups derived by applying dimensional analysis to a set of variables consisting of the maximum fracture width, fracture length, fracture height, effective viscosity, shear rate/fracture conductivity ratio, reservoir thickness, injection rate, reservoir permeability, and formation closure stress. The average error for estimating the fluid efficiency using the non-linear regression empirical model was approximately 6.17%. Since the non-linear regression model has an explicit formulation, it is easier to apply than the neural network model. The empirical regression model estimates of the fluid efficiency appeared to be unbiased and were more precise than those estimates obtained using either the KGD or the PKN 2-D models. The introduced BP model and the non-linear regression model offer fast and inexpensive alternatives to the application of three-dimensional simulators for estimating the fluid efficiency.

Geological, geophysical and mathematical analysis of synthetic bulk density logs around the world- Part II- the use of non-linear regression on empirical parameters estimation

The bulk density is a helpful petrophysics parameter, which is used in hydrocarbon oil exploration and other geophysics areas such as gravimetry and seismic. In this second part of the research, we applied a nonlinear regression to determine the coefficients of an empirical nonlinear model. The nonlinear model analyzed was the modified Gardner's traditional model as modified by Oloruntobi and Butt. Here, the inversion was performed based on the Levenberg-Marquardt method. The linear and nonlinear methods are then compared, observing the influence of geological age, geological, geophysical, and tectonic factors on the mathematical and physical aspects. The analysis of models proposed by the different authors under study was made to determine the most efficient mathematical regression for the construction of density logs. The density was estimated from the values of VSH and VP for the Oloruntobi and Butt formulation. The study results show that it is impossible to determine a stable value for the parameters (either in the linear or non-linear model) that can be applied to wells anywhere on the planet. The value of the parameters is affected by different factors that change according to the rock's content and the conditions that affect the study area. However, it is possible to determine values for a specific study zone with a margin of error of <1% (Mean Square Error-MSE). This error is lower than when compared with results from linear regression.

Development of non-linear empirical models to estimate the abundance of carbapenem resistance genes during anaerobic digestion of wastewater sludge at mesophilic and thermophilic temperatures

Antibiotic resistance genes (ARGs) encode resistance against antibiotic drugs in bacteria. Carbapenem antibiotics are one of the last lines of defence against bacterial infections and carbapenem resistance genes (CRGs) accumulate in sludge during wastewater treatment. Anaerobic digestion is the most used method for sludge treatment, and it is important to know the abundance and removal of CRGs in anaerobically digested sludge before land application due to their public health relevance. However, gene quantification is time-consuming, costly, and sensitive to contamination. Previous research indicates a nexus between ARGs, solids, and nutrients in sludge. This study aimed to develop multiple regression models to estimate the abundance of CRGs from solids and nutrient concentrations in sludge, which are routinely measured for the monitoring and design of anaerobic digesters. Batch and continuous reactors were operated at mesophilic and thermophilic temperatures. Sludge samples were taken during digestion. CRGs (blaGES, blaOXA-48 and blaIMP-27), 16S rRNA and integron class 1 were quantified. Solids, chemical oxygen demand, orthophosphate and ammonia were measured as well. Anaerobic digestion reduced the quantity of the genes. First and second-order Kinetic rate constants (K1 and K2) were affected by temperature, and K1 absolute value followed the order blaOXA-48 > blaGES > Int 1. Multiple regression modelling was conducted in linear (LM) and non-linear (NLM) modes. This study presents the first NLM models to simulate the quantities of CRGs during anaerobic digestion of wastewater sludge at mesophilic and thermophilic temperatures. Adjusted R2 ranged 0.352–0.988 and 0.916–0.996 for the LM and NLM models, respectively. NLM models estimated the gene abundance more accurately than LM models, and they may be useful for researchers and practitioners to estimate the removal rate of target genes under different operational conditions.

Hydrodynamic characteristics and application of tuned liquid dampers with internal damping devices

SummaryThe hydrodynamic characteristics of rectangular tanks with internal damping devices, including baffles and paddles, are investigated using shaking table tests excited by colored noise. The complex second‐order blind identification method is employed to decouple fluid sloshing responses and to obtain mode shapes. The modal frequency and damping ratio are also identified by the modified Bayesian spectral density approach. The influence of baffle angle, paddle width, liquid depth, and excitation amplitude on the natural frequency and damping ratio of tuned liquid dampers (TLDs) is analyzed. Results show that the natural frequency is reduced due to the added mass produced by the damping devices, and the reduction increases gradually with the increase in the size of the damping devices, indicating that the influence of the added mass should be considered in the design. This result is essentially different from the conclusion of the existing finding that the modal frequency of TLD increases continuously with the increase in the baffle angle. Therefore, the tuning of TLD cannot be realized by rotating the baffles. Moreover, the damping ratio of TLD with paddles shows a nonlinear relationship with the fluid response. The nonlinear empirical model fitted by the test results can predict the damping ratio with high accuracy and can be used in the preliminary design of TLD for the wind‐induced vibration control of super‐tall buildings.

Efficient Fluoride Removal by a Fixed-Bed Column of Self-Assembled Zr(IV)-, Fe(III)-, Cu(II)-Complexed Polyvinyl Alcohol Hydrogel Beads.

Fixed-bed column adsorption studies are performed with metal-complexed polyvinyl alcohol (PVA) hydrogel beads to remove fluoride from groundwater. The fixed-bed column (bed height = 8 ± 0.2 cm) of copper–zirconium–PVA (PCZH), zirconium–PVA (PZH), and iron–zirconium–PVA (PFZH) hydrogel beads have equilibrium fluoride removal capacities of 17.26 ± 0.05, 31.67 ± 0.05, and 11.84 ± 0.05 mg g–1 from a 10 ± 0.20 mg L–1 fluoride solution of pH 6.5 maintained at a flow rate of 1 ± 0.01 mL min–1. The breakthrough curves for fluoride adsorption are analyzed by non-linear empirical models of Thomas, Bohart–Adams, Yoon–Nelson, and semi-empirical bed depth service time models. The maximum fluoride adsorption capacities obtained from the Thomas model are 25.66 ± 0.05, 38.17 ± 0.05, and 13.75 ± 0.05 mg g–1 for PCZH, PZH, and PFZH. Moreover, the column of PZH (bed height = 4 ± 0.2 cm) removes about 1.67 ± 0.05 mg g–1 of fluoride from the alkaline groundwater sample with high total dissolved solids containing 2.84 ± 0.20 mg L–1 fluoride maintained at a flow rate of 0.5 ± 0.01 mL min–1. The fluoride removal efficiency decreases marginally (<1 ± 0.02%) in the presence of interfering ions such as chlorides, sulfates, phosphates, bicarbonates, and nitrates. Furthermore, the fixed-bed column (bed height = 4 ± 0.2 cm) of PCZH, PZH, and PFZH remove 7.40 ± 0.05, 14.85 ± 0.05, and 6.53 ± 0.05 mg g–1 fluoride, respectively, even after the third regeneration cycle. Additionally, the hydrogel beads are effective in the removal of arsenate (≤90 ± 0.02%) and chromate ions (≤96 ± 0.02%) from 100 ± 0.20 mg L–1 solution in batch adsorption studies. Therefore, the hydrogel beads could be used as potent filters for the removal of fluoride, chromate, and arsenate ions from water.

Applying interval stability concept to empirical model of middle Pleistocene transition.

Interval stability is a novel method for the study of complex dynamical systems, allowing for the estimation of their stability to strong perturbations. This method describes how large perturbation should be to disrupt the stable dynamical regime of the system (attractor). In our work, interval stability is used for the first time to study the properties of a real natural system: to analyze the stability of the earth's climate system during the last 2.6×106 years. The main abrupt shift in global climate during this period is the middle Pleistocene transition (MPT), which occurred about 1×106 years ago as a change of the periodicity of glacial cycles from 41 to 100 kyr. On the basis of the empirical nonlinear stochastic model proposed in our recent work, we demonstrate that the global climate stability to any perturbations decreases throughout the Pleistocene period (including the MPT), enhancing its response to fast (with a millennial scale or less) internal disturbances.

Optimal packaging for strawberry transportation: Evaluation and modeling of the relationship between food loss reduction and environmental impact

This study assessed the damage area ratios of different packaging systems on the life cycle of strawberry caused by vibration during transportation from environmental perspective. The relationship between food loss reduction and environmental loads was evaluated to produce an ideal package with both lower food losses and environmental impacts. Life cycle from cultivation to waste was assessed using a mass-based functional unit. The relationship between the damage area ratios and environmental loads demonstrated that the minimum point for the ratios and loads was different. The ratio minimizing the load throughout the life cycle was calculated by exponential and linear combination model. This study concludes that minimizing food loss during transportation with excessive postharvest process does not contribute to minimized load associated with the life cycle. Thus, producing an optimal packaging is required to assess the trade-offs between food loss reduction and environmental load. • Optimal packaging for strawberry transportation in Japan was evaluated by LCA method. • The empirical non-linear model showed the packaging condition minimizing the load. • Packaging causes loads for its production but reduces loads for the life cycle. • Minimizing food loss during transportation increases more loads of the life cycle.

Precise Luminous Flux and Color Control of Dimmable Red-Green-Blue Light-Emitting Diode Systems

A generic red, green, and blue (RGB) LED system encompasses complex interactions of power, heat, light, and color, which pose a major challenge for achieving precise control over luminance and color-mixing in high-quality lighting applications. In this article, new nonlinear empirical models of a practical RGB LED system with closed-loop control are formulated. They enable precise prediction of luminous flux and color coordinates by using the three distinct reference voltages as the control variables for independent current regulation across the RGB LED strings. The proposed empirical models are experimentally verified by using a hardware prototype of a dc–dc single-inductor three-output LED driver with proportional–integral compensators and time-interleaving control scheme. The measured values of luminous flux and color coordinates agree closely with the predicted values from the models.

Accurate linear and nonlinear model-based feedforward deposition control for material extrusion additive manufacturing

Additive manufacturing (AM) is gaining attention as an alternative to traditional manufacturing processes. Of the available AM methods, material extrusion (ME) AM is predominant. High-quality ME AM demands accurate synchronization between positioning (motion) control and extrusion control, as poor synchronization leads to printing defects like over- and under-extrusion. Typically, extrusion control in ME AM is achieved via feedforward (FF) control techniques due to difficulties in sensing extrusion rate in real-time for feedback control. However, existing FF extrusion control techniques rely on simple linear models to control the highly nonlinear extrusion process, leading to quality issues like over- and under-extrusion. This paper presents two FF control strategies for mitigating over- and under-extrusion defects in ME AM. The first strategy uses a standard linear model of extrusion system but applies it to FF motion control rather than FF extrusion control. This has the net effect of synchronizing motion and extrusion control while avoiding some nonlinearities associated with the extrusion process. In the second approach, an empirical nonlinear model of the extrusion process is developed and adopted for the design of a nonlinear FF extrusion controller. Both approaches were validated experimentally on a fused filament fabrication (FFF) 3D printer, and respectively demonstrated up to 40.45% and 35.98% improvement in deposition accuracy (i.e., reduced over- and under-extrusion) compared to a standard FF extrusion control approach typically used in the literature. In addition, the proposed nonlinear FF controller was shown to be more versatile and lead to faster ME AM compared to the proposed linear FF motion control approach. A practical application of the proposed techniques for improving the quality of a variable-width pattern printed using a new concept of continuously varied extrusion was demonstrated.

Temperature driven development of the rice brown planthopper, Nilaparvata lugens (Stål) (Hemiptera: Delphacidae)

Temperature driven development of rice brown planthopper (BPH), Nilaparvata lugens (Stål) (Hemiptera: Delphacidae) population (biotype 4) was examined at seven constant temperatures (15, 18, 20, 25, 30, 32 and 35°C). Complete development of BPH from egg to adult was observed at constant temperatures ranging from 15 to 32°C with linear development observed till 30°C. Total immaturedevelopmental duration decreased from 74.4 days at 15°C to 22.4 days at 30°C. Linear and non-linear models fitted to describe developmental rates of life stages as a function of temperature, gave estimates of bioclimatic thresholds (lower, optimum and upper temperature thresholds). Thermal constants estimated from Campbell linear model for egg, nymph and cumulative immature development to adult were, 198.8, 275.5 and 473.9 degree days, respectively. Among empirical non-linear models, Lactin 2 model was selected for estimates of upper temperature threshold at 35°C based on higher coefficient of determination. Application of thermodynamic SSI model explained the observed nonlinear relationship of development of BPH life stages at temperatures higher than 30°C. The estimated thermal constants and bioclimatic thresholds were used in developing temperature dependent phenology model based on Campbell equation. Phenology model predicted closely the occurrence of different life stages of BPH with those observed under field conditions.

A new clinopyroxene thermobarometer for mafic to intermediate magmatic systems

Abstract. Clinopyroxene-only thermobarometry is one of the most practical tools to reconstruct crystallization pressures and temperatures of clinopyroxenes. Because it does not require any information of coexisting silicate melt or other co-crystallized mineral phases, it has been widely used to elucidate the physiochemical conditions of crystallizing magmas. However, previously calibrated clinopyroxene-only thermobarometers display low accuracy when being applied to mafic and intermediate magmatic systems. Hence, in this study, we present new empirical nonlinear barometric and thermometric models, which were formulated to improve the performance of clinopyroxene-only thermobarometry. Particularly, a total of 559 experimental runs conducted in the pressure range of 1 bar to 12 kbar have been used for calibration and validation of the new barometric and thermometric formulation. The superiority of our new models with respect to previous ones was confirmed by comparing their performance on 100 replications of calibration and validation, and the standard error of estimate (SEE) of the new barometer and thermometer are 1.66 kbar and 36.6 ∘C, respectively. Although our new barometer and thermometer fail to reproduce the entire test dataset, which has not been used for calibration and validation, they still perform well on clinopyroxenes crystallized from subalkaline basic to intermediate magmas (i.e., basaltic, basalt-andesitic, dacitic magma systems). Thus, their applicability should be limited to basaltic, basalt-andesitic and dacitic magma systems. In a last step, we applied our new thermobarometer to several tholeiitic Icelandic eruptions and established magma storage conditions exhibiting a general consistency with phase equilibria experiments. Therefore, we propose that our new thermobarometer represents a powerful tool to reveal the crystallization conditions of clinopyroxene in mafic to intermediate magmas.

Photocatalytic activity enhancement of carbon‐doped g‐C3N4 by synthesis of nanocomposite with Ag2O and α‐Fe2O3

AbstractCarbon‐doped g‐C3N4 (CGNS) nanocomposite with Ag2O and α‐Fe2O3 has been synthesized to improve g‐C3N4 photocatalytic activity. The prepared CGNS/Ag2O/α‐Fe2O3 (GAF [with mass ratio 3:2:1]) nanocomposite exhibits the expanded visible‐light absorption region leading to the enhanced photocatalytic performance for Acid Red 14 (AR14) degradation. Besides, it is found that the recombination rate of the charge carriers effectively suppresses the nanocomposite. For a better understanding of the photocatalytic degradation mechanism, the reactions have been performed in the presence of different scavengers. The experiments indicate that superoxide anion radicals possess a more influential role in AR14 degradation in comparison with hydroxyl radicals and holes. The degradation efficiency has been decreased from 94.68 to 85.60 after five consecutive photocatalytic tests implying that the prepared nanocomposite is a stable photocatalyst. In the end, the kinetic study of AR14 degradation on nanocomposite with considering pseudo‐first‐order kinetics results in a nonlinear empirical kinetic model development for prediction of degradation efficiency of AR14 on nanocomposite.

Determination of the Sun‐Climate Relationship Using Empirical Mathematical Models for Climate Data Sets

AbstractPrevious studies have reported that human influences are required to explain the observed global warming using a linear model (LM) that relates change in solar forcing to change in global mean temperature (GMT) . This model has the shortcoming of assuming a given causes the same irrespective of the value of the initial global warming rate . Analysis of the GMT data showed that this warming rate has been increasing linearly since steady state ( for year ) as given by , where °C/year2 is the secular GMT acceleration and is the number of years of the change. The secular solar forcing due to 18% of the 11 yr solar cycle forcing of 0.19 W/ (0.08% of Total Solar Irradiance) was expressed as . Defining the climate sensitivity as °C/year per W/ removed the shortcoming of the LM and integration of the model for above and then simplifying gave a secular GMT‐solar forcing model given by that explained all of the observed global warming and increase in atmospheric , sea level and ocean heat content. Therefore, for this nonlinear empirical model, invoking human influences to explain climate change was not required. The annual GMT model predicts a pause in global warming until 2040.

Estimating the Remaining Useful Life of Proton Exchange Membrane Fuel Cells under Variable Loading Conditions Online

The major challenges for the commercialization of proton exchange membrane fuel cells (PEMFCs) are durability and cost. Prognostics and health management technology enable appropriate decisions and maintenance measures by estimating the current state of health and predicting the degradation trend, which can help extend the life and reduce the maintenance costs of PEMFCs. This paper proposes an online model-based prognostics method to estimate the degradation trend and the remaining useful life of PEMFCs. A non-linear empirical degradation model is proposed based on an aging test, then three degradation state variables, including degradation degree, degradation speed and degradation acceleration, can be estimated online by the particle filter algorithm to predict the degradation trend and remaining useful life. Moreover, a new health indicator is proposed to replace the actual variable loading conditions with the simulated constant loading conditions. Test results using actual aging data show that the proposed method is suitable for online remaining useful life estimation under variable loading conditions. In addition, the proposed prognostics method, which considers the activation loss and the ohmic loss to be the main factors leading to the voltage degradation of PEMFCs, can predict the degradation trend and remaining useful life at variable degradation accelerations.

Using CT to test the damage characteristics of the internal structure of expansive soil induced by dry–wet cycles

Damage to the internal structure of expansive soil under dry–wet cycles is the key factor for engineering damage to expansive soil. The expansive soil in Nanyang, Henan Province, China, is taken as the research object, and the damage characteristics of the internal structure of the expansive soil under dry–wet cycles are discussed. Computed Tomography (CT) images of the internal cracks of the expansive soil after zero to eight dry–wet cycles under different initial moisture contents were obtained using a CT machine, and the development of the internal structural cracks of the expansive soil was analyzed. The damage variable of the expansive soil defined by the ME value of CT and the relation between the damage variable, the number of dry–wet cycles, and the initial control moisture content are described. An empirical nonlinear damage model of the internal structure of expansive soil is established. Finally, the rationality of defining the damage variable by the ME value of CT is verified by the test results of the low-stress shear strength of the expansive soil. The results show that the first to fourth dry–wet cycles have great influence on the microstructure of the expansive soil and that internal microcracks are noticeably developed. With the increase in dry–wet cycles, the SD value increases gradually, and the anisotropy of the expansive soil becomes more significant. The dry–wet cycles result in the weakening of the connection between the particles of the expansive soil and in the damage of the internal structure, which is a nonlinear cumulative process. The ME value can be used to describe the damage evolution characteristics of expansive soil after dry–wet cycles.