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Research in the area of financial distress often uses a proportional hazards model to determine the influence of covariates on the duration of time that precedes financial distress. Acritical issue in the use of a proportional hazards model is the use of time‐invariant and time‐dependent covariates. Time‐invariant covariates remain fixed while time‐dependent covariates change during the estimation of the model. Although the choice of covariates might substantially affect the estimation of the proportional hazards model, existing literature often fails to consider the potential effect of this choice on model estimation. This paper reviews the distinction between time‐invariant and time‐dependent covariates and the effect of covariate selection on the estimation of a proportional hazards model. Using a sample of financially distressed and non‐financially distressed firms, this paper suggests the choice of time dependence substantially influences model estimation and that covariate selection should be given more serious consideration in financial distress research.

The purpose of this paper is to analyze the time-dependent reliability of harmonic drive.

The transient finite element analysis (FEA) of harmonic drive is established to calculate the stress under different loads. Combined with the residual strength model and random variables, the time-dependent reliability model of harmonic drive is deduced by the stochastic perturbation method and Edgeworth series. Based on accelerated life tests, the degradation parameters are estimated by maximizing likelihood function. Under variable load, the key stress from transient FEA is transformed into probability density function by kernel density estimation, and the residual strength model is modified by adding adjustment factors to deal with strength degradation under different loads.

The critical position of stress concentration from transient FEA is consistent with the fatigue fracture position at the accelerated life test sample. Compared with the time-dependent reliability method with equivalent circular-shell static stress or empirical degradation parameters, the proposed method has the smallest prediction error of failure life. Under variable load, the state function should be expanded to second-order series for avoiding error items relevant to variance. The failure life expectation under random variable load is smaller than that under constant load.

The time-dependent reliability method of harmonic drive is firstly proposed under constant and variable load. The transient FEA of harmonic drive is established to calculate the stress for strength analysis. The accelerated life test of harmonic drive is conducted for degradation parameters estimation. The adjustment factor is added to the residual strength model for strength degradation under different loads.

The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation.

The newly developed time-dependent model has been handled by using the Hirota’s direct method. The authors also use the complex Hirota’s criteria for deriving multiple complex soliton solutions.

The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient.

The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions.

The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function.

The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived.

This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test.

The purpose of this paper is concerned with investigating three integrable shallow water waves equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models.

The newly developed equations with time-dependent coefficients have been handled by using Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions.

The developed integrable models exhibit complete integrability for any analytic time-dependent coefficients defined though compatibility conditions.

The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients.

This study introduces three new integrable shallow water waves equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author shows that integrable equations with time-dependent coefficients give real and complex soliton solutions.

The paper presents useful algorithms for finding integrable equations with time-dependent coefficients.

The paper presents an original work with a variety of useful findings.

The purpose of this paper is concerned with developing new integrable Vakhnenko–Parkes equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the time-dependent equations.

The developed time-dependent models have been handled by using the Hirota’s direct method. The author also uses Hirota’s complex criteria for deriving multiple complex soliton solutions.

The developed integrable models exhibit complete integrability for any analytic time-dependent coefficient.

The paper presents an efficient algorithm for handling time-dependent integrable equations with time-dependent coefficients.

The author develops two Vakhnenko–Parkes equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

The work presents useful techniques for finding integrable equations with time-dependent coefficients.

The paper gives new integrable Vakhnenko–Parkes equations, which give a variety of multiple real and complex soliton solutions.

Purpose — A new method of collecting hurricane evacuation data using time-dependent stated choice is developed and evaluated in this study.

Methodology/approach — Hypothetical storms are presented in a video in a sequence of scenarios showing prevailing conditions at discrete points in time as each storm approaches land. Respondents are exposed to nine hypothetical storms representing a range of hurricane characteristics. One of the hypothetical storms is secretly the same as an actual storm the respondents experienced in the past and for which they are required to report their behaviour in a revealed preference survey.

Findings — Stated and actual behaviour was compared and general agreement was found between what people say they would do and what they did. The revealed preference (RP) data was supplemented with time-dependent data from official sources and hurricane evacuation demand models estimated on this enhanced RP data, as well as on a combination of the enhanced RP and time-dependent stated choice (SC) data. When the models were applied to a different data set than the ones on which the models were calibrated, the combined time-dependent RP/SC model performed slightly better than the enhanced RP model. Detailed accounting revealed that time-dependent SC data is 25 percent more expensive to collect than enhanced RP data, although some of this cost may be due to the first-time collection of this type of data.

Surrogate models are extensively used to substitute real models which are expensive to evaluate in the time-dependent reliability analysis. Normally, different surrogate models have different scopes of application. However, information is often insufficient for analysts to select the most appropriate surrogate model for a specific application. Thus, the result precited by individual surrogate model tends to be suboptimal or even inaccurate. Ensemble model can effectively deal with the above concern. This work aims to study the application of ensemble model for reliability analysis of time-independent problems.

In this work, a method of reliability analysis for time-dependent problems based on ensemble learning of surrogate models is developed. The ensemble of surrogate models includes Kriging, radial basis function, and support vector machine. The prediction is approximated by the weighted average model. The ensemble learning of surrogate models is updated by finding and adding the sample points with large prediction errors throughout the entire procedure.

The effectiveness of the proposed method is verified by several examples. The results show that the ensemble of surrogate models can effectively propagate the uncertainty of time-varying problems, and evaluate the reliability with high prediction accuracy and computational efficiency.

This work proposes an adaptive learning framework for the uncertainty propagation of time-dependent problems based on the ensemble of surrogate models. Compared with individual surrogate models, the ensemble model not only saves the effort of selecting an appropriate surrogate model especially when the knowledge of unknown problem is lacking, but also improves the prediction accuracy and computational efficiency.

This paper aims to develop a numerical method for analysing the time‐dependent conjugate heat and fluid flows inside and around single bubbles rising in a hot liquid.

The procedure combines the moving mesh method for flows in time‐dependent geometries and the zoned calculation algorithm for conjugate viscous flows. A moving axisymmetric boundary‐fitted mesh is used to track the deformable gas‐liquid interface, while conjugate flows in both gas and liquid sides are calculated by a two‐block zoned method. The interfacial stresses are employed to calculate the velocity value and to decide the time‐dependent bubble shape simultaneously. Governing equations for the rising velocity and acceleration of the bubble are derived according to the forces acting on the bubble.

A calculating procedure for time‐dependent conjugate heat and fluid flows inside and around a rising single bubble has been developed. The algorithm has been verified, and can be employed for further analysing heat, mass and momentum transfer phenomena and their relevant mechanisms.

The paper developed a method to obtain high fidelity results for the heat and fluid flow details in the vicinity of a time‐dependent moderately deformable rising bubble; the physically zero‐thickness of a gas‐liquid interface is guaranteed. The governing equations for the time‐dependent rising velocity and acceleration are derived.

Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

The purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models.

The newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria.

The developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model.

The paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients.

The work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

This study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients.

The paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.