Testing for stationarity with covariates: more powerful tests with non-normal errors

Previous studies suggested that the power of unit root and stationarity tests can be improved by augmenting a testing regression model with stationary covariates. However, one practical problem arises since such procedures require finding the variables that satisfy certain conditions. The difficulty of finding satisfactory covariate has hindered using such desired tests. In this paper, we suggest using non-normal errors to construct stationary covariates in testing for stationarity. We do not need to look for outside variables, but we utilize the distributional information embodied in a time series of interest. The terms driven from the information on non-normal errors can be employed as valid stationary covariates. For this, we adopt the framework of stationarity tests of Jansson (Jansson, M. 2004. “Stationarity Testing with Covariates.” Econometric Theory 20: 56–94). We show that the tests can achieve much-improved power. We then present the response surface function estimates to facilitate computing the critical values and the corresponding p-values. We investigate the nature of shocks to the US macro-economic series using the updated Nelson–Plosser data set through our new testing procedure. We find stronger evidence of non-stationarity than their univariate counterparts that do not use the covariates.

Uncertainty Updating of Finite Element Models Using Interval Analysis

Uncertainties in structural parameters and measurements can be accounted for by incorporating interval analysis into the updating scheme of finite element models using a response-surface function. To facilitate the interval arithmetic operation, two different strategies are proposed in this paper to transform the response-surface function into a corresponding interval response-surface function. These strategies minimize the inherent interval overestimation that can arise from the variable dependency of the surrogate model. In the first strategy, the natural extension and centered-form extension methods are used to mitigate the interval overestimation of the surrogate model, which may or may not contain interaction terms. In the second strategy, the natural extensión method is also adopted to realize the interval transformation of the surrogate model containing interaction terms but an affine arithmetic is further introduced to minimize the interval overestimation. To demonstrate the efficacy of the proposed method, model parameters are determined from an instrumented model of a cable-stayed bridge tested on a shaking table. Results show that the proposed updating method is feasible and effective for applications to finite element models of complex bridge structures.

Comparison of Methods for Imputing Non-Wetting Storm Surge to Improve Hazard Characterization

Joint probability methods for characterizing storm surge hazards involve the use of a collection of hydrodynamic storm simulations to fit a response surface function describing the relationship between storm surge and storm parameters. However, in areas with a sufficiently low probability of flooding, few storms in the simulated storm suite may produce surge, resulting in a paucity of information for training the response surface fit. Previous approaches have replaced surge elevations for non-wetting storms with a constant value or truncated them from the response surface fitting procedure altogether. The former induces bias in predicted estimates of surge from wetting storms, and the latter can cause the model to be non-identifiable. This study compares these approaches and improves upon current methodology by introducing the concept of “pseudo-surge,” with the intent to describe how close a storm comes to producing surge at a given location. Optimal pseudo-surge values are those which produce the greatest improvement to storm surge predictions when they are used to train a response surface. We identify these values for a storm suite used to characterize surge hazard in coastal Louisiana and compare their performance to the two other methods for adjusting training data. Pseudo-surge shows potential for improving hazard characterization, particularly at locations where less than half of training storms produce surge. We also find that the three methods show only small differences in locations where more than half of training storms wet.

Structural Modal Analysis and Optimization of SUV Door Based on Response Surface Method

Sensitivity analysis and response surface methods were employed to optimize the structural modal of SUV doors. A finite element numerical simulation model was established and was calibrated by restraint modal tests. To screen out highly sensitive panels, a sensitivity analysis for the thickness of door panels was proposed based on the fifth-order modal frequency of the door. Data points were obtained by a faced central composite design with the design variables from the thickness of the highly sensitive panels, and a second-order explicit response surface function of the fifth-order modal frequency of the vehicle door was established. An optimization model was established according to the response surface method. The final results demonstrate that the modal-frequency matching of the door and body in white was optimized after changing the thicknesses, with a 5.74% material reduction.

Cohesive slope failure analysis using methods combining smoothed particle hydrodynamics and response surface function

Purpose The paper aims to construct a method to simulate the relationship between the parameters of soil properties and the area of sliding mass of the true slip surface of a landslide. Design/methodology/approach The smoothed particle hydrodynamics (SPH) algorithm is used to calibrate a response surface function which is adopted to quantify the area of sliding mass of the true slip surface for each failure sample in Monte Carlo simulation. The proposed method is illustrated through a homogeneous and a heterogeneous cohesive soil slope. Findings The comparison of the results between the proposed method and the traditional method using the slip surface with minimum factor of safety (FSmin) to quantify the failure consequence has shown that the landslide risk tends to be attributed to a variety of risk sources, and that the use of a slip surface with FSmin to quantify the consequence of a landslide underestimates the landslide risk value. The difference of the risk value between the proposed method and the traditional method increases dramatically as the uncertainty of soil properties becomes significant. Practical implications A geotechnical engineer could use the proposed method to perform slope failure analysis. Originality/value The failure consequence of a landslide can be rationally predicted using the proposed method.

Time-dependent reliability analysis of the motor hanger for EMU based on stochastic process

Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications 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. Originality/value 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.

Point-wise model validation over experimental regions using regression confidence and tolerance intervals with Bayesian relaxations

As systems grow more complex, so does our propensity to use computers to emulate complex real-world systems. Often these real-world systems possess dynamic response behavior over the operational domain of input parameter configurations. This domain is referred to as the design space or experimental region. It is critical we ensure that computer models which emulate such dynamic behavior be validated over the full design space. This paper presents a dual-interval validation methodology. Confidence intervals and tolerance intervals are developed based on a system response surface function. Model samples are compared to each interval to develop a complete model validation conclusion. The methodology is described, its robustness to noise and model lack-of-fit examined, and then it is applied to a well-established engineering validation challenge problem.

Fuzzy optimization design-based multi-level response surface of bogie frame

Purpose In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem. Design/methodology/approach The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination. Findings The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively. Originality/value Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.