Improved Response Surface Method Based on Linear Gradient Iterative Criterion

Improved response surface method and its application to stiffened plate reliability analysis

In order to analyze the reliability and failure probability of the repaired shaft engineering, this article makes fail-safe analysis and instability risk prediction of the shaft engineering. A reliability analysis method was applied combining the improved response surface method which has improved sample points’ selection based on the traditional response surface method to decreasing the number of the structural analysis under the premise of the accuracy of the calculated results with numerical simulation. The limit state whose failure criteria was safe factor was constructed to analyze the reliability of the repaired shaft engineering, the reliability index of the repaired shaft engineering was computed by JC method. The results show the reliability index value of the repaired shaft engineering is 3.1127 slight fewer than design objective value and it’s failure probability value is 0.0929%, which show that the repaired shaft is stable and it’s deformation should be monitored to ensure it is safety application because of it is reliability index value slight fewer than design objective value.

A new method for welded joint fatigue reliability analysis on bogie frame of high-speed electric multiple unit (EMU) is proposed according to the International Union of Railways (UIC) standard, the Britain Standard Institute (BSI) standard and the Miner rule. Firstly, the fatigue calculation condition is loaded according to the UIC standard. The welded joint damage ratio is calculated by the BSI standard. Fatigue reliability analysis is conducted for a typical welded joint based on probabilistic design system (PDS) module in software ANSYS 14.0. In the system, the automatic program is prepared by ANSYS parametric design language (APDL) to calculate the welded joint fatigue damage ratio. Meantime, the relationship between the input variables and the output response is fitted by the response surface (RS) method. Then, the RS method is improved by the orthogonal design. Specifically, the selecting process optimization for the RS method based on the orthogonal design is conducted to improve the fitting efficiency of the RS method. Finally, a program of the automatic analysis documents is generated by Microsoft foundation class (MFC) technique. Through the self-defined interface, the researchers can easily import the automatic generation of the orthogonal table into the PDS module and analyze the fatigue reliability. Results show that the improved RS method can better fit the RS which covers the sample area, and the distribution law agrees well with the actual situation. At the same time, the improved RS method reduces the calculation time.

An improved response surface method (RSM) for the seismic fragility analysis of base-isolated structures is proposed so that the correlation of seismic demands on the structural components can be effectively considered. In addition, the performance levels of base-isolated structure as well as the associated quantitative indices for various structural components are discussed and defined. Taking a typical base-isolated reinforced concrete plane frame with lead-rubber-bearings as an illustrative example, the seismic fragility analysis following the computational procedure based on the improved RSM are conducted. Through the illustrative example, it is demonstrated that the obtained response surface models for the seismic demands on the components as well as the correlation of components are accurate and reliable; moreover, the computational cost for the system seismic fragility analysis is significantly reduced due to the use of Monte Carlo simulation; finally, it is indicated that it is necessary to take into account the correlation of components in order to obtain more accurate system fragility curves of base-isolated structure.

Probabilistic analysis of laterally loaded piles using response surface and neural network approaches

Reliability Based Optimization (RBO) is often computationally intensive because the coupling of reliability evaluation and cost minimization. The mean first order reliability method (MFORM) is efficient for reliability evaluation, but it may not accurate. Nevertheless, the accurate reliability index is often highly correlated with the MFORM reliability index. In this study, we suggest that one can determine the relationship between the MFORM reliability index and the accurate reliability index through a regression analysis, which is called the reliability index mapping function. Based on the reliability index mapping function, an equivalent MFORM target reliability index can be determined such that MFORM can be used for reliability evaluation in RBO. Since the computational work involved in MFORM is minimal, RBO based on reliability index mapping functions is efficient. The reliability index mapping function determined via a regression analysis may only reflect the approximate relationship between the accurate reliability index and the MFORM reliability index. How to consider uncertainties in reliability index mapping functions in RBO is also described in this paper.

Reliability analysis of a high-speed railway bridge system based on an improved response surface method

The morphological characteristics of aggregate include outline shape, angularity, and surface texture, which determine the mutual extrusion and friction between aggregates, and significantly affect the performance of asphalt pavement. At present, the research on the morphological characteristics of coarse aggregate is mainly focused on indoor visual identification technology (AIMS, XCT, etc.), in which the applicability of the proposed aggregate shape characterization index is weak, and these instruments could not serve the practical engineering well. In this article, the Coarse Aggregate Morphological Identification System (CAMIS) is developed based on computer vision technology, and the system can recognize the shape features of aggregates above 2.36 mm particle size and carry out uninterrupted feeding and removal based on the mechanical arm system, which can realize large sample detection. Based on CAMIS aggregate identification system and laboratory tests (rutting test, dynamic modulus test, and penetration shear test), the shape identification and performance test of aggregate samples from construction site are carried out, and an aggregate performance evaluation index, CEI, suitable for high-temperature areas is proposed in combination with the improved response surface method. The processing parameters of vertical shaft impact aggregate crusher are optimized based on the CEI index, and the recommended processing parameters are verified by laboratory tests. The results show that the morphological characteristics of coarse aggregate affect the high temperature performance in order angularity, needle flake, axial coefficient, and convexity. The combination of processing parameters of vertical axis impact crusher is recommended to be of 45 m/s rotational speed, 3 t/h feed quantity, and 30% air intake. Verified by laboratory tests, the aggregate identification system CAMIS developed in this article and the proposed aggregate performance evaluation index, CEI, are highly reliable.

Reliability Analysis of the Reworked Main Shaft Based on the Improved Response Surface Method

Objective: The jacket platform is made of various types of steel pipes and beams welded, mainly used in shallow water areas, such as Bohai oilfield in China. In winter, the sea area where the platform is located will freeze, and the influence of ice load on the platform can not be ignored. So the influence of ice load on the reliability of jacket platform is studied in this paper. Methods: In this research, the finite element model of the jacket platform was established in the form of beam element, and the loads were applied from different directions to find the load direction with the greatest influence on the platform state. When calculating the ultimate load of the platform structure, it is necessary to carry out nonlinear analysis. Selecting the ice load condition, increasing the ice load step by step on the platform structure. As the applied load gradually increases, the platform will appear nonlinear, then the ultimate load of the jacket platform will be obtain. The pile radius and pile thickness are uncertain components in the reliability study of the jacket platform due to manufacture, processing, and other factors, therefore the values of the pile's parameters are all random. Consider the deviation of geometric parameters with the extreme value type I distribution of ice load, the limit state equation for the strength failure of the platform under ice loads is obtained using Response Surface Method, then the reliability of the platform is calculated by the Monte Carlo method and First Order Second Moment Reliability method. Results: By nonlinear analysis, the ultimate bearing capacity of the platform studied in this paper is about 8000kN. The reliability probability of the platform calculated by Monte Carlo method is 0.9999993, and the reliability index is 4.813. The reliability probability of the platform calculated by the first order second moment method is 0.9999994, and the reliability index is 4.852. Conclusion: The results obtained by the two methods are almost the same, and the reliability index is very large, indicating that the platform can operate safely and reliably under the ice load.

This paper describes the use of response surface estimation in collaborative optimization, an architecture for large-scale multidisciplinary design. Response surfaces are used to model the disciplinary subproblem optimization results as a function of the interdisciplinary target variables. These models are then used to find a new design point, about which new disciplinary response surfaces are constructed. The utility of response surface estimation in collaborative optimization depends upon the generation of inexpensive accurate response surface models and the refinement of these models over several fitting cycles. Special properties of the subproblem optimization formulation are exploited to reduce the number of required subproblem optimizations to develop a quadratic model from O(n) to O(n). Implicit information is shown to reduce the number of required suboptimizations by a further 50% in some cases. Response surface refinement is performed using ideas from trust region methods. Results for the combined approaches are demonstrated and compared on two problems: a 44 variable tailless UAV example, using relatively simple analyses, and a substantially more complex HSCT design, with finite element structural analysis and a higher order aerodynamic model. Nomenclature a = maneuver angle of attack b = span B = coefficients in response surface fit C = coefficients in response surface fit Cj = local constraints Cm = pitching moment coefficient C[ = section lift coefficient 5e = eleven deflection angle Tl = propeller efficiency frs = response surface approximation of f m = number of unknown coefficients in RS fit n = number of targets to CO subproblem N = number of CO subproblems O()= order of R = computed aircraft range R0 = target aircraft range sfc = specific fuel consumption tj = spar cap thicknesses 0j = section jig-twist Wj = penalty weight W = weight fraction local design variable W0 = target weight fraction (winilial/wfmal) Wr t= trim ballast weight, tip and root Xj = local design variable; those with a corresponding system level specified target, x = strictly local design variables; those without corresponding system level specified targets yi = local computed state variable, a function of x or x, with a corresponding target Zj. a = maneuver angle of attack Zj = system level targets

Uncertainty quantification on reserves estimation is a fundamental task for project validation on offshore green fields and also for the selection of a development plan that is robust to those uncertainties. To test the robustness of several development plans is then fundamental to be able to evaluate the impact of this uncertainty with low computational cost. Structural, geological and dynamic uncertainties are integrated in a new workflow based on a set of embedded response surfaces. The first step consists in building an experimental design with only structural and geological parameters to evaluate the impact of such uncertainties on static responses such as oil initially in place. In the second step, this experimental design is completed with additional dynamic parameters. The novelty of the static and dynamic design merging is to incorporate the previously obtained static response surface in addition to the uncertain parameters. By embedding the static response in the variables we obtain a response surface on the reserves more regular and more predictive. In this workflow, mainly applied to green fields, the impact of local geological uncertainty is usually of second order respect to other global uncertainties and it is taken into account as random noise whose variance may depend on the static response. The method is applied to a real green field with complex multi-level heterogeneities and it is compared to more standard approaches such as Monte Carlo. We manage to obtain a very good response surface quality for the static response (oil in place) that is then embedded in the reserves response surface. The final accuracy of this response surface is sensibly increased respect to a classical approach considering only static and/or dynamic parameters at minor costs in terms of reservoir simulations. The new approach reduces sensibly the number of reservoir simulations needed for an accurate uncertainty and risk assessment when applied to select the more robust development plan selected from a set of possible candidates. It also provides useful sensitivity analysis measures to guide possible data acquisition campaign in order to reduce risks and take better decisions.

In this present work, effects of three Euler angles (Angle of Attack (AOA), Angle of Trim (AOT), Angle of Pitch (AOP)) of vertical cambered otter board on hydrodynamic characteristics (drag coefficient (Cd), lift coefficient (Cl), center-of-pressure coefficients (Cp)) were studied based on numerical simulation combined with Kriging Response Surface Methodology (KRSM) and Multi-Objective Genetic Algorithm (MOGA). Wind tunnel experiments were carried out to validate the accuracy of response surface based on numerical simulation. It was demonstrated that AOA had prominent effects on Cd and Cl, while AOT and AOP had less effects. The working posture of otter board were recommended to lean inwards (0°∼6°) and forward (−10°∼0°) to improve the lift-drag ratio without sacrificing Cl. The influences of AOT and AOP on positions of center-of-pressure point were less significant than that of AOA and decreasing with the increase of AOA. In addition, response surface of hydrodynamic coefficients around the critical AOA was a decent indicator of occurrence of stall. Finally, three candidate cases were selected to satisfy the high working efficiency by MOGA, which was consistent with the above recommendations. This study provided a scientific reference of response surface experimental investigations methodology and the configuration of Euler angles of otter board.

An efficient and accurate algorithm is proposed to evaluate the reliability of cable-stayed bridges accounting for soil-pile interaction. The proposed algorithm integrates the finite-element method and the response surface method. The finite-element method is used to model the cable-stayed bridge including soil-pile interaction. The reliability index is evaluated based on the response surface method. Uncertainties in the superstructure, the substructure and load parameters are incorporated in the proposed algorithm. A long span steel cable-stayed bridge with a main span length of 1088 m built in China is considered as an illustrative example. The reliability of the bridge is evaluated for the strength and serviceability performance functions. Results of the study show that when strength limit states for both girder and tower are considered, soil-pile interaction has significant effects on the reliability of steel cable-stayed bridges. Further, a detailed sensitivity study shows that the modulus of subgrade reaction is the most important soil-pile interaction-related parameter influencing the reliability of steel cable-stayed bridges.

Objectives: Quantification of uncertainties and its implications on stability assessment of geotechnical problems can very well be captured through probabilistic analysis in which parameters are considered to be random variables. Thus, randomness of the response of the system is also captured and safety assessment is reported in terms of a safety index, commonly called as “reliability index”. In this study, probabilistic approach in conjunction with conventional deterministic approach is used for the analysis of a deep excavation problem and advantages of probabilistic approach are highlighted. Methods/Statistical Analysis: Probabilistic analysis requires establishment of connection between input parameters and output responses, for which response surface method (RSM) concepts can effectively be utilized. RSM helps developing regression model between input and output which can be used for the probabilistic analysis through First Order Reliability Method (FORM). Advanced finite element numerical tool, i.e., PLAXIS 3D is utilized for the purpose of the analysis. Findings: Considering this typical case of deep excavation problem, it is highlighted that probabilistic analysis when used in conjunction with the deterministic approach, it brings rationality in decision making while dealing with uncertainty and provides mathematical basis for treating uncertainty. Application/Improvements: Conventionally, stability analyses of a deep excavation system are carried out through limit equilibrium based approaches and the parameter used to define extent of stability is factor of safety. With advent of computers and finite element or finite difference based computing facilities, strength reduction technique is adopted to estimate the factor of safety. These numerical tools also help in predicting the deformation pattern and judging the serviceability requirements. In either case, the soil parameters used as input in the numerical tools are taken a constant value uniformly. Choice of appropriate value of design input parameter is based on past experience, good engineering judgment and confidence in the adopted analysis methodology. Due to various uncertain sources involved in the estimation of the input properties of a natural material like soil, such as, natural variability, testing errors, model transformation, it is impractical to assign a single value to design parameter. Deterministic approach, which involves single value of design parameters for stability assessment is considered to be simple and straight forward. It is demonstrated that quantification of uncertainties and its influence on stability assessment of deep excavation problem can be captured in probabilistic framework.