Improved Response Surface Method Research Articles

The research on the failure mechanism and dynamic reliability of lubricated clearance

In the operation of mechanisms with lubricated clearances, uncertain parameters such as the temperature of lubricant, driving speed, and clearance value will lead to dynamic variations for oil film thickness of lubricated clearance. The lubrication may fail when the oil film thickness of bearing surfaces is insufficient, thereby significantly affecting the performance of the mechanism. This paper presents a novel method for the dynamic reliability of lubricated clearances by improved response surface method (IRSM). Firstly, the mathematical model of lubricated clearance is established, and the oil film load of lubricated clearance is defined, then the dynamic model of mechanism considering lubricated clearances is built through Lagrange method. Secondly, considering the failure mechanism of the lubricated clearance, the surrogate model is established using the IRSM with minimum oil film thickness as the failure criterion. Finally, taking the 9-link mechanism with multiple lubricated clearances as a numerical example, the dynamic minimum oil film thickness of the lubricated clearance considering uncertain parameters is computed. The reliability of the lubricated clearance is investigated by the surrogate model, and the applicability of the model is verified by the Monte Carlo method (MCM). The results demonstrate that the IRSM has higher accuracy compared to the traditional response surface method (TRSM). This paper provides a theoretical basis for the study of failure mechanism and reliability of lubricated clearances, and also has practical significance for engineering applications.

Study on the freeze–thaw effect on concrete arch dam using an improved response surface method

The damming materials will be deteriorated during the long-term service of concrete arch dam by weathering, seepage dissolution, freeze–thaw and other factors which will put dams at potential risk. However, there are few researches on the reliability assessment of arch dams considering the effect of material deterioration. In this paper, a prediction model of concrete mechanical properties under freeze–thaw cycles is established using regression analysis. Considering various uncertain factors, a time-varying structural reliability analysis model is established using finite element equivalent stress method and an optimized response surface method with improved sampling strategy and convergence criterion. A case study is later carried out. The results show that, at the early stage of freeze–thaw, the structural failure probability will increase steadily in a small range. However, as the tensile strength of concrete continues to decrease under long-time freeze–thaw action, the reliability of the arch dam structure will suddenly fall off a cliff. The proposed deterioration model and reliability analysis probability model are reasonable and practical and could be serve as a technical support for similar engineering projects.

Service reliability assessment of ballastless track in high speed railway via improved response surface method

The spectral feature of the track irregularity has a great impact on the running stability of high-speed trains. This study assesses the service reliability of the high-speed rail (HSR) ballastless track structure considering the effect of wavelength distribution characteristics of the track irregularities. The serviceability limit state (SLS) function of the ballastless track is established with respect to the derailment coefficient and wheel-unloading rate. To overcome the problem of high computational cost in the iteration of reliability assessment for the vehicle-track system, this study proposes an improved response surface method (RSM) and the explicit solution of the SLS function of the ballastless track can be realized. Compared with the traditional RSM, the improved RSM can adaptively adjust the variable interpolation coefficient to increase the iterative convergence speed. To obtain the vertical and lateral wheel-rail forces, a 3-D vehicle-track coupling model is established based on multibody dynamics and the finite element method (FEM). To analyze the wavelength effect of the track irregularities, a binary wavelet-based inversion algorithm is proposed to generate time series of both the vertical and alignment irregularities from the track irregularity spectrum (TIS). By comparing it with the MCS method, it is found that by using the improved RSM method, the convergence condition of the reliability index can be satisfied only by tens of iterations and the total computation time is 1.92 × 104 shorter than using MCS. Finally, the effect of different wavelengths of the track irregularity on the service reliability of track structure is discussed. The results show that the wavelength of 32 to 64 m is the main unfavorable wavelength range affecting the track service reliability under the normal operation condition of HSR.

Finite Element Model Updating of Bridge Structures Based on Improved Response Surface Methods

An accurate and reasonable finite element model is essential for bridge structural health monitoring and safety assessment. To improve the accuracy and efficiency of the finite element model updating, this paper proposes a finite element model updating method for bridge structures based on an improved response surface method. By introducing the radial basis function as the augmentation term of the polynomial function, a response surface model based on the augmentation polynomial is established, and the fitting accuracy of the global response surface model is improved. The convergence speed and accuracy of the response surface model optimization solution are improved by improving the regression step and annealing strategy in the simulated annealing algorithm. The method is validated using the numerical case of a simply supported beam and the finite element model of the main bridge of the Tonghe Songhua River Highway Bridge (Tonghe Bridge), and the safety condition of the main bridge of the Tonghe Bridge is evaluated using the updated finite element model. The results show that the maximum relative error of the updated parameters of the simply supported beam decreased from 13.011% before improvement to 0.719% after improvement, and the maximum relative error of the natural frequencies decreased from 0.728% before improvement to 0.225% after improvement; the maximum relative error of the natural frequencies of the finite element model of the Tonghe Bridge main bridge decreased from 21.68% before improvement to 4.23% after improvement. In April, May, and June of 2021, the main bridge of the Tonghe Bridge operated well and had a good security reserve.

Improved Response Surface Method Based on Linear Gradient Iterative Criterion

Aiming at the problem of big calculation error in solving reliability index by the traditional response surface method, an improved response surface method based on the linear gradient iteration criterion is proposed. First, the linear gradient iteration criterion is proposed to reduce the iteration step size with the increase of iteration times. It will improve the fitting accuracy of response surface and lead to a better convergence while approaching the limit state surface. Then, the reduction coefficient of the linear gradient iterative criterion is studied. The optimal value of coefficient is 0.2. The improved response surface method will get a more accurate reliability index quickly. Examples show that the proposed method has obvious advantages of high accuracy and efficiency. The application of this method can also be expanded in other similar engineering structure.

Competitor Benchmarking by Structure Reliability Analysis with Improved Response Surface Method

Competitor Benchmarking by Structure Reliability Analysis with Improved Response Surface Method

Improved Hybrid Response Surface Method Based on Double Weighted Regression and Vector Projection

In order to increase the accuracy and stability of the classical response surface method and relevant method, a new improved response surface method based on the idea of double weighting factors and vector projection method is proposed. The response surface is fitted by the weighted regression technique, which allows the sampling points to be weighted by their distance from the true failure surface and that from the estimated design point. It uses the vector of the gradient projection method to get new sampling points in the process of iteration, in order to make the sampling points closer to the design point, and the value of deviation coefficient is constantly adjusted. To some extent, these strategies increase the accuracy and stability of the response surface method, while the calculation time is decreased. At last, the rationality and efficiency of the proposed method are demonstrated through five examples. Besides, as revealed from this investigation, compared with other conventional algorithms, this method has a few obvious advantages; this algorithm not only has high precision and efficiency, but also has solid stability.

Robust optimization of rolling parameters of coarse aggregates based on improved response surface method using satisfaction function method based on entropy and adaptive chaotic gray wolf optimization

Determining the rolling parameter control standard for coarse aggregates by robust optimization is of great significance in reducing the sensitivity to noise in data on site and improving the measurement accuracy and stability of the compaction quality. The existing rolling parameter control standard is mainly determined by field rolling tests, which results in draining human labor and financial resources and makes it difficult to ensure the global optimum. Existing studies on the multiobjective optimization of rolling parameters usually ignore robustness, which in detail is represented by neglecting the overlap width of the rolling strip in the decision variables and rolling efficiency in optimization objectives. To overcome this limitation, a robust optimization design method for the rolling parameters based on the improved response surface method (RSM) using the satisfaction function method based on entropy (SFME) and adaptive chaotic gray wolf optimization (ACGWO) is proposed. First, the mean and standard deviation (SD) of the rolling quality and efficiency are selected as the response objectives, with the rolling thickness, rolling passes, rolling speed, and overlap width as the influencing factors. Then, RSM is used to perform a robust optimization design on the rolling parameters, in which the SFME is used to determine the weight of each response. Finally, an improved ACGWO algorithm with less calculation time, faster convergence speed, and higher accuracy is proposed to establish a robust optimization model of the rolling parameters. The engineering application results indicate that the most robust rolling parameters obtained by the proposed method are applicable and accurate. The method can improve the efficiency of the compaction while maintaining high compaction quality.

The influence of thermophysical parameters on the prediction accuracy of the spindle thermal error model

The model based on the velocity and acceleration of temperature variation (MBOTV) was established for spindle thermal growth error. However, the thermophysical parameters of MBOTV, such as the thermal expansion coefficient related to the velocity of temperature variation, Hv, the thermal expansion coefficient related to the acceleration of temperature variation, Ha, and the thermal inertia coefficient of the spindle, τ, may change during actual working. In order to analyze the influence of thermophysical parameters on the prediction accuracy of MBOTV, it is necessary to calculate the reliability of MBOTV. Actually, it is difficult to obtain the function of MBOTV. Although the improved response surface method can be used to calculate the reliability of the model with implicit function, the accuracy is not enough obviously when the implicit function is replaced by linear polynomials. Therefore, an improved response surface method based on quadratic polynomial approximation was proposed in this paper to calculate the reliability of MBOTV. In this method, the linear polynomial was replaced by a quadratic polynomial without cross product terms to replace the implicit function, which can improve the accuracy of reliability calculation. The predicted residual errors of MBOTV with single-parameter fluctuation and multi-parameter fluctuation were given in this paper. Studies reveal that MBOTV has strong robustness when the thermophysical parameters change.

A Novel Risk Evaluation Procedure Using a Kriging-Based Surrogate Modeling for Offshore Structures

An innovative reliability estimation procedure for Jacket-type offshore platforms is proposed. The information on risk is extracted using multiple deterministic analyses using advanced mathematical theories resulting in compounding beneficial effects. The platforms are modeled by finite elements. Nonlinearity and major sources of uncertainty are incorporated. The wave loading model is realistically developed to satisfy the underlying physics. It is applied in three-dimension in time domain incorporating the uncertainties in the parameters. Implicit performance functions are expressed explicitly using several advanced factorial schemes and significantly improved response surface method. The efficiency and accuracy of the method are improved using a comprehensively improved Kriging-based surrogate modeling technique. The risk is evaluated for the serviceability and strength limit state functions for a jacket-type offshore platform using about two hundred nonlinear finite element analyses. The procedure was verified using simulation techniques. The concept can be considered an alternative to the conventional random vibration techniques and the standard Monte Carlo simulation procedure.

Study on Quantitative Characterization of Morphological Characteristics and High Temperature Performance Evaluation of Coarse Aggregate Based on Computer Vision

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.

Improved response surface method based on triple weighted regression

The response surface method (RSM) is frequently used to reduce the computational burden of structural reliability analysis. In this paper, an improved RSM is proposed. The response surface is fitted by the triple weighted regression technique, which integrates weighting systems to assign weight factors to each sampling point including (1) the absolute value of the limit state function (LSF), (2) the value of the joint probability density function and (3) the distance from the design point. Numerical examples are presented to demonstrate that the proposed method gives more accurate results than RSM for both probability of failure (PoF) and LSF evaluations.

Topology optimization design of improved response surface method for time-variant reliability

This paper proposes an effective and efficient method for topology optimization with a time-variant reliability constraint. A decoupling strategy is used to decompose the time-variant reliability topology optimization into a time-variant analysis and time-invariant deterministic topology optimization, thus improving the efficiency of the optimization calculation. The reliability analysis will use the PHI2 method and an improved response surface method to estimate the time-variant reliability level and satisfy the reliability constraint. Continuously updated design points derived from a time-varying reliability analysis are used for topology optimization using the BESO method. Finally, some numerical examples of the time-variant reliability topology optimization problems are provided to illustrate the efficiency of the proposed method and its ability to determine the optimal solution.

An improved response surface method for fragility analysis of base-isolated structures considering the correlation of seismic demands on structural components

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.

Improved response surface method of reliability analysis based on efficient search method

Improved response surface method of reliability analysis based on efficient search method

Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

In a reliability-based design optimization (RBDO), computation of the failure probability (Pf) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables; Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point; Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature.

Adaptive improved response surface method for reliability-based design optimization

ABSTRACTReliability-based design optimization (RBDO) requires the evaluation of probabilistic constraints (or reliability), which can be very time consuming. Therefore, a practical solution for efficient reliability analysis is needed. The response surface method (RSM) and dimension reduction (DR) are two well-known approximation methods that construct the probabilistic limit state functions for reliability analysis. This article proposes a new RSM-based approximation approach, named the adaptive improved response surface method (AIRSM), which uses the moving least-squares method in conjunction with a new weight function. AIRSM is tested with two simplified designs of experiments: saturated design and central composite design. Its performance on reliability analysis is compared with DR in terms of efficiency and accuracy in multiple RBDO test problems.

Dynamic behavior and parameter sensitivity of the free-floating base for space manipulator system considering joint flexibility and clearance

The joint flexibility and clearance greatly affect the dynamic behavior of the free-floating base when space manipulators operate due to the dynamic coupling between the manipulators and the free-floating base. Based on the Lagrange–Euler method and momentum conservation, the dynamic model of a free-floating space manipulator system with joint flexibility and clearance is obtained. With this model, the coupling effects of joint flexibility and clearance on the dynamic response of the free-floating base are analyzed and some case studies are conducted to investigate the effects of different parameters of joint flexibility and clearance on the free-floating base. Further, the parameter sensitivity of the free-floating base for space manipulator system with joint flexibility and clearance is analyzed using the improved response surface method. According to the analysis of response surface method, we can increase the joint clearance size or decrease the dynamic friction coefficient to improve the stability and motion accuracy of the free-floating base position and attitude. This work points out the direction for reducing the base disturbance and provides a basis for the optimization design for free-floating space manipulator system.

Reliability Analysis of Lead-Free Solders in Electronic Packaging Using a Novel Surrogate Model and Kriging Concept

A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.

Reliability Analysis of Tunnel Face in Broken Soft Rocks Using Improved Response Surface Method

Reliability Analysis of Tunnel Face in Broken Soft Rocks Using Improved Response Surface Method