Response Surface Function Research Articles

Pull out strength calculator for pedicle screws using a surrogate ensemble approach

Background and objectivePedicle screw instrumentation is widely used in the treatment of spinal disorders and deformities. Currently, the surgeon decides the holding power of instrumentation based on the perioperative feeling which is subjective in nature. The objective of the paper is to develop a surrogate model which will predict the pullout strength of pedicle screw based on density, insertion angle, insertion depth and reinsertion. MethodsA Taguchi's orthogonal array was used to design an experiment to find the factors effecting pullout strength of pedicle screw. The pullout studies were carried using polyaxial pedicle screw on rigid polyurethane foam block according to American society for testing of materials (ASTM F543). Analysis of variance (ANOVA) and Tukey's honestly significant difference multiple comparison tests were done to find factor effect. Based on the experimental results, surrogate models based on Krigging, polynomial response surface and radial basis function were developed for predicting the pullout strength for different combination of factors. An ensemble of these surrogates based on weighted average surrogate model was also evaluated for prediction. ResultsDensity, insertion depth, insertion angle and reinsertion have a significant effect (p < 0.05) on pullout strength of pedicle screw. Weighted average surrogate performed the best in predicting the pull out strength amongst the surrogate models considered in this study and acted as insurance against bad prediction. ConclusionsA predictive model for pullout strength of pedicle screw was developed using experimental values and surrogate models. This can be used in pre-surgical planning and decision support system for spine surgeon.

Evaluation of Electrospinning Process Parameters of Poly Lactic-Co-Glycolic Acid and Hydroxyapatite Nanocomposite Nanofibrous Scaffolds

Electrospinning recognized as a simple and inexpensive process for producing continuous polymeric nanofibers with diameters ranging from several micrometers down to tens of nanometers. In this study, an electrospun nanofibrous scaffolds based on lactic-co-glycolic acid (PLGA) and nanohydroxyapatite (nano-HA) was developed. The fiber morphology and mean fiber diameter of prepared nanofibers were investigated by scanning electron microscopy. FTIR analysis demonstrated that there were strong intramolecular interactions between the molecules of PLGA and nano-HA. A more systematic understanding of process parameters was obtained and a quantitative relationship between electrospinning parameters and average fiber diameter was established by using response surface methodology. A response surface function was empirically determined by central composite design using fiber diameter as an observed response and the electrospinning parameters such as concentration, distance, applied voltage, temperature and flow rate as variables. The regression coefficient of the model was found to be 0.938. The predicted fiber diameter was in good agreement with the experimental result. PLGA/nano-HA nanofibrous scaffolds could be good candidates for tissue engineering applications.

A new RBDO method using adaptive response surface and first-order score function for crashworthiness design

This study presents a new Reliability-based Design Optimization method using adaptive response surface and first-order score function analysis for complex system design optimization considering the variability of design variables. The adaptive response surface using Bayesian metric and Gaussian process based model bias correction method, is developed to represent the true performance functions and replace the true limit state function. First-order score function analysis is exploited to compute the sensitivities of probabilistic responses with respect to the design variables, which are the mean values of the random variables. Numerical results indicate that the proposed methods can produce the best response surface and estimate the sensitivities of probabilistic responses accurately. The proposed methodology is demonstrated by a vehicle crashworthiness design optimization problem with full frontal and offset frontal impacts.

Interface Damage Assessment of Railway Slab Track Based on Reliability Techniques and Vehicle-Track Interactions

AbstractThe interface damage as one of the most critical damage issues in railway slab tracks is evaluated in this work on the basis of reliability techniques and vehicle-track interactions. First, a coupled dynamics model of a vehicle and the slab track is developed involving nonlinear spring-damper elements for simulation of the interface damage. Furthermore, considering the random nature of the damage length, the damage height, the rail pad stiffness, and the elastic modulus of cement asphalt (CA) mortar layer, explicit mathematical expressions between the input stochastic variables and output dynamic responses are obtained on the basis of the combination of the response surface method (RSM) and the dynamic simulations of vehicle-track system. Subsequently, Monte Carlo (MC) simulations are performed for the probability analysis by directly using the response surface functions. Finally, by adopting the amplification factor (AF) of the dynamic response as the control indices, the damage assessment criter...

Structural acoustics analysis and optimization of an enclosed box-damped structure based on response surface methodology

In this paper, the structural acoustics analysis and optimization of an enclosed box-damped structure are investigated by using the response surface methodology (RSM). Acoustic frequency response function analysis, i.e. a unit harmonic force imposing on structure and calculating the sound pressure in cavity, is applied to achieve the critical frequency. The acoustic sensitivity analysis of sound pressure level with respect to the thicknesses of damping layer panels are employed to identify the significant variables. With the help of faced central composite design, an efficient set of sample points are generated, and then the second order polynomial function of the sound pressure response at critical frequency is computed and verified by the adjusted coefficient of multiple determination. After the response surface function is verified, the effect of the thicknesses of damping layer panels on sound pressure is analyzed quantitatively, and the thicknesses of damping layer panels are further optimized to minimize the sound pressure response of the target node. The results indicate that, by using the RSM, the computational time for structural acoustic is saved and the optimization process is simple. The sound pressure of the target node is controlled effectively with less damping material used.

An improvement of the response surface method based on reference points for structural reliability analysis

The Response Surface Method (RSM) is a powerful technique to evaluate the structural reliability. However, for a Limit State Function (LSF) with highly non-linear, the accuracy of the approximation of the failure probability does not depend very much upon the design point. It is necessary for RSMs to consider the design point and the non-linear trend of actual LSF around the design point, because both of them influence the failure probability. Thus, in order to improve the fitting precision of the Response Surface Function (RSF) to the actual LSF over a larger region containing the design point, the reference points of experimental points are constructed in this paper. Experimental points used to obtain parameters of a RSF are selected according to the information of reference points. Four examples are discussed in detail. The numerical results indicate that the accuracy and the efficiency of the proposed method are both desirable for both numerical and implicit LSFs, and the proposed method is superior to the classical RSM in terms of efficiency and accuracy.

A hybrid approach to detect crack parameters using measured natural frequencies in thin walled angle section steel beams

Present study outlines a hybrid approach using Finite Element Method (FEM)–Response Surface Method (RSM)–Genetic Algorithm (GA) to predict the crack parameters, namely crack position and crack depth ratio with the help of only the measured natural frequencies of cracked thin walled beams. Numerical experimental trials of cracked beams have been conducted based on design of experiment (DOE) approach using an improved Finite element model. The improvement has been achieved by consideration of warping stiffness in cracked angle section beam. Thereafter, regression analysis has been conducted to construct Response Surface Function (RSF). Optimum crack parameters were then calculated using GA by minimizing an objective function which has been formed as the root mean square (RMS) of the residuals between RSFs and measured frequencies. Results of the study indicate that, the proposed approach performs with excellent accuracy and it does not require the response of an uncracked beam as benchmark information.

Multi-domain unified modelling and control parameters optimisation of magnetorheological brake based on Modelica

In order to solve the problem of modelling, simulation and optimisation of magnetorheological brake (MR brake) which is a multi-domain coupling system, the braking performance and control parameters optimisation of MR brake were investigated under a quarter-car model. Firstly, based on Modelica/MWorks platform, using multi-domain unified modelling method, a multi-domain unified MR brake model with anti-lock braking system (ABS) was built. Then by using response surface method (RSM), the response surface function to express the relation between braking distance and three control parameters was formulated, and the optimisation problem of control parameters was solved at MWorks. Finally, according to the optimal control parameters and the structure parameters of MR brake designed by our group before, the simulation of the multi-domain unified MR brake model was done to analyse the change regularity of vehicle speed, slip ratio, braking distance, control current, braking time, etc. under the effect of controller. Results show that MR brake with optimal control parameters has a good braking performance and can meet the requirements of GB7258-2012 standard. This lays the foundation of application of MR brake in vehicles.

Multiple-crack identification in a channel section steel beam using a combined response surface methodology and genetic algorithm

Summary The present study outlines a sequentially integrated finite-element method (FEM)–response surface method (RSM)–genetic algorithm (GA) framework and implements this to predict the crack parameters, namely, crack location and crack depth ratio. A central composite face centered response surface design of the RSM technique is used to establish the direct relationships between the input parameters (crack location and crack depth ratio) and responses (natural frequencies) to build the response surface function (RSF). Multiple edge cracks are considered, which exist on the top flange of a thin-walled channel section cantilever beam and modeled as line spring elements. In order to obtain RSFs of the first five natural frequencies in terms of process factors such as crack position and crack depth ratio, a number of numerical experiments based on FEM are conducted by using the design-of-experiment approach. An objective function obtained as the square of the difference between RSF and experimentally measured natural frequency has been minimized using GA to find out the optimum crack parameters. Twenty-four steel channel beam specimens have been tested in the laboratory to extract the crack parameters from measured natural frequencies using the proposed approach. The results of the study indicate that the proposed approach performs remarkably, yielding crack parameters with great precision. Copyright © 2015 John Wiley & Sons, Ltd.

Reliability analysis of turbine blades based on fuzzy response surface method

To improve the precision of reliability analysis on turbine blades, the fuzzy response surface method of reliability analysis is proposed by considering the fuzziness of the input variables and the vagueness of the limit state variables. Initially, the fuzzy basic variables were converted into equivalent random variables according to the method of equivalent transformation. Additionally, the mathematic model of the fuzzy response surface for structural reliability analysis was established, based on the quadratic polynomial response surface function. The mean value and variance of the blade stress and radial deformation were obtained by using the Monte-Carlo method based on generous linkage sampling to the model. Finally, the probability of failure and fuzzy random reliability index were calculated based on the probability integral method. Results indicate that the reliability probability of the blade is 97.665%, when the allowable stress and deformation are 390 MPa and 0.195 mm, respectively. It is demonstrated that with an increase of the fuzzy coefficient, the blade reliability index decreases; thus, the random reliability of the blade is slightly higher than the fuzzy reliability.

A Successive Selection Method for finite element model updating

Finite Element (FE) model can be updated effectively and efficiently by using the Response Surface Method (RSM). However, it often involves performance trade-offs such as high computational cost for better accuracy or loss of efficiency for lots of design parameter updates. This paper proposes a Successive Selection Method (SSM), which is based on the linear Response Surface (RS) function and orthogonal design. SSM rewrites the linear RS function into a number of linear equations to adjust the Design of Experiment (DOE) after every FE calculation. SSM aims to interpret the implicit information provided by the FE analysis, to locate the Design of Experiment (DOE) points more quickly and accurately, and thereby to alleviate the computational burden. This paper introduces the SSM and its application, describes the solution steps of point selection for DOE in detail, and analyzes SSM׳s high efficiency and accuracy in the FE model updating. A numerical example of a simply supported beam and a practical example of a vehicle brake disc show that the SSM can provide higher speed and precision in FE model updating for engineering problems than traditional RSM.

Risk assessment of slope failure by representative slip surfaces and response surface function

This paper develops a quantitative approach for risk evaluation of slope failure based on a finite number of Representative Slip Surfaces (RSS) with Limit Equilibrium Method (LEM). A second order polynomial response surface function (RSF) is calibrated for each RSS in order to improve the computational efficiency. The volume of sliding mass associated with each RSS is a measure of consequence of slope failure along this RSS. The risk of slope failure is evaluated by Monte Carlo Simulation (MCS) and the contribution of each RSS to risk of slope failure is quantified. Thus, the risk of slope failure is de-aggregated into each RSS. The proposed methodology is illustrated through a three-layer cohesive soil slope. The de-aggregations of probability of slope failure, pf, and risk of slope failure, R, are conducted at different scale of fluctuations, and the results for de-aggregation of pf are compared with those for de-aggregation of R. The comparison indicates that the group of key RSS that dominate pf differ considerably from those that dominate R. These different groups of key RSS may lead to different strategies in the subsequent risk mitigation, if any. The proposed approach provides an efficient and quantitative tool for identifying the key group of RSS in the planning of slope risk mitigation.

Characterization of shape and dimensional accuracy of incrementally formed titanium sheet parts with intermediate curvatures between two feature types

Abstract Single point incremental forming (SPIF) is a relatively new manufacturing process that has been recently used to form medical grade titanium sheets for implant devices. However, one limitation of the SPIF process may be characterized by dimensional inaccuracies of the final part as compared with the original designed part model. Elimination of these inaccuracies is critical to forming medical implants to meet required tolerances. Prior work on accuracy characterization has shown that feature behavior is important in predicting accuracy. In this study, a set of basic geometric shapes consisting of ruled and freeform features were formed using SPIF to characterize the dimensional inaccuracies of grade 1 titanium sheet parts. Response surface functions using multivariate adaptive regression splines (MARS) are then generated to model the deviations at individual vertices of the STL model of the part as a function of geometric shape parameters such as curvature, depth, distance to feature borders, wall angle, etc. The generated response functions are further used to predict dimensional deviations in a specific clinical implant case where the curvatures in the part lie between that of ruled features and freeform features. It is shown that a mixed-MARS response surface model using a weighted average of the ruled and freeform surface models can be used for such a case to improve the mean prediction accuracy within ±0.5 mm. The predicted deviations show a reasonable match with the actual formed shape for the implant case and are used to generate optimized tool paths for minimized shape and dimensional inaccuracy. Further, an implant part is then made using the accuracy characterization functions for improved accuracy. The results show an improvement in shape and dimensional accuracy of incrementally formed titanium medical implants.

Efficient 3-D reliability analysis of the 530 m high abutment slope at Jinping I Hydropower Station during construction

Reliability-based slope stability analysis and design show promise, but few attempts have been made to study the 3-D reliability of high rock slopes. This paper aims to investigate the 3-D reliability of practical rock slopes and to explore the effects of reinforcement measures on slope reliability. A non-intrusive stochastic finite difference method is adopted to perform 3-D reliability analysis of high rock slopes, in which response surface functions are adopted to establish the explicit functions between the factors of safety for multiple slope failure modes and the significant random variables. The left abutment slope at Jinping I Hydropower Station in China is taken as a case study. A parametric sensitivity analysis is carried out to identify the significant uncertain parameters. The effects of two reinforcement measures, namely pre-stressed cables and shear-resistant concrete plugs, on the reliability of the rock slope during construction are highlighted. The results indicate that the 3-D reliability of complex rock slopes can be efficiently evaluated using a non-intrusive stochastic finite difference method. It provides an effective tool for solving 3-D reliability problems of complex rock slopes in practice. The combined support system with pre-stressed cables and three shear-resistant concrete plugs adopted in the Jinping I left abutment slope can effectively restrain the slope deformation and ensure the slope stability during construction. The disturbances induced by the excavation blasting during construction have a significant influence on the engineered slope reliability.

The Optimization of Bank Branches Efficiency by Means of Response Surface Method and Data Envelopment Analysis: A Case of Iran

In this paper the DRC model is presented for solving multi objective problem. The proposed model is a combination of data envelopment analysis, Cuckoo algorithm and the response surface method. Due to reasons like costs, time and irreversible damages, it is not possible to analyze each and every one of the proposed models in practice, so the simulation is used. Since the number of experiments for simulation process is high then the optimization has gone to practice and directs the simulation process. The response surface method is used as one of the approaches of simulation optimization. Furthermore, data envelopment analysis is used to consider several response surfaces as efficiency response surface. Then this efficiency response surface is solved by Cuckoo algorithms. The main advantage of DRC model is to make one efficiency response surface function instate of multi surface function for every output and also using the advantages of Cuckoo algorithms. In order to demonstrate the effectiveness of the proposed approach, the branches of Refah bank in Mashhad is analyzed and the results are presented.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method (SRSM) is proposed. SRSM integrates the advantages of support vector machine (SVM) and traditional response surface method (RSM), and utilizes experimental samples to construct a suitable response surface function (RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method (MCM); while SRSM (17.296 s) needs far less running time than MCM (10958 s) and RSM (9840 s). Therefore, under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

Optimal Design of Multi-DOF Deflection Type PM Motor by Response Surface Methodology

This paper uses response surface methodology as the optimization method of torque of multi-DOF deflection type PM motor. Firstly, the application of Taguchi algorithm selects structural parameters affecting the motor torque largely which simplifies the optimization process greatly. Then, based on the central composite design (CCD), response surface equation numerical model is constructed by the finite element method. With the aid of experiment design and analysis software, the effects of the interaction among factors on the index are analyzed. The results show that the analytical method is efficient and reliable and the experimental results can be predicted by response surface functions.

Lens injection moulding condition diagnosis and form error analysis using cavity pressure signals based on response surface methodology

In this article, the condition diagnosis and form error prediction models for lens injection moulding process are developed based on a response surface method by using features extracted from in-process cavity pressure signals. In the lens injection moulding experiments, cavity pressure signals are captured by pressure sensors embedded in a lens mould, and form errors of manufactured lenses are measured afterwards. Then, three features such as filling point, maximum pressure and inflection point pressure are identified from the measured cavity pressure profile, and they are used to formulate the response surface functions for each injection moulding condition. In addition, the response surface functions for the lens form error with the input variables of the above-mentioned three features are also formulated. It is reported that the overall average accuracies for the lens injection moulding condition diagnosis and form error estimation are better than 97% and 80%, respectively, in the actual industrial site.

Characterization of shape and dimensional accuracy of incrementally formed titanium sheet parts

Single Point Incremental Forming (SPIF) is a relatively new process that has been recently used to manufacture medical grade titanium sheets for implant devices. However, one limitation of the SPIF process may be characterized by dimensional inaccuracies of the final part as compared with the original designed part model. Elimination of these inaccuracies is critical to forming medical implants to meet required tolerances. In this study, a set of basic geometric shapes were formed using SPIF to characterize the dimensional inaccuracies of grade 1 titanium sheet parts. Response surface functions are then generated to model the deviations at individual vertices of the STL model of the part as a function of geometric shape parameters such as curvature, depth, wall angle, etc. The generated response functions are further used to predict dimensional deviations in a specific clinical implant case. The predicted deviations show a reasonable match with the actual formed shape and are used to generate optimized tool paths for minimized shape and dimensional inaccuracy. Further, an implant part is then made using the accuracy characterization functions for improved accuracy. The results show an improvement in shape and dimensional accuracy of incrementally formed titanium medical implants.

A multiwavelet support vector regression method for efficient reliability assessment

As a new sparse kernel modeling technique, support vector regression has become a promising method in structural reliability analysis. However, in the standard quadratic programming support vector regression, its implementation is computationally expensive and sufficient model sparsity cannot be guaranteed. In order to mitigate these difficulties, this paper presents a new multiwavelet linear programming support vector regression method for reliability analysis. The method develops a novel multiwavelet kernel by constructing the autocorrelation function of multiwavelets and employs this kernel in context of linear programming support vector regression for approximating the limit states of structures. Three examples involving one finite element-based problem illustrate the effectiveness of the proposed method, which indicate that the new method is efficient than the classical support vector regression method for response surface function approximation.