Multi-response optimisation of WEDM process using principal component analysis

Like many other processes, the wire electrical discharge machining (WEDM) process has several performance characteristics. Determination of the optimal process settings with respect to all these performance measures (responses) is an important issue. Taguchi’s robust design method can only be applied to optimise a single-response problem. Some researchers have attempted to optimise WEDM operations using a multi-response signal-to-noise (MRSN) ratio and constraint optimisation methods. Both these methods suffer from some weaknesses. The principal component analysis (PCA)-based approach for multi-response optimisation can effectively overcome those weaknesses. In this paper, some modifications in the PCA-based approach are suggested and two sets of experimental data published by the past researchers are analysed using this modified procedure. It is observed that the PCA-based optimisation can give better results than the constrained optimisation and MRSN ratio-based methods, which can be attributed to the fact that the possible correlation among the multiple responses is taken care in the PCA-based approach.     

Comparison of performances of five prospective approaches for the multi-response optimization

The Taguchi method of experimental design is widely used for optimization of process performance. However, this method has been developed to optimize single-response processes. But, in many situations, the engineers are required to determine the process settings that can simultaneously optimize multiple responses. In the recent past, researchers have proposed several systematic procedures for multi-response optimization. Most of these methods use complicated statistical/mathematical models and are, therefore, not easily comprehendible to the engineers who do not have a strong background in mathematics. Only a few methods, e.g. weighted signal-to-noise (WSN) ratio, Grey relational analysis, multiple-response signal-to-noise ratio, VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian), and weighted principal component methods, use relatively simpler procedures. In this paper, the computational procedures for these five methods are standardized. Three sets of experimental data are analyzed using these standardized procedures and the predicted optimization performances of the five methods are compared. The results show that no method can give better optimization than the WSN method.     

The principal component analysis (PCA)-based approaches for multi-response optimization: some areas of concerns

Over the years, Taguchi method for process optimisation has become very popular among the engineers. However, Taguchi method focuses on the optimisation of a single-response variable only, whereas most of the modern manufacturing processes demand for simultaneous optimisation of multiple response variables, and some of these responses are often correlated. Several methods have been proposed in literature which aims at making the Taguchi method useful for solving multi-response optimisation problems too. However, only few of these methods take into account the possible correlations that may exist among the response variables. Among these, principal component analysis (PCA)-based approaches are quite popular among the practitioners. However, we find that the PCA-based approaches suffer from some weaknesses, e.g. problem due to using signal-to-noise ratios as input data, problem due to scaling of the input data, problem due to difference in PCA results given by different software. This article aims at drawing attention of the researchers/practitioners to these problem areas of the PCA-based approaches so that appropriate research initiatives can be taken up by the researchers/practitioners to overcome those weaknesses.     

Optimisation of multiple responses for WEDM processes using weighted principal components

Taguchi method is widely used for optimisation of various processes. Using Taguchi method, the parametric settings can be optimised with respect to one performance characteristic (response) at a time, whereas wire electrical discharge machining (WEDM) processes require optimisation of multiple performance characteristics. Researchers have attempted several approaches but determination of the optimal process settings that can optimise multiple performance measures (responses) of WEDM operations still remains an important issue. In this paper, weighted principal component (WPC) method is used to optimise the multiple responses of WEDM processes. The results show that the WPC method offers significantly better overall quality than the other approaches.     

Improving yarn quality through multi-response optimisation of electronic yarn clearer in winding machine

One of the essential post-spinning operations of yarn is winding. In winding machine, ring yarn (i.e. the yarn produced in ring frame) is passed through electronic yarn clearer (EYC) and wound into empty conical-shaped packages called cones. The purpose of EYC is to improve the yarn quality as much as possible by eliminating the various types of faults or irregularities, e.g. thin places, thick places and neps from the ring yarn. The process engineer in an Indian spinning mill was facing the problem of inaccurate detection of faults by the EYC, which led to higher number of winding breaks as well as yarn irregularities. Aiming to tackle the problem, Taguchi’s L₂₇ orthogonal array experimentation was carried out. The experimental data are analysed using weighted principal component (WPC) method and principal component analysis-based grey relational analysis that take care of correlation among multiple responses. The WPC method is found to give better optimisation. By using the optimal settings, sensitivity of the EYC to detection of faults increased and thus, yarn quality improved substantially.     

An approach to optimize correlated multiple responses using principal component analysis and desirability function

While researchers have developed several approaches to attain design variable settings that simultaneously optimize multiple-quality characteristics, the multi-response optimization has become a common practice in complicated manufacturing processes. Most of these research works assume independency of responses where their variances are constant over the experimental space. However, there are many manufacturing processes in practice where the quality characteristics under consideration are correlated. In this study, an efficient approach based on principal component analysis and a conventional desirability function is proposed to optimize correlated multiple responses. This approach not only obtains optimal operating conditions, but also considers different variance and correlation levels of responses and enforces all objectives to satisfy constraints. Experimental results obtained using a standard example show the effectiveness of the proposed method.     

Multi-objective optimization of pulsed gas metal arc welding process based on weighted principal component scores

Most welding processes present large sets of correlated quality characteristics. With this particularity in mind, we present a multi-objective optimization technique based on Principal Component Analysis (PCA) and response surface methodology (RSM). This two-fold technique utilizes PCA to factorize the original welding responses. The original responses—obtained through a Central Composite Design—are then replaced by the resulting principal component scores. The technique’s advantage is that it reduces the data set and still considers the correlation among the responses. Quite often, however, the first principal component alone cannot explain the amount of variance–covariance structure of the welding responses. In this paper, we remedy this shortfall by proposing an objective function established in terms of the most significative principal component scores (weighted by their respective eigenvalues). Experimental results were obtained with a multiresponse pulsed gas metal arc welding process. These results, when compared with other strategies of multiresponse combination, verify the adequacy of our proposed approach.     

A study on the performance of some multi-response optimisation methods for WEDM processes

Wire electrical discharge machining (WEDM) processes are having several performance measures which are affected by different process parameters. In the recent past, researchers have attempted several systematic procedures for optimising the multiple responses of WEDM processes. However, most of these approaches use complex statistical/mathematical tools and are, therefore, impractical for application by the engineers who may not have a strong background in mathematics. Only a few methods, e.g., grey relational analysis and multiple response signal-to-noise ratio approaches use relatively simpler computational procedures. On the other hand, the computational procedures for the weighted signal-to-noise (WSN) ratio and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian) methods are also quite simpler and, therefore, can easily be implemented by the engineers. However, an engineer needs to select the method that can give the best optimisation performance for the process. In this paper, the computational requirements for these four multi-response optimisation methods are standardised. Two sets of experimental data on WEDM processes are analysed using these standardised multi-response optimisation methods, and their relative performances are then compared. The results show that no method can lead to better optimisation than the WSN ratio method.     

Multi-response optimization using weighted principal component

Taguchi method is a very popular offline quality design. However, it cannot solve the multi-response problem which occurs often in today’s society. Research shows that the multi-response problem is still an issue with the Taguchi method. Researchers have tried to find a series of theories and methods in seeking a combination of factors/levels to achieve the situation of optimal multi-response instead of using engineers’ judgement to make a decision in the Taguchi method. In 1997, Su et al. submitted the multivariate method, and in 2000 Antony proposed principal component analysis (PCA), to solve this problem. But with the PCA method, there are still two main shortcomings. In this study, the weighted principal components (WPC) method is proposed to overcome these two shortcomings, and three cases in their papers will be illustrated and compared in the application of WPC method. The result shows that the WPC method offers significant improvements in quality.     

Fabrication of stepped hole on zirconia bioceramics by ultrasonic machining

Zirconia (ZrO₂) is a highly biocompatible ceramic material providing fracture strength properties that allow application as dental implants in biomedical engineering. In this present research, experimental analysis has been made for generating stepped hole on zirconia bioceramics with desired quality using ultrasonic machining (USM) process. Four independent controllable input process parameters are abrasive grain diameter, power rating, concentration of abrasive slurry, and tool feed rate. Material removal rate (MRR), overcut of larger diameter (OLD) hole, and overcut of smaller diameter (OSD) hole of stepped hole are considered as the responses. Response surface methodology (RSM) is used for modeling the performance of USM process. Multiobjective optimization has been performed to maximize the MRR and minimize the OLD hole and OSD hole of stepped holes. All the responses are improved at the optimal parametric condition and verified by confirmation test. The present research opens up the application feasibility of USM process for stepped hole generation on bioceramics and its utilization in biomedical field.     

A multivariate mean square error optimization of AISI 52100 hardened steel turning

Hardened steel turning has received special attention in recent years due to its many applications in modern industries. The characteristics that define its machinability—expressed in terms of multiple response problems—are usually represented by experimental model building strategies like response surface methodology (RSM). Such strategies, however, have a particular drawback when multiple correlated regression functions are present. The optimization of multiple process characteristics without considering the variance–covariance structure among the responses may lead to an inadequate optimum. To deal with this constraint, this paper presents a novel multiobjective optimization method; it correctly focuses the multiple correlated characteristics of the AISI 52100 hardened steel, based on the concept of multivariate mean square error. This novel approach combines principal component analysis with RSM focusing a multidimensional nominal-the-best problem. In this kind of optimization, all the characteristics (tool life, cutting time, cost, material removal rate, and surface roughness) have a specific target while maintaining a strong correlation structure. Transforming the original responses and respective targets to the plane of a multivariate principal component scores, an optimization routine is capable of finding out a compromise solution that attends all the established targets. The following AISI 52100 turning process variables were considered in this study: cutting speed, feed rate, and depth of cut. Theoretical and experimental results were convergent and confirmed in a case study.     

Experimental modeling and multi-objective optimization of traveling wire electrochemical spark machining (TW-ECSM) process

The present paper attempts to focus an application of a hybrid methodology comprising of Taguchi methodology (TM) coupled with response surface methodology (RSM) for modeling and TM coupled with weighted principal component (WPC) methodology for multiobjective optimization of a self developed traveling wire electro-chemical spark machining (TW-ECSM) process. First optimum level of input parameters is found using TM which is used as the central values in RSM to develop the second-order response model. For multiobjective optimization two quality characteristics surface roughness (R_a) and material removal rate (MRR), which are of opposite nature (R_a is the lower-the-better type, while MRR is the higher-the-better type), have been selected. The WPC is employed for the calculation of weight corresponding to each quality characteristic. The results indicate that the hybrid approaches applied for modeling and optimization of the TW-ECSM process are reasonable.     

基于主分量分析的信号白化解相关处理

介绍了主分量分析及其计算方法,论证了采用主分量分析方法对混合信号进行白化解相关处理的理论基础,对基于主分量分析方法的解相关处理进行了仿真。结果表明,对信号进行解相关处理可以大幅度降低信号之间的互相关程度。     

A multivariate surface roughness modeling and optimization under conditions of uncertainty

Correlated responses can be written in terms of principal component scores, but the uncertainty in the original responses will be transferred and will influence the behavior of the regression function. This paper presents a model building strategy that consider the multivariate uncertainty as weighting matrix for the principal components. The main objective is to increase the value of R² predicted to improve model’s explanation and optimization results. A case study of AISI 52100 hardened steel turning with Wiper tools was performed in a Central Composite Design with three-factors (cutting speed, feed rate and depth of cut) for a set of five correlated metrics (R_a, R_y, R_z, R_q and R_t). Results indicate that different modeling methods conduct approximately to the same predicted responses, nevertheless the response surface to Weighted Principal Component – case b – (WPC1^b) presented the highest predictability.     

Decision tree and PCA-based fault diagnosis of rotating machinery

After analysing the flaws of conventional fault diagnosis methods, data mining technology is introduced to fault diagnosis field, and a new method based on C4.5 decision tree and principal component analysis (PCA) is proposed. In this method, PCA is used to reduce features after data collection, preprocessing and feature extraction. Then, C4.5 is trained by using the samples to generate a decision tree model with diagnosis knowledge. At last the tree model is used to make diagnosis analysis. To validate the method proposed, six kinds of running states (normal or without any defect, unbalance, rotor radial rub, oil whirl, shaft crack and a simultaneous state of unbalance and radial rub), are simulated on Bently Rotor Kit RK4 to test C4.5 and PCA-based method and back-propagation neural network (BPNN). The result shows that C4.5 and PCA-based diagnosis method has higher accuracy and needs less training time than BPNN.     

车辆用钢板轧制控制决策支持的研究

分析了多道次轧制工艺参数对含钒钢组织性能的影响,以主成分分析法和偏最小二乘法建立工艺参数与组织参数回归模型,确定优化方向.实验方法以灰色理论为依据,建立多指标决策的灰关联度量化模型,对含钒钢综合性能进行排序,确定最优方案,为工艺参数的优化提供决策支持.研究表明:对成分、第一道次变形温度、第二道次变形量,第一二、三四道次间隔时间等参数进行控制可以得到综合性能较好的材质,其F铁素体≥75%,Ffine≥60%、纳米级析出相尺寸(σ)(10～50)nm,晶粒尺寸(r)3.4μm.     

基于多目标遗传算法的炼焦生产过程优化控制

针对某钢铁企业实际炼焦生产过程的优化控制问题,提出一种多目标分层优化控制策略.首先采用主成分分析、灰色关联分析及改进前馈神经网络方法,建立综合生产目标与局部优化目标的关联模型,将综合生产目标映射为局部优化目标.然后建立以焦炭产量最大、焦炉能耗最小为优化目标,焦炭质量与工艺要求为约束条件,局部优化目标为决策变量的多目标优化模型.通过多目标遗传算法求解多目标优化问题,获得局部优化目标值.最后将局部优化目标作为各子过程控制系统的设定值及优化调度系统的决策参数,来动态调整过程操作参数,实现企业期望的综合生产目标.实际运行结果表明,提出的优化控制策略取得了较好的应用效果.     

Coach simplified structure modeling and optimization study based on the PBM method

For the coach industry, rapid modeling and efficient optimization methods are desirable for structure modeling and optimization based on simplified structures, especially for use early in the concept phase and with capabilities of accurately expressing the mechanical properties of structure and with flexible section forms. However, the present dimension-based methods cannot easily meet these requirements. To achieve these goals, the property-based modeling (PBM) beam modeling method is studied based on the PBM theory and in conjunction with the characteristics of coach structure of taking beam as the main component. For a beam component of concrete length, its mechanical characteristics are primarily affected by the section properties. Four section parameters are adopted to describe the mechanical properties of a beam, including the section area, the principal moments of inertia about the two principal axles, and the torsion constant of the section. Based on the equivalent stiffness strategy, expressions for the above section parameters are derived, and the PBM beam element is implemented in HyperMesh software. A case is realized using this method, in which the structure of a passenger coach is simplified. The model precision is validated by comparing the basic performance of the total structure with that of the original structure, including the bending and torsion stiffness and the first-order bending and torsional modal frequencies. Sensitivity analysis is conducted to choose design variables. The optimal Latin hypercube experiment design is adopted to sample the test points, and polynomial response surfaces are used to fit these points. To improve the bending and torsion stiffness and the first-order torsional frequency and taking the allowable maximum stresses of the braking and left turning conditions as constraints, the multi-objective optimization of the structure is conducted using the NSGA-II genetic algorithm on the ISIGHT platform. The result of the Pareto solution set is acquired, and the selection strategy of the final solution is discussed. The case study demonstrates that the mechanical performances of the structure can be well-modeled and simulated by PBM beam. Because of the merits of fewer parameters and convenience of use, this method is suitable to be applied in the concept stage. Another merit is that the optimization results are the requirements for the mechanical performance of the beam section instead of those of the shape and dimensions, bringing flexibility to the succeeding design.     

Chipping minimization in drilling ceramic materials with rotary ultrasonic machining

Ultrasonic machining (USM) has been considered as a new cutting technology that does not rely on the conductance of the workpiece. USM presents no heating or electrochemical effects, with low surface damage and small residual stresses on workpiece material, such as glass, ceramics, and others; therefore, it is used to drill microholes in brittle materials. However, this process is very slow and tool wear dependent, so the entire process has low efficiency. Therefore, to increase microhole drilling productivity or hole quality, rotary ultrasonic machining (RUM) is considered as a strong alternative to USM. RUM, which presents ultrasonic axial vibration with tool rotation, is an effective solution for improving cutting speed, precision, tool wear, and other machining responses beyond those of the USM. This study aims to reduce the microchipping or cracking at the exit of the hole, which inevitably occurs when brittle materials are drilled, with consideration of tool wear. To this end, response surface analysis and desirability functions are used for experimental optimization. The experimental results showed that the proposed RUM scheme is suitable for microhole drilling.     

Fatigue and impact analysis and multi-objective optimization design of Mg/Al assembled wheel considering riveting residual stress

The multi-material assembled light alloy wheel presents an effective lightweight solution for new energy vehicles, but its riveting connection remains a problem. To address this problem, this paper proposed the explicit riveting-implicit springback-implicit fatigue/explicit impact sequence coupling simulation analysis method, analyzed the fatigue and impact performance of the punching riveting connected magnesium/aluminum alloy (Mg/Al) assembled wheel, and constructed some major evaluation indicators. The accuracy of the proposed simulation method was verified by conducting physical experiments of single and cross lap joints. The punching riveting process parameters of the assembled wheel joints were defined as design variables, and the fatigue and impact performance of the assembled wheel was defined as the optimization objective. The connection-performance integration multi-objective optimization design of the assembled wheel considering riveting residual stress was designed via Taguchi experiment, grey relational analysis, analytic hierarchy process, principal component analysis, and entropy weighting methods. The optimization results of the three weighting methods were compared, and the optimal combination of design variables was determined. The fatigue and impact performance of the Mg/Al assembled wheel were effectively improved after optimization.