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.     

Modified multivariate process capability index using principal component analysis

The existing research of process capability indices of multiple quality characteristics mainly focuses on nonconforming of process output, the concept development of tmivariate process capability indices, quality loss function and various comprehensive evaluation methods. The multivariate complexity increases the computation difficulty of multivariate process capability indices（MPCI）, which makes them hard to be used in practice. In this paper, a new PCA-based MPCI approach is proposed to assess the production capability of the processes that involve multiple product quality characteristics. This approach first transforms the original quality variables into standardized normal variables. MPCI measures are then provided based on the Taam index. Moreover, the statistical properties of these MPCIs, such as confidence intervals and lower confidence bound, are given to let the practitioners understand the capability indices as random variables instead of deterministic variables. A real manufacturing data set and a synthetic data set are used to demonstrate the effectiveness of the proposed method. An implementation procedure is also provided for quality engineers to apply our MPCI approach in their manufacturing processes. The case studies demonstrate the effectiveness and feasibility of this new kind of MPCI, which is easier to be used in production practice. The proposed research provides a novel approach of MPCI calculation.     

改进MKPCA方法及其在发酵过程监控中的应用

针对间歇发酵过程缓慢时变和非线性等特点,提出一种基于滑动窗技术的多向核主元分析(MWMKPCA)方法.该方法结合了核主元分析(KPCA)和滑动窗口技术的优点,其中KPCA能有效解决过程数据的非线性问题,保证数据信息抽取的完整性;而滑动窗口技术能有效避免MKPCA在线应用时预报未来测量值所引入的误差,提高监控性能.对于已判断正常的新批次过程数据,将其加入模型参考数据库进行更新,从而提高间歇过程性能检测的准确性.将该方法应用到工业青霉素发酵过程的监控中,并与MPCA、MKPCA方法的监测性能进行了比较.结果表明:该方法能有效提取过程变量间的非线性关系,降低运行过程的误报率,对缓慢时变的间歇过程具有更可靠的检测性能.     

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.     

The fault feature extraction and classification of gear using principal component analysis and kernel principal component analysis based on the wavelet packet transform

The vibration signal of a gear system is selected as the original information of fault diagnosis and the gear system vibration equipment is established. The vibration acceleration signals of the normal gear, gear with tooth root crack fault, gear with pitch crack fault, gear with tooth wear fault and gear with multi-fault (tooth root crack & tooth wear fault) is collected in four kinds of speed conditions such as 300 rpm, 900 rpm, 1200 rpm and 1500 rpm. Using the method of wavelet threshold de-noising to denoise the original signal and decomposing the denoising signal utilizing the wavelet packet transform, then 16 frequency bands of decomposed signal are got. After restructuring the decomposing signal and obtaining the signal energy in each frequency band, the signal energy of the 16 bands is as the shortlisted fault characteristic data. Based on this, using the methods of principal component analysis (short for PCA) and kernel principal component analysis (short for KPCA) to extract the feature from the fault features of shortlisted 16-dimensional data feature, then the effect of reducing dimension analysis are compared. The fault classifications are displayed through the information that got from the first and the second principal component and kernel principal component, and these demonstrate they have a different and good effect of classification. Meanwhile, the article discusses the effect of feature extraction and classification that caused by the kernel function and the different options of its parameters. These provide a new method for a gear system fault feature extraction and classification.     

指数加权主元分析法及其在故障诊断中的应用

在研究主元分析法(PCA)理论的基础上,提出指数加权主元分析(EWPCA)算法。这种算法通过不断更新相关矩阵来实时监视动态生产过程中的超时趋势和设定点改变等状态。实验结果表明,该方法可以较好地反映生产过程中的实时信息,并能有效检测出系统的异常状况,具有广阔的实际应用前景。     

基于函数主元分析的多阶段退化过程建模与预测

退化过程建模与预测作为设备健康管理的基础,是降低运行风险和维护成本的有效途径。为解决实际中退化过程所表现出的随机性、非线性和多阶段复杂性,提出了一种基于函数主元分析的多阶段退化过程自适应建模与预测方法。通过将退化测量值视为连续函数的离散采样值,从而将退化建模问题转换为函数型数据分析问题。在此基础上,利用函数主元分析方法对退化数据进行降维,提取设备退化的共性信息以及个体差异性信息。结合贝叶斯推理,利用在线监测数据更新退化模型参数,实现健康状态的在线实时预测。最后,将所提的方法用于散热风扇的加速寿命试验数据,验证了本方法的有效性。结果表明,所提方法可以地很好建模多阶段的复杂随机退化过程,具有潜在的工程应用价值。     

Fault diagnosis method of rolling bearing using principal component analysis and support vector machine

To effectively extract the fault feature information of rolling bearings and improve the performance of fault diagnosis, a fault diagnosis method based on principal component analysis and support vector machine was presented, and the rolling bearings signals with different fault states were collected. To address the limitation on effectively dealing with the raw vibration signals by the traditional signal processing technology based on Fourier transform, wavelet packet decomposition was employed to extract the features of bearing faults such as outer ring flaking, inner ring flaking, roller flaking and normal condition. Compared with the previous literature on fault diagnosis using principal component analysis (PCA) and support vector machine (SVM), one-to-one and one-to-many algorithms were taken into account. Additionally, the effect of four kernel functions, such as liner kernel function, polynomial kernel function, radial basis function and hyperbolic tangent kernel function, on the performance of SVM classifier was investigated, and the optimal hype-parameters of SVM classifier model were determined by genetic algorithm optimization. PCA was employed for dimension reduction, so as to reduce the computational complexity. The principal components that reached more than 95 % cumulative contribution rate were extracted by PCA and were input into SVM and BP neural network classifiers for identification. Results show that the fault feature dimensionality of the rolling bearing is reduced from 8-dimensions to 5-dimensions, which can still characterize the bearing status effectively, and the computational complexity is reduced as well. Compared with the raw feature set, PCA has a higher fault diagnosis accuracy (more than 97 %), and a shorter diagnosis time relatively. To better verify the superiority of the proposed method, SVM classification results were compared with the results of BP neural network. It is concluded that SVM classifier achieved a better performance than BP neural network classifier in terms of the classification accuracy and time-cost.     

Grey relational analysis coupled with principal component analysis for optimisation design of the process parameters in in-feed centreless cylindrical grinding

This paper investigates optimisation design of an in-feed centreless cylindrical grinding process performed on EN52 austenitic valve steel (DIN: X45CrSi93). The major performance characteristics selected to evaluate the process are surface roughness, out of cylindricity of the valve stem and diametral tolerance, and the corresponding centreless cylindrical grinding parameters are dressing feed, grinding feed, dwell time and cycle time. In this study, since the process is with multiple-performance characteristics, therefore, the grey relational analysis that uses grey relational grade as performance index is specially adopted to determine the optimal combination of centreless cylindrical grinding parameters. Moreover, the principal component analysis is applied to evaluate the weighting values corresponding to various performance characteristics so that their relative importance can be properly and objectively described. The results of confirmation experiments reveal that grey relational analysis coupled with principal component analysis can effectively be used to obtain the optimal combination of centreless cylindrical grinding parameters. Hence, this confirms that the proposed approach in this study can be a useful tool to improve the centreless cylindrical grinding performance of valve stem in in-feed centreless cylindrical grinding process.     

主成分分析在光全散射特征波长选择中的应用

为了能在用光全散射法测量颗粒粒径时选择对粒径影响较显著的特征波长进行测量,通过在可见及可见-红外波段内对粒径服从单峰R-R分布颗粒系的消光光谱,一阶微分以及二阶微分消光光谱进行主成分变换,提出一种特征波长选择方法。该方法首先对颗粒系的一阶微分消光光谱进行主成分变换,然后将每个波长下的一阶微分消光谱对主成分贡献率的大小作为特征波长选择的主要依据,并将光谱范围的边界波长也作为特征波长。分别对粒径服从单峰及双峰R-R分布的颗粒系进行数值仿真,并采用标准颗粒的实测数据进行验证。验证结果显示,采用基于主成分分析的波长选择方法计算方便、易于实现,得到的标准颗粒粒径反演误差均小于3%,表明采用提出的波长选择方法能够保证选出的光谱消光值具有较高的信息量。     

Mapping titanium and tin oxide phases using EELS: an application of independent component analysis

We study materials that present challenges for conventional elemental mapping techniques and can in some cases be treated successfully using independent component analysis (ICA). In this case the material in question is obtained from a TiO₂-SiO₂ solid solution that is spinodally decomposed into TiO₂ rich-SnO₂ rich multilayers. Conventional elemental mapping is difficult because the edges most easily mapped for these elements (Ti-L, Sn-M and O-K) all have onsets within the same 80 eV range. ICA is used to separate entire spectral signals corresponding to particular material phases or molecular units rather than particular elements and is thus able to distinguish between TiO₂ and SnO₂. We show that quantification of oxide species can be performed by different methods that require extra assumptions, but nevertheless should be feasible in many cases.     

Optimization of multiple responses using principal component analysis and technique for order preference by similarity to ideal solution

Optimizing multi-response problems has become an increasingly relevant issue when more than one correlated product quality characteristic must be assessed simultaneously in a complicated manufacturing process. This study proposes a novel optimization procedure for multiple responses based on Taguchi’s parameter design. The signal-to-noise (SN) ratio is initially used to assess the performance of each response. Principal component analysis (PCA) is then conducted on the SN values to obtain a set of uncorrelated components. The optimization direction for each component is determined based on the corresponding variation mode chart. Finally, the relative closeness to the ideal solution resulting from the technique for order preference by similarity to ideal solution (TOPSIS) is determined as an overall performance index (OPI) for multiple responses. Engineers can easily employ the proposed procedure to obtain the optimal factor/level combination for multiple responses. A case study involving optimization of the chemical-mechanical polishing of copper (Cu-CMP) thin films from an integrated circuit manufacturer in Taiwan is also presented to demonstrate the effectiveness of the proposed procedure.     

Localization and quantification of damage in beam-like structures using sensitivities of principal component analysis results

Principal component analysis (PCA) is known as an efficient method for dynamic system identification and diagnosis. This paper addresses a damage diagnosis method based on sensitivities of PCA in the frequency domain for linear-form structures. The aim is not only to detect the presence of damage, but also to localize and to evaluate it. The Frequency response functions measured at different locations on the beam are considered as data for the PCA process. Sensitivities of principal components obtained from PCA to beam parameters are computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. The damage can be evaluated next providing that a structural model is available; this evaluation is based on a model updating procedure. It is worth noting that the diagnosis process does not require a modal identification achievement. Both numerical and experimental examples are used for better illustration.     

Determination of the major dimensions of femoral implants using morphometrical data and principal component analysis

This paper describes the work that leads to the establishment of a set of major parameters for the design of symmetrical prosthetic implants for the Asian population. In the study, 62 sets of femurs harvested from cadavers were used. The morphometrical data obtained are compared with known results and found to be in good agreement with Asian knees. Subsequently, the data are treated and analysed using the principal component analysis, a statistical technique for analysing multivariate data. The analysis has resulted in the establishment of the major design parameters for six different sizes of femoral implants. Details of the analysis are presented. The major parameters obtained in this work are compared with those of existing implants. Results of the comparison are presented. The relationship between the anterio-posterior and medio-lateral dimensions is also examined and reported.     

Quality monitoring based on dynamic resistance and principal component analysis in small scale resistance spot welding process

The present study aims at solving weld quality monitoring problem in small scale resistance spot welding of titanium alloy. Typical dynamic resistance curves were divided into several stages based on the weld nugget formation process. A smaller electrode force or lower welding current was found to promote the initial resistance peak. The bulk material heating stage could not be detected under very high welding current condition. Electrode force effect on dynamic resistance and failure load was much smaller than that of welding current. Principal component analysis was made on discrete dynamic resistance values. The first principal component was selected as independent variable in regression analysis for quality estimation. A back propagation neural network model was then proposed to simultaneously predict the nugget size and failure load. The electrode force, welding current, welding time, and first five principal components were designed as network inputs. Effectiveness of the developed model was validated through data training, testing, and validation. The realtime and online quality monitoring purpose could be realized.     

Evaluation of scanning electron microscopy images of a model dressing using image feature extraction techniques and principal component analysis

Twelve dressing systems made by varying protein type, oil level, CaCl₂, NaCl, and sucrose, were examined using scanning electron microscopy. Images from the 12 systems were quantitatively analysed using methods of feature extraction. These methods were based on vectorisations of the images followed by principal component analysis on the extracted vectors. These techniques were used to examine the reproducibility of the acquired images as well as to relate the images to rheologic and sensory texture parameters. Two feature extraction methods were used: the angle measure technique (AMT) and the absolute difference method (ABDF). The ABDF method used fewer principal components to extract information from images relevant to the complex modulus/sensory viscosity of the system, but the information seemed equally well preserved by the two-feature extraction methods. The AMT was more efficient in classifying the images with respect to protein type. A fair correlation between images and complex modulus was obtained (R=0.73). It is suggested that a better correlation might be obtained by adding more systems, increasing the number of areas imaged for each system as well as avoiding systems of low viscosity.     

近红外显微图像的主成分法图像处理

介绍主成分分析算法在近红外显微图像分析中的应用,用该方法成功地提取出样品成分相关特征信息,并通过不同主成分的得分图像来描述样品的显微结构特征和特定化学成分分布。     

Dynamic multi-response optimization using principal component analysis and multiple criteria evaluation of the grey relation model

The application of parameter design methodology has been considerable in recent years to make system performance robust over a wide range of input conditions. This notion has been referred to as a robust design with dynamic characteristics. Due to product complexity, multiple correlated characteristics must be simultaneously evaluated for improving product quality. Dynamic multi-response optimization is becoming an important issue to contemporary industry. This study developed a novel procedure of optimizing dynamic multi-responses using principal component analysis (PCA) and multiple criteria evaluation of the grey relation model. PCA can consider the correlations among multiple quality characteristics to obtain uncorrelated components. These components are then substituted into multiple criteria evaluation of the grey relation model to determine the optimal factor level combination. A case study demonstrates the effectiveness of the proposed procedure for optimizing dynamic multi-response processes.     

Virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method

Gear systems are an essential element widely used in a variety of industrial applications. Since approximately 80% of the breakdowns in transmission machinery are caused by gear failure, the efficiency of early fault detection and accurate fault diagnosis are therefore critical to normal machinery operations. Reviewed literature indicates that only limited research has considered the gear multi-fault diagnosis, especially for single, coupled distributed and localized faults. Through virtual prototype simulation analysis and experimental study, a novel method for gear multi-fault diagnosis has been presented in this paper. This new method was developed based on the integration of Wavelet transform (WT) technique, Autoregressive (AR) model and Principal Component Analysis (PCA) for fault detection. The WT method was used in the study as the de-noising technique for processing raw vibration signals. Compared with the noise removing method based on the time synchronous average (TSA), the WT technique can be performed directly on the raw vibration signals without the need to calculate any ensemble average of the tested gear vibration signals. More importantly, the WT can deal with coupled faults of a gear pair in one operation while the TSA must be carried out several times for multiple fault detection. The analysis results of the virtual prototype simulation prove that the proposed method is a more time efficient and effective way to detect coupled fault than TSA, and the fault classification rate is superior to the TSA based approaches. In the experimental tests, the proposed method was compared with the Mahalanobis distance approach. However, the latter turns out to be inefficient for the gear multi-fault diagnosis. Its defect detection rate is below 60%, which is much less than that of the proposed method. Furthermore, the ability of the AR model to cope with localized as well as distributed gear faults is verified by both the virtual prototype simulation and experimental studies.