Johnson Transformation Research Articles

Novel method for numerical reconstruction of grinding surfaces with specified roughness parameter set

Surface roughness parameters play a decisive role on grinding surface service performance. Among 26 surface roughness parameters, closely related to the surface performance and defined by ISO25178, in the 6 categories, numerical reconstruction of grinding surfaces can only control 7 height parameters and 2 spatial parameters with inability to achieve precise control of other parameter-defined features. Therefore, a novel numerical reconstruction method for grinding surfaces with specified rough parameter set (SRPS) was proposed to solve the problem of feature loss caused by other uncontrollable parameters. Combine three characteristic coefficients of height probability density function in Johnson transformation method with four characteristic coefficients of autocorrelation function expression to construct surface reconstruction coefficient set (SRCS) and build SRPS with number of 22 in consideration of the measurement error influence and industrial application frequency. Use BP neural network to establish quantitative mapping model between SRCS and SRPS for inversion. Through introducing genetic algorithm to invert SRPS corresponding SRCS, numerical reconstruction of grinding surfaces with SRPS will be realized. Experimental results show that compared with the measured grinding surfaces, the average error in SRPS of reconstructed surfaces is basically within 10%. The research provides a new means for the study of the surface performance, which solves the problem that the traditional rough surface modeling method based on random process theory could only associate 9 roughness parameters.

Improving the Accuracy of Surface Roughness Modeling when Milling 3x13 Steel

In this study, a milling experiment was performed, with 3x13 steel selected as the experimental material along with TiAlN coated inserts. The Box-Behnken method was used to design the experimental matrix with a total of eighteen experiments. Cutting speed, feed amount, and depth of cut were selected as the input parameters. Three regression models of surface roughness have been established, one using the experimentally measured surface texture, one using the Johnson transform to convert the surface texture data, and one using Box-Cox transformation to convert the surface texture data. A comparison of the accuracy of the three models was performed. The results show that the model using the Box-Cox transformation has the highest accuracy, followed by the model using the Johnson transformation. In addition, the influence of cutting parameters on surface roughness is also discussed in detail.

Study of the Flood Frequency Based on Normal Transformation in Arid Inland Region: A Case Study of Manas River in North-Western China

Flood disaster is one of the natural disasters which cause the most serious economic losses, the most casualties, and the greatest social impact. Flood frequency analysis is very important for reducing flood disaster. In this paper, based on the flood data of Manas River and tools of Box–Cox and Johnson normal transformation, the nonparametric statistical method for flood frequency analysis is studied in order to analyze the adaptability between it and the rivers in arid region of north-western China. The calculation result of the fitness index is divided into two parts: high flood discharge and low flood discharge. One of the two evaluation indexes has an advantage in fitting, and the number of advantages of the three methods in each part has been counted. After analysis, for the flood peak discharge frequency of rivers in arid region of north-western China, the frequency curve of Johnson transformation fits best with empirical data. The high flood discharge advantage is 6, and the low flood discharge is 4. For the flood volume frequency of rivers in arid region of north-western China, Box–Cox transform fits well with empirical data at the high flood discharge frequency curve, and its advantage is 12; Johnson transformation has a better fit between the low flood discharge frequency curve and empirical data, and its advantage is 12. Therefore, it is the way of improving the precision of flood frequency analysis to use the method of P-III distribution and normal transformation comprehensively.

Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression

The paper introduces an automatic procedure for the parametric transformation of the response in regression models to approximate normality. We consider the Box–Cox transformation and its generalization to the extended Yeo–Johnson transformation which allows for both positive and negative responses. A simulation study illuminates the superior comparative properties of our automatic procedure for the Box–Cox transformation. The usefulness of our procedure is demonstrated on four sets of data, two including negative observations. An important theoretical development is an extension of the Bayesian Information Criterion (BIC) to the comparison of models following the deletion of observations, the number deleted here depending on the transformation parameter.

PFCMVO: Political fractional competitive multi-verse optimization enabled deep neuro fuzzy network for student performance estimation in spark environment

Student performance calculation is an essential process in online learning scheme, which intends to afford students along with admittance to active learning. Student performance forecast is most concerning problem in education and training field, particularly in educational data mining (EDM). The prediction process provisions the students to choose courses and intend suitable training strategies for themselves. Furthermore, student performance calculation permits lecturers and educational supervisors to designate which students should be observed and maintained to finish their plans with finest outcomes. These provisions can decrease the official notices and exclusions from universities because of students’ poor performance. In this paper, Political Fractional Competitive Multi-verse Optimization enabled Deep Neuro fuzzy network (PFCMVO enabled DNFN) uses spark framework for student performance calculation. Moreover, Yeo–Johnson transformation is applied for transforming the input data for effectual student performance prediction. In addition, Damerau–Levenshtein (DL) distance is applied to select appropriate features. The DNFN classifier is utilized to execute student performance prediction where the classifier is trained by PFCMVO algorithm. The developed student performance prediction model outperforms than the other existing techniques with respect to Precision, Recall, [Formula: see text]-measure, and Prediction accuracy of 0.9259, 0.9321, 0.9290, and 0.9372 for dataset-1 and 0.9126, 0.9271, 0.9198, and 0.9248 for dataset-2, respectively.

Effect of Normal Transformation Methods on Performance of Multivariate Normal Distribution

Multivariate normal distribution is used widely to characterize the uncertainties and correlations for correlated geotechnical data. The success of constructing a multivariate normal distribution depends on the reliable estimation of the marginal probability density functions (PDFs) and the correlation matrix. This paper focused on the normal transformation which is related to the fitted marginal PDFs and investigated its effect on the performance of the constructed multivariate normal distributions, i.e., the normality of the multivariate normal distribution, the fitness of the simulated data with the original data, the rationality of the derived point estimate equations, and validation of the equations based on validation data sets. Three normal transformation methods with different types of fitted marginal PDF, namely Johnson transformation, three-parameter lognormal transformation, and Box–Cox transformation, were compared based on their application to a real soil database. It was found that all the three normal transformation methods are applicable in the framework of multivariate normal distribution, although the transformed variables do not follow the multivariate normal distribution. The consistence of normality of the transformed variables with the performance of the constructed multivariate normal distribution in estimating the unknown parameters using Bayesian updating technique was verified. The Johnson transformation method is the recommended method for constructing the multivariate normal distribution for the real databases due to its robustness and superiority in normal transformation.

Simulation of stationary non-Gaussian multivariate wind pressures based on moment-based piecewise Johnson transformation model

Fast and accurate simulation of non-Gaussian wind pressures are desired sometimes in the wind-resistant design of buildings under stationary winds. Recently, attracted by its wide application range, the moment-based Johnson transformation model (JTM) has been successfully applied by some authors of this paper. However, the simulation accuracy and efficiency of the moment-based JTM still need to be improved. Inspired by the successful application of the proposed newly defined statistical moments to the moment-based Hermite polynomial model (HPM), this paper applies these moments to the JTM named moment-based piecewise JTM (PJTM) and proposes a novel PJTM-based simulation method. In this method, a set of close-form formulas to estimate the parameters of PJTM are firstly proposed. Secondly, the analytical formula to determine the correlation distortion relationship by PJTM is further developed. Finally, the performance of the proposed method is verified by the very long non-Gaussian wind pressure data from a wind tunnel test. Results shown the proposed method by PJTM can not only present higher simulation efficiency but also better simulation accuracy compared with JTM and can present higher simulation efficiency compared with moment-based piecewise HPM.

Synthesis of random vibration environment spectra for the fatigue analysis and optimization of railway vehicles

In railway vehicle environments, mechanical and electronic equipment are subjected to repeated environmental vibration loads. A possible qualifying method for such loads involves shock and vibration tests utilizing shakers or simulations. However, the input excitations provided by shakers considering standards such as IEC 61373 cannot reflect the real vibration environment, especially considering wheel/rail wear and wheel polygons. Considering these shortcomings, an environmental vibration profile synthesis method using field-tested power spectral density (PSD) data and a corresponding fatigue prediction model were proposed in this study. For the non-normally distributed vibration data of railway vehicles, the Johnson transformation was applied to calculate the upper tolerance limit of the profile. Then, the pseudo-excitation method was introduced to connect the synthesised spectrum to the simulation model, and the calculation procedure using a vibration fatigue algorithm was investigated. To validate the proposed methods, the potential causes of failure, fatigue damage, and optimisation of a shackle on an axle box were investigated using the proposed methods. The results show that the synthesised PSD can reflect the characteristics of environmental vibrations, including the additional excitation of rail wear, and compared with the fatigue results of the tests and simulations conducted under the standard spectrum, the predicted results under the synthesised spectrum were determined to be most similar to real-world scenarios, while the use of the standard spectrum exhibited infinite life. In addition, the potential advantage of optimisation using a synthesised spectrum instead of traditional transmissibility is presented and supported by the results of this case study.

MATHEMATICAL MODELING IN PROBLEMS OF ESTIMATING THE SIZE OF APPLICABLE OPEN-SOURCE SOFTWARE IN C #

Estimating the size of software, including open-source applications in C#, is currently an especially important part of the development of such projects. Knowing the size of application software in the initial stages of development and using models such as COCOMO, COCOMO II or methods and models of algorithmic modeling and others that perform calculations based on quantitative values of application software it can be calculated labor costs and project cost and anticipate risks related to development. In this paper it was analyzed existing regression equations for estimating the software size of different programming languages which in turn indicated the need to construct a nonlinear regression equation for open-source application software in C# using the universal one-dimensional Johnson normalizing transformation for the SB family, which allowed to construct a nonlinear regression equation of high quality (R2 = 0.974, MMRE = 0.198, PRED(0.25) = 0.778), and which has better performance compared to the linear regression equation without using of normalizing transformations for empirical data (R2 = 0.887, MMRE =1.028, PRED(0.25) = 0.361), as well as in compared with the nonlinear regression equation using the natural logarithm as a normalizing transformation (R2 = 0.819, MMRE = 0.222, PRED(0.25) = 0.694). In addition, the use of the universal one-dimensional normalizing Johnson transformation of the SB family made it possible to construct a narrower confidence interval and prediction interval for the nonlinear regression equation compared to the intervals that were constructed using the natural logarithm as a normalizing transformation. As a result, a software application was developed for estimating the size of open source application software in C#, using a nonlinear regression equation based on the universal one-dimensional Johnson normalizing transformation for the SB family, which automates the calculation process and simplifies the using constructed nonlinear regression equations that reduced the time of relevant calculations and reduced the number of calculation errors.

Optimized principal component analysis and multi-state Bayesian network integrated method for chemical process monitoring and variable state prediction

Considering the weaknesses of traditional principal component analysis (PCA) in dealing with nonlinear correlations and non-Gaussian distribution data, PCA is optimized by replacing covariance matrix with Spearman ranking correlation coefficient (SRCC) matrix and introducing Gaussian transition by Johnson transformation. Because the commonly used BN that simply identifies a node as faulty or normal states sometimes fails to diagnose critical operation information, multi-state Bayesian network (MBN) is developed to recognize a node into multiple states. To fulfill process monitoring task, the optimized PCA (OPCA) and MBN integrated method (OPCA-MBN) is proposed in this paper. OPCA is utilized to detect faults and provide evidence to MBN for diagnosing fault or normal oscillation propagation pathways. In the modeling process of MBN, the causal relationships between tangled internal variables are determined using Transfer entropy and process knowledge. The practicability and effectiveness of the proposed method are demonstrated through the application in the Tennessee Eastman (TE) process in comparison with two-state BN.

A Study on Surface Roughness when Milling C45 Steel

In this paper, a study is presented on the milling process of C45 steel by face milling cutters. An experimental process was performed according to an experimental matrix constructed by the Box-Behnken method. At each experiment, three cutting parameters were changed, namely cutting speed, feed rate, and depth of cut. Surface roughness has been selected as a parameter to evaluate the milling process. Analysis of experimental results has determined the influence of cutting parameters as well as their interactions on surface roughness. Two regression models for surface roughness have been proposed. In which one model uses the Johnson transformation. These two models were used to predict the surface roughness and then compared with the experimental results. The results show that the model using the Johnson transformation has higher accuracy than the model not using the data transformation.

Study on model for cutting force when milling SCM440 steel

This article presents empirical study results when milling SCM440 steel. The cutting insert to be used was a TiN coated cutting insert with tool tip radius of 0.5 mm. Experimental process was carried out with 18 experiments according to Box-Behnken matrix, in which cutting speed, feed rate and cutting depth were selected as the input parameters of each experiment. In addition, cutting force was selected as the output parameter. Analysis of experimental results has determined the influence of the input parameters as well as the interaction between them on the output parameters. From the experimental results, a regression model showing the relationship between cutting force and input parameters was built. Box-Cox and Johnson data transformations were applied to construct two other models of cutting force. These three regression models were used to predict cutting force and compare with experimental results. Using parameters including coefficient of determination (R-Sq), adjusted coefficient of determination (R-Sq(adj)) and percentage mean absolute error (% MAE) between the results predicted by the models and the experimental results are the criteria to compare the accuracy of the cutting force models. The results have determined that the two models using two data transformations have higher accuracy than model not using two data transformations. A comparison of the model using the Box-Cox transformation and the model using the Johnson transformation was made with a t-test. The results confirmed that these two models have equal accuracy. Finally, the development direction for the next study is mentioned in this article

Development of surface roughness model in turning process of 3X13 steel using TiAlN coated carbide insert

Surface roughness that is one of the most important parameters is used to evaluate the quality of a machining process. Improving the accuracy of the surface roughness model will contribute to ensure an accurate assessment of the machining quality. This study aims to improve the accuracy of the surface roughness model in a machnining process. In this study, Johnson and Box-Cox transformations were successfully applied to improve the accuracy of surface roughness model when turning 3X13 steel using TiAlN insert. Four input parameters that were used in experimental process were cutting velocity, feed rate, depth of cut, and insert-nose radius. The experimental matrix was designed using Central Composite Design (CCD) with 29 experiments. By analyzing the experimental data, the influence of input parameters on surface roughness was investigated. A quadratic model was built to explain the relationship of surface roughness and the input parameters. Box-Cox and Johnson transformations were applied to develop two new models of surface roughness. The accuracy of three surface roughness models showed that the surface roughness model using Johnson transformation had the highest accuracy. The second one model of surface roughness is the model using Box-Cox transformation. And surface roughness model without transformation had the smallest accuracy. Using the Johnson transformation, the determination coefficient of surface roughness model increased from 80.43 % to 84.09 %, and mean absolute error reduced from 19.94 % to 16.64 %. Johnson and Box-Cox transformations could be applied to improve the acuaracy of the surface roughness prediction in turning process of 3X13 steel and can be extended with other materials and other machining processes

The Box–Cox Transformation: Review and Extensions

The Box–Cox power transformation family for nonnegative responses in linear models has a long and interesting history in both statistical practice and theory, which we summarize. The relationship between generalized linear models and log transformed data is illustrated. Extensions investigated include the transform both sides model and the Yeo–Johnson transformation for observations that can be positive or negative. The paper also describes an extended Yeo–Johnson transformation that allows positive and negative responses to have different power transformations. Analyses of data show this to be necessary. Robustness enters in the fan plot for which the forward search provides an ordering of the data. Plausible transformations are checked with an extended fan plot. These procedures are used to compare parametric power transformations with nonparametric transformations produced by smoothing.

Transforming variables to central normality

Many real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Improving accuracy of surface roughness model while turning 9XC steel using a Titanium Nitride-coated cutting tool with Johnson and Box-Cox transformation

The surface roughness model for predicting surface roughness during machining is built in order to deal with time constraints of adjusting and testing. This study aims to achieve this purpose. The 9XC steel turning experiment is performed on a CNC lathe with the cutting tool is Titanium Nitride-coated. The input parameters selected for the test matrix include cutting velocity, feed rate, depth of cut and tool nose radius. The experiments were carried out based on Central Composite Design (CCD) with 29 trials. The analysis of results using Minitab software reveals that feed rate is the most influential parameter, while the others have a negligible impact on surface roughness. The response surface method (RSM) is applied for modeling surface roughness. Johnson and Box-cox transformations are also used to develop two new models of surface roughness. The comparison of predicted results from these three models with experimental results shows that the Box-Cox-based model has the highest accuracy, followed by the Johnson while the model not using these transformation is the least. Mean absolute error and mean square error of the RSM-based model are 17.264% and 2.712% respectively; while they are 10.373% and 1.280% in the Johnson-based and 10.208% and 1.284% when using the Box-Cox transformation.

Estimating the Efforts of Mobile Application Development in the Planning Phase Using Nonlinear Regression Analysis

Abstract The authors consider the construction of a nonlinear multiple regression model, its confidence and prediction intervals to evaluate the efforts of mobile application development in the planning phase based on the multivariate normalizing transformation and outlier detection. The constructed model is compared to the linear regression model and nonlinear regression models based on the univariate transformations, such as the decimal logarithm, Box–Cox, and Johnson transformation. This model, in comparison with other regression models, has better prediction accuracy.

An efficient simulation algorithm for non-Gaussian nonstationary processes

A novel algorithm is proposed for simulating univariate non-Gaussian nonstationary processes (NNP) with the specified evolutionary power spectral density (EPSD)/nonstationary auto-correlation function (NACF) and first four-order time-varying marginal moments (TVMMs). The sample realizations of the target NNP are generated as the outputs from a specific time-varying auto-regressive (TVAR) model via filtering the non-Gaussian and nonstationary white noise inputs. These white noise inputs are also non-Gaussian and nonstationary, and their first four-order TVMMs are predetermined using an approach developed herein according to the specified EPSD/NACF and first four-order TVMMs of the outputs. The conventional Johnson transformation is updated to accommodate the nonstationary cases for producing desired white noise inputs. This algorithm is developed from the linear filtering method (LFM), and inherits the simplicity and high efficiency from LFM. It fills the gaps in LFM-based algorithms for simulating NNP. Two numerical examples, i.e., a ground motion acceleration and a downburst velocity, are presented to fully demonstrate the capabilities of the proposed algorithm by comparing the simulation statistics with the targets.

Modeling And Improvement of the Surface Roughness Model in Hole Turning Process 3x13 Stainless Steel by Using Johnson Transformation

Modeling And Improvement of the Surface Roughness Model in Hole Turning Process 3x13 Stainless Steel by Using Johnson Transformation

Evaluating capability of a process with ordinal responses

Evaluating the capability of a manufacturing process is an important initial step in any quality improvement program. Methodologies have been reported in literature for evaluating capability of processes with quantitative characteristics of different natures. However, quantifying capability of a process with qualitative responses remains a difficult task. In this paper, a novel method is presented for measuring capability of a process with ordinal responses involving three ordered categories. The proposed method makes use of the process area of proportions and specification area of proportions defined in a two-dimensional plane. Extensive simulation studies reveal that in general, the defined process area does not always follow a normal distribution. However, by using Johnson transformation, it can be transformed to normal distribution and thus capability of a process with ordinal responses can be evaluated easily. Application of the proposed method to a real life problem is presented.