Prediction of surface roughness of various machining processes by a hybrid algorithm including time series analysis, wavelet transform and multi view embedding
Introduction
In today's world of economics, reducing the production time and modifying the machining parameters online, in order to achieve the high quality of the surface roughness of the manufactured workpieces is an achievable dream. In order to control and improve the surface texture of the manufactured workpiece in machining processes, various attempts have been made to estimate the optimized conditions of machining. But there are so many influential variables that it is very difficult to control them simultaneously and are considered the main challenge faced in optimization machining processes. These attempts can be divided into two main categories including applying the image processing methods on the manufactured surface and analyzing the cutting parameters during the machining process. Unfortunately, in the first category, most of the image processing methods have been implemented for measuring the surface roughness of the machined surface in the offline condition. But some of the suggested methods such as the presented method by Pour in Ref. [1] have the special ability to expand in the online measurement condition. The initial principles of these methods were established based on analyzing the information latent in pixels of image. On the other hand, in the latter category, Misaka et al. utilized Kriging and Co-Kriging methods for predicting surface roughness from cutting tool vibration signals which do depend too much on data [2]. They illustrated that their suggested methods had the reliable prediction even for the condition where the training data is insufficient. A step forward is done in Ref [3]. They suggested using the time-series analyses for prediction of the future vibration signal. Although the extensive efforts have been conducted in simulating various machining processes, most of the proposed methods in this category are based on the use of expensive or special equipment. Therefore, since utilizing a camera to control the surface roughness is more cost-effective than using the above equipment, image-based methods have received more attention.
The first investigation of surface roughness determination had begun based on image processing techniques since three decades ago by Locke et al [4]. Despite the advantages of this method such as low cost, rapid measurement speed, high accuracy, reliability and slight depreciation of equipment [5], problems such as surface luminosity [6] and peripheral noise [7] led to raise an error in determining surface roughness. Three classifications including the fields of statistical methods, frequency domain [8], and time–frequency domain [9], [10] to eliminate the above errors have received more attention and are presented. Also, the ability of the high accuracy of the Artificial Neural Networks (ANN) on the feature classification, especially on the non-linear patterns, is considered [11], [12]. Morala et al. [13] have utilized a combination of wavelet and ANN for the surface roughness classification. After this research, to reduce the errors in non-contact methods in the estimation of surface roughness, Pour in Ref [1] presented a new method that used a combination the time series and wavelet transform for detecting the surface roughness in offline conditions. This method was implemented on different machining processes and the maximum error of the proposed method was equal or less than 8%. All of these methods were introduced for the measurement in offline form.
In recent years, researchers have attempted to online predict the surface roughness of the workpiece being produced using innovative methods. For this purpose, some of the studies pay attention to the 2-D images of the nose area of tool tips [14] and the Fiedler number of surface images of workpiece that are extracted in situ during machining [15]. It should be noted that all offline and online methods can estimate surface roughness parameters based on the evidence on the current surface. But the presented method in this paper can predict the surface texture and surface roughness parameters , which will be manufactured in the coming moments, based on the evidence on the current surface. This method is an important step forward for the development of smart equipment in measurement industry of surface roughness that could be applied in the smart machining industry in next years.
Indeed, this method is implemented based on the fact that each signal has unique dynamic characteristics. Thus, in this study, the surface texture of the machined surface is considered as a signal or a dynamic phenomenon finding the time series analysis characteristics of which can be useful to make a comprehensive recognition of the intrinsic characteristics and predict its future.
In this paper, images of the standard surface roughness samples are utilized to extract the surface texture signals. They are prepared to process using eliminating the noise of the image in the wavelet transform method. Then, the suitable time delay, the suitable embedding dimension and the suitable false nearest neighbors for each surface by running the Imperialist Competitive Algorithm (ICA) method are extracted. In the final step, the prediction algorithm for predicting the surface roughness values is conducted in MATLAB software.
To clarify the paper organization, Fig. 1 illustrates a comprehensive sequence of the paper in a flowchart. Also, this figure clarifies the development of this paper compared with Ref [1] (in last steps). As can be observed, the proposed method progresses from the estimation of the surface roughness of the imaged section toward the prediction of the surface roughness of surface which will be manufactured in future.
Section snippets
Surface profiles
In all machining processes, various parameters such as cutting depth, progress rate, cutting speed, tool material, tool vibrations and clamping torque of tool and workpiece, workpiece temperature and the tool contact conditions with the workpiece can be effective in creating surface roughness. Obviously, extracting surface roughness conditions can help control, improve and correct momentarily the cutting parameters.
Various definitions have been expressed for the surface roughness of products
Extract surface texture using wavelet transform Eq. (3)
The existence of multi-scale characteristics of the discrete wavelet transform makes it possible to properly evaluate images at different resolutions. The base of the two-dimensional wavelet transform is the continuous wavelet transform presented in Eq. (2) and has two functions of expansion and transmission. These two functions are defined by two coefficients a and b which are the parameter of scaling and position, respectively.
By controlling the coefficients 'a' and 'b', the
Application of time series analysis for prediction of signal's future
Time series analysis is used as a tool for determining system dynamics and also for predicting the future behavior of the system [20]. Random processes have a certain behavioral pattern at the same time with the apparent disorder [21]. Surface roughness, due to its random nature, can be analyzed in a series of time [1], [19], [22]. It is important to identify the behavioral patterns of processes, determine the correct dimension of the process, and remove any additional information. Although, at
Multi-objective optimization method
In this paper, the authors decided to apply the Imperialist Competitive Algorithm (ICA) method to find the optimum number of samples/embedding dimension, since, according to the results of [20], ICA has many advantages such as higher convergence rate than PSO and GA algorithms. A prevalent method is utilized to obtain the optimal solution based on an objective function that is generated by combining the objective functions. In this paper, the weigth of each objective functions is equal and both
Simulation and prediction of surface roughness signal
By extracting the surface profiles from the 'cA' matrices, one can enter the surface roughness prediction stage. Since the data in 'cA' have surface roughness and surface wave, therefore, the surface roughness extraction from 'cA' data should be performed. For this purpose, a Gaussian algorithm is used. By subtracting the amplitude of different points from the surface wave designated, the amplitude of the deviation from the surface wave is determined at different points. In contact methods, the
Conclusion
It is impossible to use the contact methods for measuring of surface roughness during the execution of manufacturing processes. The method suggested in this paper is based on the combination of discrete wavelet transform of captured images and time series analysis. Using the previous data, it is possible to determine the future data of the surface roughness signal at any moment. In this paper, authors use the image processing techniques presented in their previous articles and develop a new
CRediT authorship contribution statement
Sepehr Nouhi: Investigation, Software, Visualization, Data curation, Writing – review & editing. Masoud Pour: Conceptualization, Methodology, Investigation, Software, Data curation, Formal analysis, Supervision, Validation, Visualization, Visualization, Writing – review & editing, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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