Joint Multifractal and Lacunarity Analysis of Image Profiles for Manufacturing Quality Control

The modern manufacturing industry faces increasing demands to customize products according to personal needs, thereby leading to the proliferation of complex designs. To cope with design complexity, manufacturing systems are increasingly equipped with advanced sensing and imaging capabilities. However, traditional statistical process control methods are not concerned with the stream of in-process imaging data. Also, very little has been done to investigate nonlinearity, irregularity, and inhomogeneity in the image stream collected from manufacturing processes. This paper presents the joint multifractal and lacunarity analysis to characterize irregular and inhomogeneous patterns of image profiles, as well as detect the hidden dynamics in the manufacturing process. Experimental studies show that the proposed method not only effectively characterizes surface finishes for quality control of ultraprecision machining but also provides an effective model to link process parameters with fractal characteristics of in-process images acquired from additive manufacturing. This, in turn, will allow a swift response to processes changes and consequently reduce the number of defective products. The proposed multifractal method shows strong potentials to be applied for process monitoring and control in a variety of domains such as ultraprecision machining and additive manufacturing.