Article
Gaussian Process Based Bayesian Inference System
for Intelligent Surface Measurement
Ming Jun Ren
1
, Chi Fai Cheung
2
and Gao Bo Xiao
1,
*
1
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering,
Shanghai Jiao Tong University, Shanghai 200245, China; renmj@sjtu.edu.cn
2
State Key Laboratory of Ultra-Precision Machining Technology, The Hong Kong Polytechnic University,
Hong Kong, China; mfbenny@inet.polyu.edu.hk
* Correspondence: gaobo.xiao@sjtu.edu.cn; Tel.: +86-21-3420-4616
Received: 29 October 2018; Accepted: 19 November 2018; Published: 21 November 2018
Abstract:
This paper presents a Gaussian process based Bayesian inference system for the realization
of intelligent surface measurement on multi-sensor instruments. The system considers the surface
measurement as a time series data collection process, and the Gaussian process is used as
mathematical foundation to establish an inferring plausible model to aid the measurement process
via multi-feature classification and multi-dataset regression. Multi-feature classification extracts and
classifies the geometric features of the measured surfaces at different scales to design an appropriate
composite covariance kernel and corresponding initial sampling strategy. Multi-dataset regression
takes the designed covariance kernel as input to fuse the multi-sensor measured datasets with
Gaussian process model, which is further used to adaptively refine the initial sampling strategy by
taking the credibility of the fused model as the critical sampling criteria. Hence, intelligent sampling
can be realized with consecutive learning process with full Bayesian treatment. The statistical nature
of the Gaussian process model combined with various powerful covariance kernel functions offer the
system great flexibility for different kinds of complex surfaces.
Keywords:
Surface measurement; multi-sensor measurement; surface modelling; data fusion;
Gaussian process
1. Introduction
Surface size, geometry and texture are some of the most influential subjects in the field of precision
engineering [
1
]. The development of advanced machining technologies allows vast application of
complex surfaces superimposing multiple scales of feature in mechanical and optical engineering for
their superior performance in terms size reduction and versatile functions [
1
–
3
]. There is a growing
awareness of the importance of these new types of surfaces in modern science and technologies [
4
].
To ensure the functionality of the components, these surfaces are required to be fabricated with high
precision in terms of form accuracy in sub-micron range and surface finishing at nanometric level.
However, the geometric complexity of these advanced surfaces requires multi-scale measurement and
characterization, which imposes a lot challenges for current precision surface metrology [5,6].
Extensive research has been conducted on developing various measurement instruments to fulfill
a wide range of metrological needs [
7
–
10
], such as high precision coordinate measuring machines [
7
,
8
],
micro topographical instruments [
11
], electron microscopy [
12
], optical interferometry [
13
–
15
], etc.
Although these instruments are capable of performing accurate and efficient measurement at specific
measurement range, few of them could realize high dynamic range multi-scale measurement with
high efficiency and accuracy. Integrating several complementary sensors into an instrument therefore
becomes a promising solution to address complicated measurement tasks. For instance, integrating
Sensors 2018, 18, 4069; doi:10.3390/s18114069 www.mdpi.com/journal/sensors
