Stochastic Kriging (SK) is a generalized variant of Gaussian process regression, and it is developed for dealing with non-i.i.d. noise in functional responses. Although SK has achieved substantial success in various engineering applications, its intrinsic modeling strategy by focusing on the sample mean limits its flexibility and capability of predicting individual functional samples. Moreover, the performance of SK can be impaired under scarce data scenarios, which are commonly encountered in engineering applications, especially for start-up or just deployed systems. In this paper, we propose a novel transfer learning framework to address the challenges of individualization and data scarcity in traditional SK. The proposed framework features a within-process model to facilitate individualized prediction and a between-process model to leverage information from related processes for resolving the issue of data scarcity. The within- and between-process models are integrated through a tailored convolution process, which quantifies interactions within and between processes using a specially designed covariance matrix and corresponding kernel parameters. Statistical properties are investigated on the parameter estimation of the proposed framework, which provide theoretical guarantees for the performance of transfer learning. The proposed method is compared with benchmark methods through various numerical and real case studies, and the results demonstrate the superiority of the proposed method in dealing with individualized prediction of functional responses, especially when limited data are available in the process of interest. The reproducibility code is available in the supplementary materials.

Dictionary learning is an effective tool for pattern recognition and classification of time series data. However, real-world time series data often exhibit temporal misalignment due to temporal delay, scaling or other temporal transformations, which poses significant challenges for effective dictionary learning. Dynamic time warping (DTW) is commonly used for dealing with such misalignment issues. Nevertheless, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparse coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparison with various benchmark methods.

The rapid development of sensor technologies allows the acquisition of high dimensional sensing data. Multi-output modeling techniques have been developed to leverage the data for decision making. However, the data often contain segments of missing values, which cause great information loss and thus affect the modeling performance. This study explores the missing pattern and the correlation structure of missing segments and maximally exploits useful information in the data to improve multi-output modeling accuracy. Specifically, a new multi-output modeling method is developed based on Gaussian Process Latent Variable Model (GPLVM). A decision score is developed to seek an optimal modeling strategy and then a tailored Expectation-Maximization (EM) algorithm based on GPLVM is designed to estimate the missing segments while optimizing model parameters. The proposed method demonstrates superior performance in both a simulation study and a case study, which makes it a powerful tool to enable process automation. Note to Practitioners—In real-life applications, missing values are constantly present in multi-output sensing data, which greatly affects data-driven decision-making. Modeling of such data becomes more difficult when consecutive observations within or across different outputs are missing. Existing methods often discard the missing values and extract information only from the available observations. However, the pattern of missing values may contain important messages that can potentially boost the modeling performance. This research develops a new framework based on GPLVM to model multi-output data with segmented missing patterns. A tailored EM algorithm is developed to iteratively impute the missing values and optimize model parameters. In addition, a decision score that quantifies both the missing pattern and correlation is designed to determine an optimal modeling strategy. The proposed method can benefit many applications across different industries that require modeling of multi-output incomplete data, especially when the data have many segments of missing observations.

Multi-output Gaussian process (MGP) has been attracting increasing attention as a transfer learning method to model multiple outputs. Despite its high flexibility and generality, MGP still faces two critical challenges when applied to transfer learning. The first one is negative transfer, which occurs when there exists no shared information among the outputs. The second challenge is the input domain inconsistency, which is commonly studied in transfer learning yet not explored in MGP. In this paper, we propose a regularized MGP modeling framework with domain adaptation to overcome these challenges. More specifically, a sparse covariance matrix of MGP is constructed using convolution process, where penalization terms are added to adaptively select the most informative outputs for knowledge transfer. To deal with the domain inconsistency, a domain adaptation method is proposed by marginalizing inconsistent features and expanding missing features to align the input domains among different outputs. Statistical properties of the proposed method are provided to guarantee the performance practically and asymptotically. The proposed framework outperforms state-of-the-art benchmarks in comprehensive simulation studies and one real case study of a ceramic manufacturing process. The results demonstrate the effectiveness of our method in dealing with both the negative transfer and the domain inconsistency.

Paracentesis is a high-demanding and routine operation, which has great potentials and benefits if semi-autonomous procedures can be developed. One of the most important techniques that facilitate semi-autonomous paracentesis is to segment the ascites from ultrasound images accurately and efficiently. The ascites, however, is usually with significantly different shapes and noise among different patients, and its shape/size changes dynamically during the paracentesis. This makes most of existing image segmentation methods either time consuming or inaccurate for segmenting ascites from its background. In this article, we propose a two-stage active contour method to facilitate accurate and efficient segmentation of ascites. First, a morphological-driven thresholding method is developed to locate the initial contour of the ascites automatically. Then, the identified initial contour is fed into a novel sequential active contour algorithm to segment the ascites from background accurately. The proposed method is tested and compared with state-of-the-art active contour methods on over 100 real ultrasound images of ascites, and the results show the superiority of our method in both accuracy and time efficiency.

The revolution of Industry 4.0 and Internet of Things facilitate large and cheap data acquisition from complex systems. However, the online processing and analytics of such multistream data still suffer difficulties. The key reason is that data from different sensors (multistream data) contain nonlinear within-and-cross sensor correlations, which poses challenges in the modeling and analysis of such data, especially for the online scenarios. To jointly model multistream data, multioutput Gaussian process (MGP) has become popular and achieved a great success. However, the existing methods assume that different outputs are linearly correlated, which significantly limits their applications. In this article, we propose a nonlinear online MGP framework to simultaneously realize nonlinear correlation modeling and online processing of multistream data. Specifically, a tailored covariance structure is developed based on the convolution process, which can capture nonlinear self-and-cross correlations. To realize online processing, Bayesian analysis and the marginalized particle filter are applied to estimate function values and model parameters. Comparing to the existing methods, the proposed method features superiorities in the nonlinear characterization of self-and-cross correlations and the efficient modeling and prediction capability. These features make the proposed method especially appropriate for industrial informatics with complex relationship and large-scale datasets. The proposed method is validated with simulation studies and a real-case study of biophysical signals.