Bioelectrochemical systems (BES) are promising technologies to convert organic compounds in wastewater to electrical energy through a series of complex physical-chemical, biological and electrochemical processes. Representative BES such as microbial fuel cells (MFCs) have been studied and advanced for energy recovery. Substantial experimental and modeling efforts have been made for investigating the processes involved in electricity generation toward the improvement of the BES performance for practical applications. However, there are many parameters that will potentially affect these processes, thereby making the optimization of system performance hard to be achieved. Mathematical models, including engineering models and statistical models, are powerful tools to help understand the interactions among the parameters in BES and perform optimization of BES configuration/operation. This review paper aims to introduce and discuss the recent developments of BES modeling from engineering and statistical aspects, including analysis on the model structure, description of application cases and sensitivity analysis of various parameters. It is expected to serves as a compass for integrating the engineering and statistical modeling strategies to improve model accuracy for BES development.

Additive manufacturing (AM) enables flexible part geometry and functionality, and reduces product development life cycle by direct layer-wise fabrication from CAD files. In the last decade, great achievements are made on AM materials, machines, processes, etc. However, the quality of the AM parts is still questionable for industrial specifications. On the one hand, AM part quality variables can be either quantitative, such as dimensional accuracy, or qualitative, such as binary indicators for voids, missing features, or surface roughness. On the other hand, both offline process setting variables and functional it in situ process variables can be measured and modeled with both quantitative and qualitative (QQ) quality response variables. In this paper, the QQ quality response variables are modeled by offline process setting variables and in situ process variables via functional QQ models. The modeling of these in situ process variables provides the basis for real-time monitoring and control for AM processes. Simulation studies and experimental data from a fused deposition modeling process are performed to demonstrate the effectiveness of the proposed method.

Aerosol jet printing (AJP) is a direct write technology that enables fabrication of flexible, fine scale printed electronics on conformal substrates. AJP does not require the time consuming mask and postpatterning processes compared with traditional electronics manufacturing techniques. Thus, the cycle time can be dramatically reduced, and highly personalized designs of electronics can be realized. AJP has been successfully applied to a variety of industries, with different combinations of inks and substrates. However, the quality of the printed electronics, such as resistance, is not able to be measured online. On the other hand, the microscopic image sensors are widely used for printed circuit boards (PCBs) quality quantification and inspection. In this paper, two widely used quality variables of printed electronics, resistance and overspray, will be jointly modeled based on microscopic images for fast quality assessment. Augmented quantitative and qualitative (AUGQQ) models are proposed to use features of microscopic images taken at different locations on the printed electronics as input variables, and resistance and overspray as output variables. The association of resistance and overspray can be investigated through the AUGQQ models formulation. A case study for fabricating silver lines with Optomec^® aerosol jet system is used to evaluate the model performance. The proposed AUGQQ models can help assess the printed electronics quality and identify important image features in a timely manner.

A manufacturing system with both quantitative and qualitative (QQ) quality responses (as a QQ system) is widely encountered in many cases. For example, in a lapping process of the semiconductor manufacturing, the quality of wafer’s geometrical characteristics is often measured by the total thickness variation as a quantitative response and the conformity of site total indicator reading as a binary qualitative response. The QQ responses are closely associated with each other in a QQ system, but current methodologies often model the two types of quality responses separately. This article presents a novel modeling approach, called “QQ models,” to jointly model the QQ responses through a constrained likelihood estimation. The QQ models can jointly select significant predictors by incorporating inherent features of QQ systems, leading to accurate variable selection and prediction. Both simulation studies and a case study in a lapping process are used to evaluate the performance of the proposed method. Supplementary materials to this article are available online.

Additive manufacturing (AM) has advantages over production cycle time, flexibility, and precision compared with traditional manufacturing. Spatial data, collected from optical cameras or in situ sensors, are widely used in various AM processes to quantify the product quality and reduce variability. However, it is challenging to extract useful information and features from spatial data for modeling because of the increasing spatial resolutions and feature complexities due to the highly diversified nature of AM processes. Motivated by the aerosol jet^® printing process in printed electronics, we propose a smooth spatial variable selection (SSVS) procedure to extract meaningful predictors from spatial contrast information in high-definition microscopic images to model the resistances of printed wires. The proposed method does not rely on extensive feature engineering, and has the generality to be applied to a variety of spatial data modeling problems. The performance of the proposed method in prediction and variable selection through simulations and a real case study has proven to be both accurate and easy to be interpreted.

In many manufacturing processes, equipment reliability plays a crucial role for product quality assurance. It is important to consider the effect of equipment degradation for the quality-process model. In this article, we propose a dynamic quality-process model to characterize the varying effects of a process to product quality due to equipment degradation. The proposed model considers the effects of process variables on product quality as piecewise linear functions with respect to the equipment degradation. It can automatically estimate the dynamic effects via a meaningful parameter regularization, leading to accurate parameter estimation and model prediction. The merits of the proposed method are illustrated by both simulations and a real case study in a crystal growth manufacturing process.