Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem. Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences. Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems

Inspection by exception: a new machine learning-based approach for multistage manufacturing

Manufacturing processes usually consist of multiple different stages, each of which is influenced by a multitude of factors. Therefore, variations in product quality at a certain stage are contributed to by the errors generated at the current, as well as preceding, stages. The high cost of each production stage in the manufacture of high-quality products has stimulated a drive towards decreasing the volume of non-added value processes such as inspection. This paper presents a new method for what the authors have referred to as ‘inspection by exception’ – the principle of actively detecting and then inspecting only the parts that cannot be categorized as healthy or unhealthy with a high degree of certainty. The key idea is that by inspecting only those parts that are in the corridor of uncertainty, the volume of inspections are considerably reduced. This possibility is explored using multistage manufacturing data and both unsupervised and supervised learning algorithms. A case study is presented whereby material conditions and time domain features for force, vibration and tempering temperature are used as input data. Fuzzy C-Means (FCM) clustering is implemented to achieve inspection by exception in an unsupervised manner based on the normalized Euclidean distances between the principal components and cluster centres. Also, deviation vectors for product health are obtained using a comparator system to train neural networks for supervised learning-based inspection by exception. It is shown that the volume of inspections can be reduced by as much as 82% and 93% using the unsupervised and supervised learning approaches, respectively

Development of a new machine learning-based informatics system for product health monitoring

Manufacturing informatics aims to optimize productivity by extracting information from numerous data sources and making decisions based on that information about the process and the parts being produced. Manufacturing processes usually include a series of costly operations such as heat treatment, machining, and inspection to produce high-quality parts. However, performing costly operations when the product conformance to specifications cannot be achievable is not desirable. This paper develops a new machine learning-based informatics system capable of predicting the end product quality so that non-value-adding operations such as inspection can be minimized and the process can be stopped before completion when the part being manufactured fails to meet the design specifications

A perturbation signal based data-driven Gaussian process regression model for in-process part quality prediction in robotic countersinking operations

A typical manufacturing process consists of a machining (material removal) process followed by an inspection system for the quality checks. Usually these checks are performed at the end of the process and they may also involve removing the part to a dedicated inspection area. This paper presents an innovative perturbation signal based data generation and machine learning approach to build a robust process model with uncertainty quantification. The model is to map the in-process signal features collected during machining with the post-process quality results obtained upon inspection of the finished product. In particular, a probabilistic framework based on Gaussian Process Regression (GPR) is applied to build the process model that accurately and reliably predicts key process quality indicators. Raw data provided by multiple sensors including accelerometers, power transducers and acoustic emissions is first collected and then processed to extract a large number of signal features from both time and frequency domains. A strategy for the selection of most relevant features is also explored in this work in order to reduce the input space dimension and achieve faster training times. The proposed GPR model was tested on a multi-robot countersinking application for monitoring of the machined countersink depths in composite aircraft components. Experimental results showed that the model can be used as a tool to predict the part quality through in-process sensory information, which in turn, helps to reduce the total inspection time by identifying the parts that would require further investigation

A systematic approach to the scale separation problem in the development of multiscale models

Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such ‘multiscale’ problems, that of defining a ‘scale’ remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering

A data-driven framework for neural field modeling

This paper presents a framework for creating neural field models from electrophysiological data. The Wilson and Cowan or Amari style neural field equations are used to form a parametric model, where the parameters are estimated from data. To illustrate the estimation framework, data is generated using the neural field equations incorporating modeled sensors enabling a comparison between the estimated and true parameters. To facilitate state and parameter estimation, we introduce a method to reduce the continuum neural field model using a basis function decomposition to form a finite-dimensional state-space model. Spatial frequency analysis methods are introduced that systematically specify the basis function configuration required to capture the dominant characteristics of the neural field. The estimation procedure consists of a two-stage iterative algorithm incorporating the unscented Rauch–Tung–Striebel smoother for state estimation and a least squares algorithm for parameter estimation. The results show that it is theoretically possible to reconstruct the neural field and estimate intracortical connectivity structure and synaptic dynamics with the proposed framework

A two-step machining and active learning approach for right-first-time robotic countersinking through in-process error compensation and prediction of depth of cuts

Robotic machining processes are characterised by errors arising from the limitations of the industrial robots. These robot-related errors can compromise the overall manufacturing process performance, resulting in final products with dimensions different from the nominal specifications. To avoid accumulation of errors through several manufacturing stages, a quality inspection step is usually performed after the cutting operation. This work presents an innovative two-step manufacturing method for achieving right-first-time characteristics in robotic machining operations through in-process inspection and compensation of the systematic errors, whilst collecting suitable training data for building predictive models. The key idea behind the proposed method is based on the observation that under certain conditions, the robotic machining errors remain largely consistent, and therefore by splitting the process into two similar steps and having an inspection step in between, a prediction and then compensation of the systematic errors would be possible. A Gaussian Process Regression (GPR) framework is applied for the creation of robust process models that predict the post-process inspection result from in-process signal features, with the associated confidence intervals. An active learning algorithm that makes online decisions on the inspection task based on the current confidence of the models, is also proposed. The two-step machining method and the active learning approach were both tested on a robotic countersinking process experiment. The results showed that the in-process inspection and error compensation of the proposed two-step machining method was able to achieve final countersink depths very close to the desired target, confirming the potential for right-first-time robotic machining. In addition, the active learning results highlighted the ability of the algorithm to reduce the number of required post-process inspections, thus saving both time and costs, whilst also identifying novel data relevant for the model training

An Intelligent Metrology Informatics System based on Neural Networks for Multistage Manufacturing Processes

The ability to gather manufacturing data from various workstations has been explored for several decades and the advances in sensory and data acquisition techniques have led to the increasing availability of high-dimensional data. This paper presents an intelligent metrology informatics system to extract useful information from Multistage Manufacturing Process (MMP) data and predict part quality characteristics such as true position and circularity using neural networks. The input data include the tempering temperature, material conditions, force and vibration while the output data include comparative coordinate measurements. The effectiveness of the proposed method is demonstrated using experimental data from a MMP

A Bayesian framework to estimate part quality and associated uncertainties in multistage manufacturing

Manufacturing is usually performed as a sequence of operations such as forming, machining, inspection, and assembly. A new challenge in manufacturing is to move towards Industry 4.0 (the fourth Industrial revolution) concerning the full integration of machines and production systems with machine learning methods to enable for intelligent multistage manufacturing. This paper discusses Multistage Manufacturing Processes (MMPs) and develops a probabilistic model based on Bayesian linear regression to estimate the results of final inspection associated with comparative coordinate measurement given in-process measured coordinates. The results of two case studies for flatness tolerance evaluation demonstrate the effectiveness of the probabilistic model which aims at being part of a larger metrology informatics system to be developed for predictive analytics and agent-based advanced control in multistage manufacturing. This solution relying on accurate models can minimise post-process inspection in mass production with independent measurements

A probabilistic framework for product health monitoring in multistage manufacturing using Unsupervised Artificial Neural Networks and Gaussian Processes

The emergence of highly instrumented manufacturing systems has enabled the paradigm of smart manufacturing that provides high levels of prognostics functionality. Of particular interest is to precisely determine geometric conformance or non-conformance of workpieces during manufacturing. This paper presents a new dimensional product health monitoring system that learns from in-process sensor data and updates the prediction of the product quality as the product is manufactured. The system uses data from multiple manufacturing stages, unlike from a single stage at a time, to predict the dimensional quality of the finished product that is updated with subsequent measurements such as On-Machine Measurements (OMMs), in on-line incremental learning fashion. It is based on self-supervised neural networks for dimensionality reduction, Gaussian Process Regression (GPR) models for probabilistic prediction about the end product condition and the associated uncertainty, and Bayesian information fusion for updating the conditional probability distribution of the end product quality in the light of new information. The monitoring approach was tested on the prediction of diameter deviations with validation results showing its ability to achieve an average accuracy better than 5 μm in terms of the Root Mean Squared Error (RMSE). Having obtained a Probability Density Function (PDF) for the measurand of interest, the conformance and non-conformance probabilities given the tolerance specifications are computed to support the principle of inspection by exception. This ability to construct a conformance probability-based product quality monitoring system using probabilistic machine learning methods constitute a step change to manufacturing prognostics