Fisher information matrix based time-series segmentation of process data

Recent studies have suggested that Model Predictive Controllers (MPC) could benefit single-input single-output (SISO) systems. However, some key factors inhibiting MPC implementation are the efforts associated with plant tests and the need for expert knowledge on the design and tuning. Moreover, plant tests are time-consuming; they interfere with process operations and can even lead to instability in extreme cases. This paper mitigates these problems by generating a model predictive controller starting with a pre-tuned PI controller and routine plant data. This paper presents the studies of relevant methodologies, which was then harmonized into a concise algorithm. A genetic algorithm was used with routine plant data to obtain the MPC parameters. These parameters are used to design an MPC that gives similar performance to a pre-tuned PI Controller. Monte Carlo simulations were used to demonstrate the method’s viability. Results show that the respective MPC-parameters’ mean values converges to their actual values. Hence, this is critical in developing MPC from routine plant data.

Based on the concepts laid out in an earlier article (Jaeckle and MacGregor, 1998), this paper defines the problem of moving the production of a particular product grade from a plant A to another plant B when both plants have already produced a similar range of grades. Since the two plants may differ in size, configurations, and so on, the process conditions required to produce any given product grade may be very different in the two plants. How historical process data on both plants may be utilized to assist in this problem is investigated. A multivariate latent variable method is proposed that uses data from both plants to predict process conditions for plant B for a grade previously produced only in plant A. The approach is illustrated by a simulation example.

The Process Chemometrics Approach to Process Monitoring and Fault Detection

Basic oxygen steel making is a complex chemical and physical industrial process that reduces a mix of pig iron and recycled scrap into low-carbon steel. Good understanding of the process and the ability to predict how it will evolve requires long operator experience, but this can be augmented with process target prediction systems. Such systems may use machine learning to learn a model of the process based on a long process history, and have an advantage in that they can make use of vastly more process parameters than operators can comprehend. While it has become less of a challenge to build such prediction systems using machine learning algorithms, actual production implementations are rare. The hidden reasoning of complex prediction model and lack of transparency prevents operator trust, even for models that show high accuracy predictions. To express model behaviour and thereby increasing transparency we develop a reinforcement learning (RL) based agent approach, which task is to generate short polynomials that can explain the model of the process from what it has learnt from process data. The RL agent is rewarded on how well it generates polynomials that can predict the process from a smaller subset of the process parameters. Agent training is done with the REINFORCE algorithm, which enables the sampling of multiple concurrently plausible polynomials. Having multiple polynomials, process developers can evaluate several alternative and plausible explanations, as observed in the historic process data. The presented approach gives both a trained generative model and a set of polynomials that can explain the process. The performance of the polynomials is as good as or better than more complex and less interpretable models. Further, the relative simplicity of the resulting polynomials allows good generalisation to fit new instances of data. The best of the resulting polynomials in our evaluation achieves a better R^2 score on the test set in comparison to the other machine learning models evaluated.

This paper describes the use of self-service analytics on time series process data for the troubleshooting and optimization of refinery operations in the context of data visualization principles and best practices. Refining-relevant examples are used to demonstrate how end-users can access real-time and historical process data and apply the following analytics operations across several refining functions, including (1) incident troubleshooting – identifying periods of interest and methods available to investigate related plant data, patterns, events and disturbances leading up to the incident, and (2) data cleansing – filtering sensor data to remove outliers and bad quality data, splicing and aligning data streams for more accurate analysis and to improve the confidence in the outputs of subsequent analysis, such as the outputs of multivariate, regression-based system identification. The paper also provides examples of how ad hoc analyses can be scaled up to plantwide analytics and evolve into routine, automated tasks. The importance of analytic provenance and collaboration in sharing new insights from data is also discussed. To address the human factors associated with self-service analytics innovation, the paper concludes with lessons learnt, observations and adaptations compared to the traditional “business-as-usual approaches, best practices for data governance, and the implications for engineers that operate in a safety-critical environment.

The calibration of large-diameter flow meters is performed in the calibration station where real flow passes through. The typical calibration process is manipulated by human operators, which is time-consuming and easily affected. Since most of the process parameters are detectable, the smart calibration system was aided by the on-line modeling process and consisted of three parts: the digital twin model, the process controller, and the human-machine interface (HMI). The digital twin model was based on the basic partial differential equations of the gas flow in pipelines and was meant for the flow behavior prediction over short periods and provided decision-making assistance for human operators. The verification of the digital model was based on both the historical process data and the real-time process data. The process controller represented the manipulator meant to replace the human operator. The function of the controller included process control and calibration flow point adjustment. The HMI was designed based on the industrial supervisory control and data acquisition (SCADA) system. Since the process control was essential, the scheduling scheme and command sequence feedback to the SCADA system was rechecked by human operators via the HMI. The result of the active control was displayed in the HMI based on the digital twin model. Since smart control was the tendency in the piping system, the automated process verification and control formed the basis of the smart system. By entering the size and range of the flow meters into the HMI, the entire industrial system inside the calibration station was executed automatically.

Industrial processes generally have various operation modes, and fault detection for such processes is important. This paper proposes a method that integrates a variational Bayesian Gaussian mixture model with canonical correlation analysis (VBGMM-CCA) for efficient multimode process monitoring. The proposed VBGMM-CCA method maximizes the advantage of VBGMM in automatic mode identification and the superiority of CCA in local fault detection. First, VBGMM is applied to unlabeled historical process data to determine the number of operation modes and cluster the data in each mode. Second, local CCA models that explore input and output relationships are established. Fault detection residuals are generated in each local CCA model, and monitoring statistics are derived. Finally, a Bayesian inference probability index that integrates monitoring results from all local models is developed to increase the monitoring robustness. The effectiveness of the proposed monitoring scheme is verified through experimental studies on a numerical example and the multiphase batch-fed penicillin fermentation process. Note to Practitioners —Process monitoring is important in guaranteeing process safety and improving product quality. Large amounts of unlabeled process data with multiple operation modes generally exist in industrial processes. Labeling these data is difficult or costly. Hence, this paper presents a VBGMM-CCA method for monitoring multimode processes. The key advantage of the proposed method is that it automatically identifies the number of operation modes in historical data and clusters the data. Then, local CCA monitors are established to model the process input and output relationships. During online monitoring, the running-on operation mode is identified through a density function, and the process status is evaluated by the corresponding CCA monitor. A probabilistic monitoring index is also developed to increase the robustness of the monitoring. In comparison with the results of conventional methods, the monitoring results of the proposed approach are more reliable and informative because the process status and the type of the detected fault are presented.

Segmentation Methods for Model Identification from Historical Process Data

Process mining is a discipline that uses techniques to extract knowledge from event logs recorded by information systems in most companies these days. Among main perspectives of process mining, organizational and time perspectives focus on information about resources stored on the event logs and timing and frequency of the events, respectively. In this paper we introduce a method that combines organizational and time perspectives of process mining with a decision support tool called decision trees. The method takes the information of historical process data by means of an event log, generates a decision tree, annotates the decision tree with processing times, and recommends the best performer for a given running instance of the process. We finally illustrate the method through several experiments using a developed plug-in for the process mining framework ProM, first using synthetic data and then using a real-life event log.

A data‐based approach for developing robust processes is presented and illustrated with an application to an industrial membrane manufacturing process. Using historical process data, principal component analysis and partial least squares are used to extract models of the process and of the sensitivities of the process to various disturbances, including raw material variations, environmental conditions, and process equipment differences. Robustness measures are presented to quantify the robustness of the process to each of these disturbances. The process is then made robust (insensitive) to the disturbances over which one has some control (e.g., by modifying the equipment units to which the process is sensitive and imposing specification regions on sensitive raw materials). It is also made robust to disturbances over which one has little control (e.g., environmental variations) by optimizing the process operating conditions with respect to performance and robustness measures. The optimization is easily performed in the low‐dimensional space of the latent variables even though the number of process variables involved is very large. After applying the methodology to historical data from the membrane manufacturing process, results from several months of subsequent operation are used to demonstrate the large improvement achieved in the robustness of the process. © 2010 American Institute of Chemical Engineers AIChE J, 2011

The Fisher information matrix (FIM) is a widely used measure for applications including statistical inference, information geometry, experiment design, and the study of criticality in biological systems. The FIM is defined for a parametric family of probability distributions and its estimation from data follows one of two paths: either the distribution is assumed to be known and the parameters are estimated from the data or the parameters are known and the distribution is estimated from the data. We consider the latter case which is applicable, for example, to experiments where the parameters are controlled by the experimenter and a complicated relation exists between the input parameters and the resulting distribution of the data. Since we assume that the distribution is unknown, we use a nonparametric density estimation on the data and then compute the FIM directly from that estimate using a finite-difference approximation to estimate the derivatives in its definition. The accuracy of the estimate depends on both the method of nonparametric estimation and the difference Δθ between the densities used in the finite-difference formula. We develop an approach for choosing the optimal parameter difference Δθ based on large deviations theory and compare two nonparametric density estimation methods, the Gaussian kernel density estimator and a novel density estimation using field theory method. We also compare these two methods to a recently published approach that circumvents the need for density estimation by estimating a nonparametric f divergence and using it to approximate the FIM. We use the Fisher information of the normal distribution to validate our method and as a more involved example we compute the temperature component of the FIM in the two-dimensional Ising model and show that it obeys the expected relation to the heat capacity and therefore peaks at the phase transition at the correct critical temperature.

Confidence intervals for the maximum likelihood estimates (MLEs) are commonly used in statistical inference. To accurately construct such confidence intervals, one typically needs to know the distribution of the MLE. Standard statistical theory says normalized MLE is asymptotically normal with mean zero and variance being a function of the Fisher Information Matrix (FIM) at the unknown parameter. Two common estimates for the variance of MLE are the observed FIM (same as Hessian of negative log-likelihood) and the expected FIM, both of which are evaluated at the MLE given sample data. We show that, under reasonable conditions, the expected FIM tends to outperform the observed FIM under a mean-squared error criterion. This result suggests that, under certain conditions, the expected FIM is a better estimate for the variance of MLE when used in confidence interval calculations.

A Convolutional Autoencoder Approach for Feature Extraction in Virtual Metrology

Design of Smart Wellhead Controllers for Optimal Fluid Injection Policy and Producibility in Petroleum Reservoirs: A Neuro-Geometric Approach Masoud Nikravesh, Lawrence Berkeley National Laboratory, BISC Program, Computer Science Division, University of California at Berkeley, SPE, Masoud Soroush, Drexel University, M.R. Johnston, CalResources, LLC., SPE, and Tad W. Patzek, University of California at Berkeley, SPE Abstract In this paper, we present the next generation of "smart" controllers based on neural networks and geometric control techniques. In addition, we discuss an innovative Neural Network and Geometric Model-Based Control Strategy for developing and maintaining optimal fluid injection policy. First, the smart controller acquires data on wellhead pressures and rates continuously from the injectors. Second, a neural network model is "taught" the reservoir rate response to fluid injection pressure and vice versa. In the first case, the neural network learns how to predict the future injection rate based on injection pressure and rate. In the second case, the neural network learns how to predict the future injection pressure based on injection rate and pressure. The appropriately trained neural network can then recognize the symptoms of efficient or inefficient fluid injection around the operating point of the process. Third, feedback from the neural network models, in conjunction with geometric control, is used to design an optimal control strategy. In particular, the developed neural network-differential geometric models can be used to control and predict the behavior of individual and multiple fluid injectors. Introduction Oil Recovery from Petroleum Reservoirs: Fluids, such as water, carbon dioxide or steam, are injected into reservoirs to maintain pressure and displace oil. The process of fluid injection into petroleum reservoirs is known to exhibit an inherently complex, nonlinear, time varying and nonstationary behavior. Although an oil field is a complex and highly coupled system, injectors are usually controlled individually on the basis of past experience and pilots. Usually, simple single-input single-output controllers, such as Proportional-Integral-Derivative (PID) are used. Compared with carefully-controlled and maintained pilot injectors, field injectors have a more stochastic nature and their injectivity patterns are often different. These features have made the development of first-principle models for these injectors very challenging, if not impossible. Neural networks, however, have been able to provide sufficiently accurate models of fluid injectors by using historical process data such as flow rates and pressures. Despite our incomplete knowledge, neural network models are able to predict the complex behavior of petroleum reservoirs. These models can be used to synthesize model-based controllers that are capable of providing more effective control in these processes. In this project, we are creating an innovative Computer Assisted Operations (CAO) tool for developing and maintaining optimal injection policy for water or steam. Figure 1 shows a simplified schematic of optimal fluid injection policy. First, the CAO system acquires continuously data from the injectors (wellhead pressures (WHPs), rates, and temperatures) and producers (WHPs, rates, etc.). Second, the pattern-by-pattern responses are inverted to "back-out" the evolution of reservoir properties such as permeability and the extent of fracturing. P. 405^

Classification of process dynamics with Monte Carlo singular spectrum analysis