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A multivariate statistical process monitoring scheme should be able to describe multimodal data. Multimodality typically arises in process data due to varying production regimes. Moreover, multimodality may influence how easy it is for process operators to interpret the monitoring results. To address these challenges, this paper proposes an on-line monitoring framework for anomaly detection where an anomaly may either indicate a fault occurring and developing in the process or the process moving to a new operating mode. The framework incorporates the Dirichlet process, which is an unsupervised clustering method, and kernel principal component analysis with a new kernel specialized for multimode data. A monitoring model is trained using the data obtained from several healthy operating modes. When on-line, if a new healthy operating mode is confirmed by an operator, the monitoring model is updated using data collected in the new mode. Implementation issues of this framework, including the parameter tuning for the kernel and the selection of anomaly indicators, are also discussed. A bivariate numerical simulation is used to demonstrate the performance of anomaly detection of the monitoring model. The ability of this framework in model updating and anomaly detection in new operating modes is shown on data from an industrial-scale process using the PRONTO benchmark dataset. The examples will also demonstrate the industrial applicability of the proposed framework.

Kernel Principal Component Analysis (KPCA) using Radial Basis Function (RBF) kernels can capture data nonlinearity by projecting the original variable space to a high-dimensional kernel feature space and obtaining the kernel principal components. This article examines the tuning of the kernel width when using RBF kernels in KPCA, showing that inappropriate kernel widths result in RBF-KPCA being unable to capture nonlinearity present in data. The paper also considers the choice of monitoring statistics when RBF-KPCA is applied to anomaly detection. Linear PCA requires two monitoring statistics. The Hotelling’s $T^{2}$ monitoring statistic detects when a sample exceeds the healthy operating range, while the Squared Prediction Error (SPE) monitoring statistic detects the case when the sample does not follow the model of the training data. The analysis in this article shows that SPE for RBF-KPCA can detect both cases. Moreover, unlike the case of linear PCA, the $T^{2}$ monitoring statistic for RBF-KPCA is non-monotonic with respect to the magnitude of the anomaly, making it not optimal as a monitoring statistic. The paper presents examples to illustrate these points. The paper also provides a detailed mathematical analysis which explains the observations from a theoretical perspective. Tuning strategies are proposed for setting the kernel width and the detection threshold of the monitoring statistic. The performance of optimally tuned RBF-KPCA for anomaly detection is demonstrated via numerical simulation and a benchmark dataset from an industrial-scale facility.

Normal practice in a compressor station with compressors in parallel is to allocate the mass flows equally. However, this strategy is not optimal if the compressors are not identical. A common reason why compressors become non-identical is because their performance degrades over time. Degradation increases the power necessary to run the compressor station and changes the optimal allocation of mass flows. This paper presents a framework for optimal operation in a compressor station with degrading compressors. The optimisation framework proposed in this work explicitly includes a model of degradation in the optimisation problem and analyses how the optimal load-sharing changes when the compressors are degrading. The optimisation framework was applied in an industrial case study of a compressor station in which three parallel compressors are subject to degradation. The case study confirms that it is possible to minimise the extra power consumption due to degradation by adjusting the operating conditions of the compressor station. The analysis also gives insights into the impact of degradation on the optimal solution when compressors work at their limits.

Alarm systems based on engineering and safety considerations are the prime source of information for operators when it comes to abnormal situations. Conversely, the presence of fault detection and diagnosis algorithms in process plants is still limited, in comparison with other process control technologies. This work presents a simple way to integrate the information contained in the alarm systems into the fault detection and diagnosis algorithm. A normalisation of the process measurements based on the alarm thresholds is proposed, improving the robustness of the algorithm with regard to the variability of the measurements across fault occurrences in industrial systems.

Oscillations occurring in industrial process plants often reflect the presence of severe disturbances affecting process operations. Accurate detection and root-cause analysis of oscillations is of great interest for the economic viability of the process operation. Standard oscillation detection and root cause analysis methods require a large enough number of data samples. Unrelated transient changes superimposed on the oscillation pattern reduce the number of useful data samples. The present paper proposes simple heuristic methods to effectively detect and remove two types of transient changes from oscillatory signals, namely step changes and spikes. The proposed methods are used to pre-process oscillatory time series. The accuracy gained when using auto-correlation function method for oscillation detection and transfer entropy method for oscillation propagation is experimentally evaluated. The methods are carried out on a 1.3-Butadiene production process where several measurements showed an established oscillation occurring after a production level change.

The paper provides a detailed first principles analysis of a process of liquefaction of natural gas in which the refrigeration compressors are driven by electric motors. The aim is to determine and understand the impact of the operation of the refrigeration cycles on the power consumption of the process. This study gives insights into the relationship between the discharge pressure of the compressors and the thermodynamic performance of the refrigeration cycles. By doing this, the findings of this research highlight the importance of the vapour liquid equilibrium. The results show that, for a given production rate, there is a minimum in the power consumption when the discharge pressures are close to the refrigerant saturation points. The paper provides a discussion and analysis of the advantages and disadvantages of operating at such points.

Performance-based maintenance of machinery relies on detection and prediction of performance degradation. Degradation indicators calculated from process measurements need to be approximated with degradation models that smooth the variations in the measurements and give predictions of future values of the indicator. Existing models for performance degradation assume that the performance monotonically decreases with time. In consequence, the models yield suboptimal performance in performance-based maintenance as they do not take into account that performance degradation can reverse itself. For instance, deposits on the blades of a turbomachine can be self-cleaning in some conditions. In this study, a data-driven algorithm is proposed that detects if the performance degradation indicator is increasing or decreasing and adapts the model accordingly. A moving window approach is combined with adaptive regression analysis of operating data to predict the expected value of the performance degradation indicator and to quantify the uncertainty of predictions. The algorithm is tested on industrial performance degradation data from two independent offshore applications, and compared with four other approaches. The parameters of the algorithm are discussed and recommendations on the optimal choices are made. The algorithm proved to be portable and the results are promising for improving performance-based maintenance.

This paper presents the control loop data of industrial controllers that are recently made available online. All data is confirmed and some of it has been published previously to develop fault detection and diagnosis methods. Methods to detect faults that occur during the operation of an industrial process are important and have attracted attention previously but are not always widely used in industry. One of the reasons is that any method needs to be robust and fully automated. The purpose of the data repository is to present data to test methods so that false positives and negatives are reduced to an insignificant number. Three previously published methods – oscillation detection based on the autocorrelation function, the idle index and a method for quantization detection – together with a simple, novel saturation detection method and one new detection methods are applied to all industrial data. The results are discussed and ways to improve the robustness and automation potential of these methods.