Multimode Process Monitoring Based on Aligned Mixture Factor Analysis

Multiplicity analysis gives practical guidance for process design to eliminate difficult operating regions associated with input and output multiplicities. Continuous stirred tank reactors (CSTRs) present challenging operational problems due to complex behavior such as input and output multiplicities, ignition/extinction, parametric sensitivity, and nonlinear oscillations. In the absence of a unified mathematical theory for representing various nonlinear system characteristics, the present study was aimed at understanding the dynamic behavior of CSTRs by means of experiments and to link the experimental data to theoretical considerations for further detection and elimination of operating problems. Theoretical modeling and analysis of a non‐isothermal CSTR with acid‐catalyzed hydrolysis of an acetic anhydride system for input multiplicity are discussed. Theoretical modeling of a non‐isothermal CSTR using a root‐finding technique was carried out for predicting steady‐state temperatures. Alternatively, a mathematical model for a non‐isothermal CSTR using unsteady‐state mass and energy balance equations is proposed. Computer‐based simulation was carried out using a program developed in MATLAB for final transient temperature and time‐temperature data of the CSTR system under investigation. The results of a theoretical analysis conducted for confirming the existence of input multiplicity in non‐isothermal CSTRs with acid‐catalyzed hydrolysis of acetic anhydride were compared with experimental investigations for validation.

Industrial processes typically have multiple operating modes with complex data distribution and locality faults, which challenges the traditional multivariate statistical process monitoring methods. To address this problem, a double‐level local information‐based local outlier factor (LOF) method is proposed in this work for multimode complex process monitoring. First, to handle the multimodality, the local neighborhood standardization strategy is adopted to utilize the statistical information of local data structure. Second, the variable LOF method is proposed to determine reasonable boundary for complex data distribution and simultaneously reflect local variable behaviors. For better online monitoring, a weighting strategy is applied to emphasize the local variable information, and the Bayesian inference is employed to integrate the LOF value of each variable. To isolate the fault variables, a contribution plot is designed. Finally, a numerical example and the benchmark Tennessee Eastman process are used to demonstrate the effectiveness and superiority of the proposed method.

Mixtures of Gaussian copula factor analyzers for clustering high dimensional data

On the design of feedback controllers for the continuous stirred tank reactor by Zakian's method of inequalities

This work develops a numerical algorithm for the calculation of an optimal nonlinear state feedback law for nonlinear systems. A quadratic performance index is used which contains quadratic error terms, and quadratic input penalty terms. The optimization problem is solved using the Hamilton-Jacobi equations, which determine the optimal nonlinear state feedback law. A Newton-Kantorovich iteration is developed for the solution of the pertinent Hamilton-Jacobi equations, which involves solving a Zubov partial differential equation, at each step of the iteration, using a power series method. At step N of the iteration, the method generates the (N + 1)-th order truncation of the Taylor series expansion of the optimal state feedback function. The method is applied to the problem of controlling a system of two non-isothermal continuous stirred tank reactors (CSTR), where an exothermic reaction takes place

Key principal components with recursive local outlier factor for multimode chemical process monitoring

A multimode process possesses dynamic behaviors, especially in between-mode transitions. Motivated by that dynamic models are well-suited for interpretation of process dynamics, we initially propose a dynamic model-level method for multimode process monitoring to detect abnormal operations quickly and accurately. It mainly includes three parts. First, a piecewise affine (PWA) model is identified offline to represent different dynamic patterns of a multimode process, which can avoid model redundancy compared with existing achievements. Owing to the utilization of the PWA model, the proposed method is still valid when unknown transitions occur. Second, in online monitoring, local autoregressive exogenous (ARX) models, obtained by just-in-time learning (JITL), can sufficiently extract local dynamic patterns so as to facilitate evaluating dynamic changes in the process. Finally, a novel measurement, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega $ </tex-math></inline-formula> -metric, is devised to analyze the dynamic variations in the process by directly measuring the similarity between local models and the PWA model, which is more beneficial for detecting abnormal operations than data distances. The superiority of the proposed method is validated by a continuous stirred tank reactor (CSTR) and a real air separation process compared with the existing multimode process monitoring approaches.

Catalyst ignition and extinction: A microkinetics-based bifurcation study of adiabatic reactors for oxidative coupling of methane

Multimode processes may be operating under different statuses, revealing different process characteristics and variations. It can be an interesting issue to check how the process variations change from one mode to another and thus how they can be used for multimode analysis and monitoring. In the present work, a between-mode relative analysis algorithm is proposed to explore the between-mode relationship. Comprehensive subspace decomposition is performed in each mode regarding their relative changes from the reference mode and influences on process monitoring. Each mode is separated into three different systematic subspaces and one residual subspace based on the between-mode changes of process variations, including the increased part, the decreased part, and the unchanged part. These different variations are then modeled respectively and different monitoring statistics are defined for online monitoring to identify mode affiliation and detect the fault status. By separating and monitoring different types of between-mode relative variations, the proposed method can not only efficiently distinguish different modes and detect faults but also offer enhanced process understanding. Theoretical support is framed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with multimode data generated from the Tennessee Eastman (TE) benchmark process.

Enhanced robust multimode process monitoring under dirty data via difference-based decomposition of matrix

Successful modeling of wastewater treatment plant (WWTP) processes requires an accurate description of the plant hydraulics. Common methods such as tracer experiments are difficult and costly and thus have limited applicability in practice; engineers are often forced to rely on their experience only. An implementation of grammar-based genetic programming with an encoding to represent hydraulic reactor models as program trees should fill this gap: The encoding enables the algorithm to construct arbitrary reactor models compatible with common software used for WWTP modeling by linking building blocks, such as continuous stirred-tank reactors. Discharge measurements and influent and effluent concentrations are the only required inputs. As shown in a synthetic example, the technique can be used to identify a set of reactor models that perform equally well. Instead of being guided by experience, the most suitable model can now be chosen by the engineer from the set. In a second example, temperature measurements at the influent and effluent of a primary clarifier are used to generate a reactor model. A virtual tracer experiment performed on the reactor model has good agreement with a tracer experiment performed on-site.

Abstract. Global chemical transport models (CTMs) are used extensively to study air pollution and transport at a global scale. These models are limited by coarse horizontal resolutions that do not allow for a detailed representation of small-scale nonlinear processes over the pollutant source regions. Here we couple the global GEOS-Chem CTM and its three high-resolution nested models to simulate the tropospheric carbon monoxide (CO) over the Pacific Ocean during five High-performance Instrumented Airborne Platform for Environmental Research (HIAPER) Pole-to-Pole Observations (HIPPO) campaigns between 2009 and 2011. We develop a two-way coupler, the PeKing University CouPLer (PKUCPL), allowing for the exchange and interaction of chemical constituents between the global model (at 2.5° long. × 2° lat.) and the three nested models (at 0.667° long. × 0.5° lat.) covering Asia, North America, and Europe. The coupler obtains nested model results to modify the global model simulation within the respective nested domains, and simultaneously acquires global model results to provide lateral boundary conditions (LBCs) for the nested models. Compared to the global model alone, the two-way coupled simulation results in enhanced CO concentrations in the nested domains. Sensitivity tests suggest the enhancement to be a result of improved representation of the spatial distributions of CO, nitrogen oxides, and non-methane volatile organic compounds, the meteorological dependence of natural emissions, and other resolution-dependent processes. The relatively long lifetime of CO allows for the enhancement to be accumulated and carried across the globe. We found that the two-way coupled simulation increased the global tropospheric mean CO concentrations in 2009 by 10.4%, with a greater enhancement at 13.3% in the Northern Hemisphere. Coincidently, the global tropospheric mean hydroxyl radical (OH) was reduced by 4.2%, resulting in a 4.2% enhancement in the methyl chloroform lifetime (MCF; via reaction with tropospheric OH). The resulting CO and OH contents and MCF lifetime are closer to observation-based estimates. Both the global and the two-way coupled models capture the general spatiotemporal patterns of HIPPO CO over the Pacific. The two-way coupled simulation is much closer to HIPPO CO, with a mean bias of 1.1 ppb (1.4%) below 9 km compared to the bias at −7.2 ppb (−9.2%) for the global model alone. The improvement is most apparent over the North Pacific. Our test simulations show that the global model alone could resemble the two-way coupled simulation (especially below 4 km) by increasing its global CO emissions by 15% for HIPPO-1 and HIPPO-3, by 25% for HIPPO-2 and HIPPO-4, and by 35% for HIPPO-5. This has important implications for using the global model alone to constrain CO emissions. Thus, the two-way coupled simulation is a significantly improved model tool for studying the global impacts of air pollutants from major anthropogenic source regions.

Adaptive Local Outlier Probability for Dynamic Process Monitoring

This paper considers the problem of robust H∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.

Continuous stirred-tank reactors (CSTRs) are integral to industrial chemical processes due to their uniform mixing and steady-state operation. The saponification of ethyl acetate with sodium hydroxide is a widely used model reaction for studying kinetics in CSTRs. Understanding the sensitivity of reaction kinetics to operating conditions is critical for enhancing reactor performance, ensuring consistent product quality, and minimizing inefficiencies. Reaction kinetics in a CSTR are influenced by reactant concentrations, temperature, and flow rate. Misidentifying or poorly optimizing these parameters can result in suboptimal performance and reduced conversion efficiency, posing challenges for industrial applications. This study conducts a detailed sensitivity analysis to identify the key parameters influencing the saponification reaction in a CSTR. It quantifies how variations in these parameters affect conversion efficiency and overall reaction performance, providing actionable insights for process optimisation. A reaction kinetics model was selected and validated using robust pilot-plant experimental data. Parameters, including reactor temperature, were systematically analysed through numerical simulations to assess their sensitivity and impact on system performance. The validated model demonstrated strong agreement with experimental results, yielding RMSE values ranging from 0.0007 to 0.0013 and R² values between 0.9996 and 0.9999 across 30, 40, 50, and 60 °C. Maximum deviation remained below 0.6 %, highlighting the model’s predictive accuracy and industrial applicability. Sensitivity analysis showed the greatest marginal benefit between 30 and 40 °C, with a peak sensitivity ratio of 0.00072, indicating that small temperature adjustments in this range have the greatest impact on the final conversion of ethyl acetate. This study sets itself apart from classical saponification research by integrating pilot-plant data with MATLAB-based analysis, offering a validated dataset and a meaningful contribution to chemical reaction engineering.