Multirate Process Research Articles

Enhanced Dynamic Dual-Latent Variable Model for Multirate Process Monitoring and Its Industrial Application

Quality-related process monitoring is an important tool to ensure process safety and product quality. However, the existence of process dynamics and multirate sampling makes it difficult to construct an efficient monitoring model. In order to handle process dynamics and multirate sampling, a multirate process monitoring method based on a dynamic dual-latent variable model is proposed. The model involves two sets of latent variables modeled as first-order Markov chains, which are used to capture both quality-related and quality-unrelated dynamic information. In addition, to deal with multiple sampling rates in the process data, the proposed model is combined with a multirate Kalman filtering technique. An expectation-maximization (EM) algorithm is used to estimate the unknown parameters, and a fault detection strategy is developed. The higher fault detection rate of the proposed method is verified by two application studies including a real industrial experiment and the Tennessee Eastman (TE) process.

Wiener models robust identification of multi-rate process with time-varying delay using expectation-maximization algorithm

Multi-rate systems exist widely in the field of computer process control. Research on the multi-rate issue of linear systems is relatively mature and is gradually turning to multi-rate issues of nonlinear systems. Concurrently, irregular process disturbances (impulse noise, outliers, non-zero mean noise) and varying transmission delay problems are often overlooked or considered alone, which is lacking generality. Thus, the main objective of this paper is to formulate and solve the identification problem of multi-rate nonlinear Wiener models with time-varying delay and irregular process disturbances simultaneously. The probability graph model of the Wiener process is constructed. Under the expectation–maximization (EM) framework, the Scale outlier model and Location outlier model (both based on Gaussian mixture distribution) are separately introduced to model the contaminated output data. The time-varying delay at each sampling instant is assumed as a uniform distribution. An auxiliary model is applied to acquire the unmeasured middle variable. Then, a robust EM identification algorithm is developed and its convergence is analyzed. The validity of the developed approach is illustrated through two numerical examples and a simulation of the continuous stirred tank reactor.

Nonstationary and Multirate Process Monitoring by Using Common Trends and Multiple Probability Principal Component Analysis

Process monitoring plays a critical role in guaranteeing the stability and safety of the industrial process. To obtain sufficient information from industrial processes, the measurements usually con...

Characterization and upscaling of hydrodynamic transport in heterogeneous dual porosity media

We study the upscaling of pore-scale transport of passive solute in a carbonate rock sample. It is characterized by microporous regions displaying heterogeneous porosity distribution that are accessible due to diffusion only, and a strongly heterogeneous mobile pore space, characterized by a broad distribution of flow velocities. We observe breakthrough curves that are characterized by strong tailing, which can be attributed to velocity variability in the flowing medium portion, and solute retention in the microporous space. Using accurate numerical flow and transport simulations, we separate these two mechanisms by analyzing the statistics of residence times in the mobile phase, and the trapping and residence time statistics in the mmobile phase. We employ a continuous time random walk framework in order to upscale transport using a particle based implementation of mobile-immobile mass transfer, and heterogeneous advection. This approach is based on the statistics of the characteristic mobile and immobile residence times, and mass transfer rates between the two continua. While classical mobile-immobile approaches model mass transfer as a constant rate process, we find that the trapping rate increases with increasing mobile residence times until it reaches a constant asymptotic value. Based on these findings and the statistical characteristics of travel and retention times, we derive an upscaled Lagrangian transport model that separates the processes of heterogeneous advection and diffusion in the immobile microporous space, and provides accurate descriptions of the observed non-Fickian breakthrough curves. These results shed light on transport upscaling in highly complex dual-porosity rocks for which mobile-immobile mass transfer are controlled by a dual multirate process controlled by the heterogeneity of both the flow field in the connected porosity and the diffusion in the no-flow regions.

On-line model identification for the machining process based on multirate process data

Accurate identification of the model parameters of the machining process based on on-line process data is a crucial prerequisite for its model-based control and diagnostics. A typical machining process generates multi-output and multirate data streams. Whereas various sensors provide in-process information about the process, many important process outcomes including product qualities can be only measured in postprocess manner. This paper proposes to improve the identification by using both in-process and postprocess data and by analyzing the identifiability of model parameters. The identification of the model parameters based on multirate output is formulated using the maximum-likelihood estimation and the Fisher information matrix for a multirate-sampled system is derived to study the identifiability of model parameters. A strategy is developed to improve accuracy and robustness of the model identification considering the identifiability. The proposed method is tested on two batches of multirate process data from the cylindrical grinding process. The test results demonstrate using both in-process and postprocess data improves the identifiability and the proposed identification strategy results in improved prediction performance.

Gas Diffusion in Coal Powders is a Multi-rate Process

Gas migration in coal is strongly controlled by surface diffusion of adsorbed gas within the coal matrix. Surface diffusion coefficients are obtained by inverse modelling of transient gas desorption data from powdered coals. The diffusion coefficient is frequently considered to be dependent on time and initial pressure. In this article, it is shown that the pressure dependence can be eliminated by performing a joint inversion of both the diffusion coefficient and adsorption isotherm. A study of the log–log slope of desorbed gas production rate against time reveals that diffusion within the individual coal particles is a multi-rate process. The application of a power-law probability density function of diffusion rates enables the determination of a single gas diffusion coefficient that is constant in both time and initial pressure.

Multirate Dynamic Process Monitoring Based on Multirate Linear Gaussian State-Space Model

Multivariate statistical process monitoring (MSPM) has been widely used in modern industries and most of traditional MSPM methods are developed using uniformly sampled measurements. However, process variables are often sampled with different rates in practical industries. On the other hand, most of the industries are dynamic processes in which the measurements are highly autocorrelated. Thus, it is difficult to build a dynamic process model with incomplete data sets in multirate processes. In this paper, a multirate linear Gaussian state-space model is exploited to deal with the above issues. Both the offline model training and online process monitoring schemes are developed in the present of incomplete multirate process data sets. The proposed method is validated through a numerical example and the Tennessee Eastman benchmark process. Note to Practitioners —Process monitoring is essential to industrial process maintenance and safety. Typical monitoring methods focus on uniformly sampled variables which are rarely satisfied in practical industries. On the other hand, most industries are dynamic processes which bring more difficulties to process monitoring with multirate variables. This paper proposed a new scheme for multirate dynamic process monitoring based on the multirate linear Gaussian state-space model. To fully implement this approach: 1) the multirate process data need to be well divided into multiblocks. Each of the block should contain at least one variable; 2) the amount of latent variable’s dimension needs to be properly determined; and 3) the sampling rates of the process cannot be extremely distinguished otherwise will lead to a poor model performance. Two cases studied on both numerical example and Tennessee Eastman benchmark are given to validate the efficiency of the proposed algorithm on multirate dynamic process monitoring.

Multiple probability principal component analysis for process monitoring with multi-rate measurements

To obtain the informative enough data from the modern chemical processes, various sensors and measuring instruments have been applied. Among them, both the online measurements and offline laboratory analyser results are collected and used for multivariate statistical process monitoring purpose. Hence, it indicates that the obtained measurements indeed contain different sampling rates due to the different demands of the control systems and the equipment constraints. To handle the multi-rate process monitoring problem, it is desirable to effectively integrate the measurements with different sampling rates. In this paper, a multiple probability principal component analysis (MPPCA) model is proposed for efficient collection of data and the improvement of the performance on model prediction and process monitoring. In the proposed model, it has been derived as a general form for any multi-rate systems and the model parameters are calibrated by the expectation–maximization algorithm. Based on it, several statistics are constructed for different sampling rates in the process monitoring scenario. Finally, two case studies are presented to show the effectiveness of the proposed method.

Cromex appoints Plaza as US distributor for its masterbatches

In most chemical processes, both online measurements and offline laboratory analysis can be obtained at different sampling rates. Usually, the online process variables are frequently sampled while the key quality indicators are analyzed at irregular time, sometimes on hourly and sometimes daily basis. To effectively integrate different classes of measurements in a multi-rate process, a multi-rate probability principal component analysis (MPPCA) model is proposed to utilize the efficiently collected data and to improve the performance on both model prediction and process monitoring. In MPPCA, the model parameters are calibrated by the expectation-maximization algorithm. The proposed method is able to handle irregular samples in measurements and incorporate all the observations for model training. Also, the corresponding statistics based on MPPCA is developed for the fault detection purpose. Finally, a TE benchmark is presented to illustrate the effectiveness of the proposed methods.

Parameter identification of nonlinear multirate time-delay system with uncertain output delays

The joint parameter and time-delay estimation problems for a class of nonlinear multirate time-delay system with uncertain output delays are addressed in this paper. The practical process typically has time-delay properties and the process data are often multirate, sampled with output data inevitably corrupted by uncertain delays. The linear parameter varying (LPV) finite impulse response (FIR) multirate time-delay model is initially built to describe the considered system. The problems of over-parameterization and the existence of both continuous model parameters and discrete time-delays have made the conventional maximum likelihood difficult to solve the considered problems. In order to handle these problems, the joint parameter and time-delay estimation for the LPV FIR multirate time-delay model are formulated in the expectation-maximization scheme, and the algorithm to estimate the model parameters and time-delays is derived, simultaneously based on multirate process data. The efficacy of the proposed method is verified through a numerical simulation and a practical chemical plant.

Multiple Fault Detection Using Multi-rate Probability Principal Component Analysis Models

In most chemical processes, both online measurements and offline laboratory analysis can be obtained at different sampling rates. Usually, the online process variables are frequently sampled while the key quality indicators are analyzed at irregular time, sometimes on hourly and sometimes daily basis. To effectively integrate different classes of measurements in a multi-rate process, a multi-rate probability principal component analysis (MPPCA) model is proposed to utilize the efficiently collected data and to improve the performance on both model prediction and process monitoring. In MPPCA, the model parameters are calibrated by the expectation-maximization algorithm. The proposed method is able to handle irregular samples in measurements and incorporate all the observations for model training. Also, the corresponding statistics based on MPPCA is developed for the fault detection purpose. Finally, a TE benchmark is presented to illustrate the effectiveness of the proposed methods.

Determining the propagation path of a disturbance in multi-rate process and electromechanical systems

This paper proposes a multi-rate method to identify the propagation path of a persistent disturbance in an enlarged system envelope which includes the process plant and its electromechanical equipment. The need to integrate process and equipment diagnosis has been highlighted by industrial commentators. However, process and electromechanical measurements often have different sampling rates. The multi-rate method proposed extends a state-of-the-art propagation path method so that it combines fast-sampled electromechanical measurements and slow-sampled process measurements. The method is based on non-linear mutual prediction, which yields the directionality in the relationship between two time series. The method was demonstrated and validated, giving the expected outcome in an experimental case study, in which the root cause and propagation path of the disturbance were known.

Performance Analysis and Implementation of SISO Iterative Receiver for SCCC

Serial concatenated convolutional codes (SCCC) have gained a great interest in recent years for outperforming PCCC at high SNR and lower error floor. In this paper, the BER performance of SCCC based on different decoding algorithm such as Log-MAP algorithm, Max-Log-MAP algorithm and improved Max-Log-MAP algorithm are investigated. In order to achieve a flexible high throughput, low complexity and multi-rate decoding process, some improved methods are proposed.

Constraining prior probabilities of phylogenetic trees

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form.

A Novel Filter Bank Design Method with CEM FRM Technique

Modulation filter banks can be obtained by modulating one or two prototype filters, which reduce the design complexity of the filter banks. Furthermore, this kind of filter can be realized by using DFT or FFT with very high computationally efficiency. The proposition of a modulation filter bank reduces the computation complexity of designing the filter bank consumedly, which has very high computation efficiency. However, with the increasing of channels, the request for transition of the prototype filter is very high. This makes the length of the prototype filter longer, which decreases the computation efficiency. Frequency-response masking technique, which was proposed by Lim in 1986, is a very efficient way for designing the sharp transition filter. It is composed of three sub-filters and a delay chain. The basic thought is designing a low complexity filter before compressing its frequency response, and then eliminating the useless periodic images of the prototype filter and its compensation filter by two masking filters. The complexity of the FRM filter can also be reduced by modifying its architecture. According to it, the paper deduces a Novel FRM low-pass filter based on Complex Exponential Modulation (CEM). The deduced filter is very suitable to the multi-rate digital signal process, apart from applying a single rate digital signal process. In the application of software defined radio, the most bandwidth needs to be separated because it may has many narrowband channels. The need is very stringent for the filter to attenuate the closer channels. The filter banks encounter a main problem when it is used to separate channels, which is that the prototype filter must be a sharp transition bandwidth filter. Furthermore, the length of the prototype filter becomes longer in the DFT filter banks when the number of sub-filters is large and the transition band is very sharp. So it is very important to use a high efficiency digital filter, which can reduce the number of coefficient observably. Based on the advantage of deduced novel low-pass filter, the paper proposes a new analysis filter bank architecture, which makes use of the high efficiency low-pass filter as a prototype filter. So it can decrease the computation complexity consumedly when the transition bandwidth of prototype filter is especially very sharp. It is the same with the alterable bandwidth system. At last, an eight channels filter bank design example is used to illustrate its feasibility. It reduces the computationally complexity of the sharp transition filter by using a CEM FRM prototype filter. At last, an application example has been given to illustrate the design of analysis filter banks, showing that the resulting filter bank reduces the computation complexity, which adapt to use in engineering implementation.

Stability Analysis of a Flexible Spacecraft with a Sampled-Data Attitude Sensor

The pitch attitude control system for a flexible communications satellite is analyzed using sampled-data techniques. The sampling arises mainly from the use of discrete-time attitude measurement rather than from the digital controller implementation. It is found that Nyquist techniques lead to a relatively simple stability analysis that models the multirate sampling process with considerable fidelity, eliminating guesswork associated with equivalent delays. Controller modifications that improve stability are arrived at by this route. Finally, flexiblemode frequency and damping are varied to evaluate their influence on stability. There seems to exist a critical frequency at which stability margins are very small. Increasing the damping, predictably, improves matters.