Minimum Variance Index Research Articles

An alternative method for estimating Hurst exponent of control signals based on system dynamics

One of the indices for evaluating the performance of control systems based on the routine operation data is the Hurst index. It is shown that the Hurst index value is very close to that of the minimum variance index which measures the performance of a control loop in terms of minimum variance benchmark. The advantage of Hurst index over minimum variance index is that it does not require the system model and its parameters. The Hurst index is based on the Hurst exponent, which measures the time series correlations. This paper analytically scrutinizes the effect of parameters and dynamics of a stochastic control system on the output Hurst exponent, which helps better comprehend the Hurst index and its relationship with the minimum variance index. For this purpose, the control system output is modeled as an Autoregressive Moving Average (ARMA) process, and the relationship between the parameters of the ARMA process and the output Hurst exponent is examined. Furthermore, the characteristics of the autocorrelation function of a signal under minimum variance conditions are extracted. This paper also proposes a new technique for estimating the Hurst exponent of control signals based on the autocorrelation function. Simulation examples illustrate the efficiency of the proposed approaches.

Practical control performance assessment method using Hurst exponents and crossover phenomena

This paper proposes a new Hurst exponent-based method to evaluate the performance of control loops by estimating Minimum Variance Index (MVI). Incorrect estimation of time delays dramatically affects MVI-based performance assessment accuracy. The main advantage of the proposed method over existing methods is that it only requires routine operation data, without any need for prior information of the system model parameters and time delays. Hence, this method is more suitable to be applied on various industrial control processes. Recently, crossover phenomena have been reported in the graphs used to estimate the Hurst exponent of different control signals, which complicate deciding the Hurst exponents values. To address this problem, the crossover phenomenon is investigated for control signals, then the Hurst index is modified based on it. The proposed method is successfully used to assess performance of various types of control loops such as the cascade loop and verified through simulation results.

Performance evaluation method of closed-loop system considering sensor degradation

To improve the closed loop control system in the accuracy of the parts when degraded performance evaluation, this paper proposes a new performance evaluation method based on improved relative entropy index, first of all, the original asymmetric relative entropy distance measure improvement for symmetric distance measure, and then through the unbounded function mapping index improved to (0, 1) range of bounded indicators. In the Gaussian case, the index value can be calculated from the mean and variance of the data. Finally, the influence of sensor degradation in the control system on the performance of the control system is considered, and a simulation model including sensor degradation is established by Matlab/Simulink. The improved relative entropy index is used to evaluate the performance. Compared with the minimum variance index, this method can evaluate the performance of the control system flexibly and effectively when the sensor degradation.

Data-driven performance assessment of multivariable control loops using a modified Hurst exponent–based index

Control system performance assessment is significant, especially in practical applications. One of the most important indices for the performance assessment of control systems is minimum variance. Calculating the minimum variance index in multivariate systems requires prior knowledge of system parameters and models, and is therefore an obstacle in practical applications. In this article, an index is proposed for the performance assessment of multivariate control loops, evaluating the system performance with the minimum variance criterion and using only the system’s routine operation data. This index can quantify the performance using neither any prior knowledge of system parameters nor the system’s optimal operation data. The proposed index is based on the Hurst exponent, a parameter for measuring correlations in time series data. In this article, detrended fluctuation analysis and rescaled range analysis are used to estimate the Hurst exponents of system outputs. Using a combination of these Hurst exponents, an index is defined for the performance assessment of multivariate systems. The results of simulation examples illustrate that the proposed index can assess the performance efficiently.

Design of a Performance-Driven Controller with 1-Parameter tuning

In process industries, it is important to maintain the desired control performance in steady state because of requirement of high-quality products and energy saving. This is the main motivation in the development of a performance-driven control scheme based on the minimum variance control law. In that scheme, controller parameters are adjusted when the control performance based on the MV-Index (Minimum Variance Index) deteriorates. However, this MV-Index based tuning scheme only takes into account only controller error variance unfortunately with no regard for manipulative variable activity. To circumvent this omission, this paper describes a design of a new performance-driven control system whose control performance assessment scheme takes into account controller error variance as well as the manipulating variable variance. Furthermore, in this newly proposed scheme, controller parameters are calculated using a fictitious reference iterative tuning (FRIT) scheme which is one of the data-driven tuning scheme. The effectiveness of the proposed scheme is demonstrated by evaluation on a numerical example.

Constrained generalised minimum variance controller design using projection‐based recurrent neural network

In this study, a generalised minimum variance control (GMVC) method using the projection-based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non-linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed-loop stability. The proposed control method is applied to the non-linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed.

Multivariate Control Loop Performance Assessment With Hurst Exponent and Mahalanobis Distance

A novel data-driven technique for performance assessment of multivariate control loops that takes into account the interactions within the system is proposed. The technique merges the Hurst-exponent-based single-input single-output controller performance index with Mahalanobis distance to devise a multiple-input multiple-output (MIMO) controller performance index. The distinct advantage over the standard minimum variance index and novelty of the proposed approach lies in its ability to quantify the performance of MIMO controller without the knowledge of interactor matrix or system description, which leads to the technique being insensitive to model plant mismatch and easily applicable to nonlinear systems. Only closed-loop routine operating data are required. This new methodology is tested on benchmark systems from the literature and simulation results are presented. Comparison with minimum variance index-based techniques reveals excellent agreement in the trends of both approaches. The results establish the proposed approach as a promising tool for interactor-matrix-independent MIMO control loop performance assessment.

The Impact of Constraints on Minimum-Variance Portfolios

Optimized minimum-variance strategies tend to have low liquidity; high turnover; high tracking error; and concentrated stock, sector, and country positions. Minimum-variance index providers typically mitigate these implementation problems by imposing constraints. The authors construct minimum-variance portfolios for the United States, global developed markets, and emerging markets and apply commonly used constraints to determine their effect on simulated portfolio characteristics, performance, and trading costs. The constraints they test succeed in improving investability but shift portfolio characteristics toward those of the capitalization-weighted benchmark. In particular, each additional constraint increases volatility. Nonetheless, minimum-variance strategies are a valid choice for risk-averse investors.

A novel framework for integrating data mining with control loop performance assessment

Data driven control loop performance assessment techniques assume that the data being analyzed correspond to single plant‐controller configuration. However, in an industrial setting where processes are affected due to the presence of feedstock variability and drifts, the plant‐controller configuration changes with time. Also, user‐defined benchmarking of control loops (common in industrial plants) requires that the data corresponding to optimal operation of the controller be known. However, such information might not be available beforehand in which case it is necessary to extract the same from routine plant operating data. A technique that addresses these fundamental requirements for ensuring reliable performance assessment is proposed. The proposed technique performs a recursive binary segmentation of the data and makes use of the fact that changes in controller settings translate to variations in plant output for identifying regions corresponding to single plant‐controller configurations. The statistical properties of the data in each such window are then compared with the theoretically expected behavior to extract the data corresponding to optimal configuration. This approach has been applied on: (1) raw plant output, (2) Hurst exponent, and (3) minimum variance index of the process data. Simulation examples demonstrate the applicability of proposed approach in industrial settings. A comparison of the three routes is provided with regard to the amount of data needed and the efficacy achieved. Key results are emphasized and a framework for applying this technique is described. This tool is of significance to industries interested in an automated analysis of large scale control loop data for multiple process variables that is otherwise left unutilized. © 2015 American Institute of Chemical Engineers AIChE J, 62: 146–165, 2016

Impact of model plant mismatch on performance of control systems: An application to paper machine control

Model-based controllers based on incorrect estimates of the true plant behaviour can be expected to perform poorly. This work studies the effect of model plant mismatch on the closed loop behaviour and system performance for a certain class of MIMO systems. Performance is measured using a minimum variance index and a closely related user-specified criterion. We study the effect of model plant mismatch on the output variance and performance indices. Under mild assumptions, the performance of each output in a MIMO system can be analysed independently. Moreover, we propose an approach to distinguish the effect of model–plant mismatch from the effect of changes in disturbance characteristics on closed-loop performance. We define a sensitivity measure that relates system performance to model–plant mismatch, and use it to explore this sensitivity for three realistic types of parametric modelling errors. Next, we suggest a quantitative method that compares a system's actual output to its desired response in a transient setting. The performance of the transient response is demonstrably more sensitive to the model–plant mismatch than the steady state performance. The results are illustrated on industrial paper machine data.

Control of a Weigh Feeder Based on Performance Assessment

This study discusses a design method to determine one of the design parameters in generalized minimum variance control (GMVC) law from the viewpoint of the control assessment. In this paper, a PI control law is designed based on GMVC. In addition, the control performance of the designed controller is evaluated by using a minimum variance index, and the design parameter in GMVC is automatically changed such that the control performance is optimized. In the proposed method, unknown plant parameters are estimated, and the PI control law based on GMVC is updated using estimated parameters. Finally, the effectiveness of the proposed method is shown through an experiment.

Control loop performance assessment using detrended fluctuation analysis (DFA)

A new index is developed for assessing the performance of a single-input single-output (SISO) linear feedback control loop. The proposed metric is a specific scaling of the generalized Hurst exponent, computed through the method of detrended fluctuation analysis (DFA). We refer to this scaled exponent as the Hurst index. The new method compares favorably with the widely used minimum variance index (MVI), with both indices showing similar trends under changes in controller tunings during closed-loop simulations. The main advantage of the Hurst index over the MVI and other existing performance measures is that its determination does not require a priori knowledge of any loop parameters. Instead, computation of the index relies solely upon process output data collected during routine plant operation. Therefore, this new technique could potentially allow engineers to more efficiently identify problematic control loops.

Concentration of the UK Stock Market

Abstract: During 1999 and 2000 a large number of articles appeared in the financial press which argued that the concentration of the FTSE 100 had increased. Many of these reports suggested that stock market volatility in the UK had risen, because the concentration of its stock markets had increased. This study undertakes a comprehensive measurement of stock market concentration using the FTSE 100 index. We find that during 1999, 2000 and 2001 stock market concentration was noticeably higher than at any other time since the index was introduced. When we measure the volatility of the FTSE 100 index we do not find an association between concentration and its volatility. When we examine the variances and covariance's of the FTSE 100 constituents we find that security volatility appears to be positively related to concentration changes but concentration and the size of security covariances appear to be negatively related. We simulate the variance of four versions of the FTSE 100 index; in each version of the index the weighting structure reflects either an equally weighted index, or one with levels of low, intermediate or high concentration. We find that moving from low to high concentration has very little impact on the volatility of the index. To complete the study we estimate the minimum variance portfolio for the FTSE 100, we then compare concentration levels of this index to those formed on the basis of market weighting. We find that realised FTSE index weightings are higher than for the minimum variance index.

Performance assessment of control systems in rolling mills – application to strip thickness and flatness control

This contribution takes the control performance monitoring (CPM) technology into a new industrial area, the metal processing, where not much work has been done before. It is shown how to explore not yet discovered opportunities for controller performance improvement in this industrially interesting field, where special aspects have to be considered. This includes online vs. batch-wise performance evaluation, time-based vs. length-based assessment, and oscillation diagnosis. The paper presents two industrial case studies of the performance evaluation of control systems in a tandem cold rolling mill: (1) a feedforward/feedback strip thickness controller; and (2) an internal model control of the strip flatness. Routine operating data are analysed to obtain the performance monitoring metrics in terms of minimum variance index, oscillation index, and to suggest improvement measures. A monitoring tool for calculating and displaying the performance indices has been developed, and tailored to the applications in this field. The results indicate that tuning the feedback thickness controller is suggested to better handle entry thickness disturbances for specific coils. The performance of the flatness controller is found to be satisfactory, thus no actions are needed.