Multiple Local Linear Models Research Articles

Data-driven fault tolerant predictive control for temperature regulation in data center with rack-based cooling architecture

Recently increasing amount of data centers (DCs) have been constructed for the development of information and communications technology (ICT). Meanwhile, more energy consumption is required to support the operation of DCs, where nearly thirty percent of the consumption is used for cooling system. Therefore, this paper studies an efficient cooling architecture named rack mountable cooling unit (RMCU) for DCs, and provides a novel data-driven fault tolerant predictive controller to regulate the temperature accordingly. In order to circumvent the complicated physics modeling in DC, a data-driven modeling method is developed. In this method, multiple local linear models in form of auto-regressive exogenous (ARX) model are selected to describe the strongly nonlinear system. Besides, the multiple sub-models are identified through partial least square (PLS) and corresponding training data is partitioned by fuzzy c-means (FCM). Then, on the basis of developed data-driven model, a predictive controller considering actuator faults is designed to manage the temperature in DC. Finally, real experimental results are presented and demonstrate the superior performance of our proposed controller.

A Laplacian SVM Based Semi‐Supervised Classification Using Multi‐Local Linear Model

Semi‐supervised learning considers a classification problem of learning from both labeled and unlabeled data. This paper proposes a semi‐supervised classification method, in which the potential separation boundary is detected and its information is ingeniously incorporated into a Laplacian support vector machine (LapSVM) in both kernel level and graph level. By applying a pseudo‐labeling approach, the input space is first divided into several linear separable partitions along the potential separation boundary. A multi‐local linear model is then built for the separation boundary, by interpolating multiple local linear models assigned to the local linear separable partitions. The multi‐local linear model is further formulated into a linear regression form with a new input vector in the spanned feature space, which contains the information of potential separation boundary. Then the linear parameters are estimated globally by a LapSVM algorithm. Furthermore, the input in the spanned feature space and pseudo labels are used to construct a label guided graph. Numerical experiments on various real‐world datasets and visual representation on toy example exhibit the effectiveness of the proposed method. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Temperature distribution estimation via data-driven model and adaptive Kalman filter in modular data centers

With the rapid development of information and communications technology, increasing number of data centers is required to support the cloud computing, and critical web-based services that run our daily lives. The conventional cloud data centers usually adopt computer room air conditioner or inRow units as the cooling sytem, while the rack mountable cooling unit is a more promising equipment due to the economy, exact controllability, flexibility, and scalability. To ensure the efficiency of control system in rack mountable cooling unit and the security of servers in the data centers, the information of temperature distribution is very essential. Basically, the temperature distribution could be obtained through physical sensors easily. However, considering the cost of whole system and the burden of fault diagnosis in sensor networks, the number of temperature sensors should be kept down to a bare minimum. Therefore, it is necessary to develop an effective and real-time observer to estimate the temperature distribution in the system. Besides, due to the complex air flow and heat transfer in the container, it is quite difficult to construct a physics model. To this end, a novel observer embracing data-driven model and adaptive Kalman filter is proposed in this work. Auto regression exogenous model is adopted as the framework of data-driven model, and the model is identified through a algorithm of partial least square. Moreover, to represent the nonlinear behaviors in the system, fuzzy c-means is applied for data classification and getting multiple local linear models. Finally, adaptive Kalman filter is utilized to estimate the temperature distribution on the basis of proposed data-driven model. The estimation results based on experimental data indicate the performance of proposed approach is remarkable.

Compact Piecewise Linear Model Based Temperature Control of Multicore Systems Considering Leakage Power

Temperature control of the new-generation integrated multicore system is challenging. This is because the leakage power, which is significant in modern systems, is nonlinearly related to temperature, resulting in a complex nonlinear control problem in thermal management. In this article, a new dynamic thermal management (DTM) method with compact piecewise linear (PWL) model based predictive control is proposed to solve the nonlinear control problem. First, a compact PWL thermal model, which takes dynamic power as input, is built by combining multiple local compact linear thermal models expanded at several Taylor expansion points. These local compact linear thermal models are obtained by sampling-based model order reduction with high accuracy. Their Taylor expansion points are selected by a systematic scheme, which exploits the thermal behavior property of the multicore chips. Based on the compact PWL thermal model, a new predictive control method is proposed to compute the future power recommendation for DTM. By approximating the nonlinearity accurately with the compact PWL thermal model and being equipped with predictive control technique, the new DTM achieves an overall high quality temperature management with smooth and accurate temperature tracking. Experimental results show that the new method outperforms the linear model predictive control based method and the echo state network based predictive thermal management method in temperature management quality with lower computing overhead.

Data-Driven Modeling and UFIR-Based Outlet NO$_{x}$ Estimation for Diesel-Engine SCR Systems

An accurate and efficient model for selective catalytic reduction (SCR) systems plays an important role in diagnosis and control of diesel-engine after-treatment systems. In this paper, we investigate the data-driven modeling of SCR systems and outlet NO $_{x}$ concentration estimation based on the developed data-driven model and the algorithm of unbiased finite impulse response (UFIR) filtering. The structure used for the data-driven model is an autoregressive exogenous (ARX) model and the method of partial least square is utilized to identify the parameters of the corresponding ARX model. Moreover, the approach of fuzzy c-means is employed to partition the data and derive multiple local linear models with a better performance on approximating the system nonlinearities. Finally, the algorithm of UFIR filtering is adopted to estimate the outlet NO $_{x}$ concentration due to its strong robustness without the statistics of process and measurement noises. The performance of proposed approaches on SCR systems is validated with simulations based on experimental data. In addition, comparisons show the improvement of the adopted algorithm on the estimation accuracy.

Inlet NOx and NH3 Concentration Estimation for Diesel-engine SCR Systems by Combining Data-Driven Model and Unbiased FIR Filter

Selective catalytic reduction (SCR) systems have been widely used in diesel engine applications. In an SCR system, input NOx and NH3 concentration information are of critical importance for the urea dosage controller design and system fault detection. Generally, the NOx and NH3 concentration are obtained by physical sensors. However, the physical sensors do not only increase the cost of overall system, but also induce measurement delays. To deal with this issue, an input observer combining a data-driven model and an unbiased finite impulse response (FIR) filter is proposed. The structure of data-driven model is auto-regressive exogenous (ARX) model and partial least square (PLS) is utilized to identify the parameters in the ARX model. Nevertheless, fuzzy c-means (FCM) is also employed to partition the data and obtain multiple local linear models for describing the nonlinearities of the system. At last, an unbiased FIR filter is adopted to estimate the input NOx and NH3 concentration simultaneously due to its strong robustness against the noise. The comparisons between the unbiased FIR filter algorithm and Kalman filter algorithm are carried out in MATLAB/SIMULINK. The simulation results demonstrate that the performance of proposed estimator is outstanding.

Multiple-model predictive control for component content of CePr/Nd countercurrent extraction process

A new multiple-model predictive control scheme is proposed for the control of the component content in the rare earth extraction process. Multiple local linear models with two-input and two-output of the rare earth countercurrent extraction process are constructed, each of which is established under an operation condition. A component content predictive controller is designed for a local linear model, based on the dynamic compensation of the extraction liquid flow and the scrubbing liquid flow. A switching algorithm based on the minimum accumulative error is formed to select the most appropriate model and controller to meet the productive purity requirements. Simulation results for the CePr/Nd countercurrent extraction process are presented to show the desired performance of the proposed approach.

Vibration control of a pneumatic driven piezoelectric flexible manipulator using self-organizing map based multiple models

A kind of hybrid pneumatic-piezoelectric flexible manipulator system has been presented in the paper. A hybrid driving scheme is achieved by combining of a pneumatic proportional valve based pneumatic drive and a piezoelectric actuator bonded to the flexible beam. The system dynamics models are obtained based on system identification approaches, using the established experimental system. For system identification of the flexible piezoelectric manipulator subsystem, parametric estimation methods are utilized. For the pneumatic driven system, a single global linear model is not accurate enough to describe its dynamics, due to the high nonlinearity of the pneumatic driven system. Therefore, a self-organizing map (SOM) based multi-model system identification approach is used to get multiple local linear models. Then, a SOM based multi-model inverse controller and a variable damping pole-placement controller are applied to the pneumatic drive and piezoelectric actuator, respectively. Experiments on pneumatic driven vibration control, piezoelectric vibration control and hybrid vibration control are conducted, utilized proportional and derivative (PD) control, SOM based multi-model inverse controller, and the variable damping pole-placement controller. Experimental results demonstrate that the investigated control algorithms can improve the vibration control performance of the pneumatic driven flexible piezoelectric manipulator system.

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013

Data-Based Modeling and Control of Nylon-6, 6 Batch Polymerization

This work addresses the problem of modeling the complex nonlinear behavior of the nylon-6, 6 batch polymerization process and then subsequently tracking trajectories of important process variables, namely the reaction medium temperature and reactor pressure, using model predictive control. To this end, a data-based multi-model approach is proposed in which multiple local linear models are identified from previous batch data using latent variable regression and then combined using an appropriate (continuous) weighting function that arises from fuzzy c-means clustering. The proposed approach unifies the concepts of auto-regressive exogenous (ARX) modeling, latent variable regression techniques, fuzzy c-means clustering, and multiple local linear models in an integrated framework capable of capturing the nonlinearities and multivariate nature of batch data. The resulting data-based model is then used to formulate a trajectory tracking predictive controller. Through simulation studies, the modeling approach is shown to capture the major nonlinearities in the nylon-6, 6 polymerization process and closed-loop simulation results demonstrate the efficacy of the proposed predictive controller and illustrate its advantages over existing trajectory tracking approaches such as conventional proportional-integral control and latent variable model predictive control.

Design of a Self-Tuning Controller using Multiple Local Linear Models for Nonlinear Systems

Design of a Self-Tuning Controller using Multiple Local Linear Models for Nonlinear Systems

Integrating data‐based modeling and nonlinear control tools for batch process control

AbstractA data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Process analysis and product quality estimation by Self-Organizing Maps with an application to polyethylene production

The huge amount of data recorded by modern production systems definitely have the potential to provide information for product and process design, monitoring and control. This paper presents a soft-computing (SC)-based approach for the extraction of knowledge from the historical data of production. Since Self-Organizing Maps (SOM) provide compact representation of the data distribution, efficient process monitoring can be performed in the two-dimensional projection of the process variables. For the estimation of the product quality, multiple local linear models are identified, where the operating regimes of the local models are obtained by the Voronoi diagram of the prototype vectors of the SOM. The proposed approach is applied to the analysis of an industrial polyethylene plant. The detailed application study demonstrates that the SOM is very effective in the detection of the typical operating regions related to different product grades, and the model can be used to predict the product quality (melt index and density) based on measured process variables.

Observers for Takagi-Sugeno fuzzy systems

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

Speed control design for an experimental vehicle using a generalized gain scheduling approach

Describes the design and experimental evaluation of a nonlinear automotive speed control system. The approach implemented is based on interpolation of multiple linear controllers designed using multiple local linear models. This is a generalized form of gain scheduling since the models and controllers take explicit account of both stationary and nonstationary (off-equilibrium) operating points. The paper focuses on engineering aspects and experimental evaluation in a test vehicle. The nonlinear controller is tested on a range of speed-profile tracking tasks, and in a disturbance rejection task (the vehicle is driven up a 10% slope). For comparison, linear controllers are implemented. The proposed nonlinear control approach gives excellent performance over the complete operational range. The nonlinear controller can directly account for the strong plant nonlinearities and the engineering constraints.

Neurofuzzy Approach to Fault Detection of Nonlinear Systems

This paper proposes a neurofuzzy approach to fault detection in linear systems. The system diagnosed is described by using a neurofuzzy model called LimNet that consists of a linear model and multiple local linear models with interpolation of a "fuzzy basis function". Fault detection is considered in two cases: when faults occur in the linear model part, a KDI-based robust fault detection is applied, where a multi-local-model part is treated as error due to nonlinear undermodeling; when faults occur in the multi-local-model part, a multi-model based fault detection method is developed, in which the identified LimNet is interpreted as several local ARMAX models, and KDI is used as an index to discriminate between each local model and its reference. This paper mainly concentrates discussions on multi-model based fault detection.