Identification Of State-space Models Research Articles

Automated Seizure Detection Based on State-Space Model Identification.

In this study, we developed a machine learning model for automated seizure detection using system identification techniques on EEG recordings. System identification builds mathematical models from a time series signal and uses a small number of parameters to represent the entirety of time domain signal epochs. Such parameters were used as features for the classifiers in our study. We analyzed 69 seizure and 55 non-seizure recordings and an additional 10 continuous recordings from Thomas Jefferson University Hospital, alongside a larger dataset from the CHB-MIT database. By dividing EEGs into epochs (1 s, 2 s, 5 s, and 10 s) and employing fifth-order state-space dynamic systems for feature extraction, we tested various classifiers, with the decision tree and 1 s epochs achieving the highest performance: 96.0% accuracy, 92.7% sensitivity, and 97.6% specificity based on the Jefferson dataset. Moreover, as the epoch length increased, the accuracy dropped to 94.9%, with a decrease in sensitivity to 91.5% and specificity to 96.7%. Accuracy for the CHB-MIT dataset was 94.1%, with 87.6% sensitivity and 97.5% specificity. The subject-specific cases showed improved results, with an average of 98.3% accuracy, 97.4% sensitivity, and 98.4% specificity. The average false detection rate per hour was 0.5 ± 0.28 in the 10 continuous EEG recordings. This study suggests that using a system identification technique, specifically, state-space modeling, combined with machine learning classifiers, such as decision trees, is an effective and efficient approach to automated seizure detection.

Masked Multiple State Space Model Identification Using FRD and Evolutionary Optimization

Masked Multiple State Space Model Identification Using FRD and Evolutionary Optimization

Reduced-Order Identification of Aeroelastic Systems with Constrained and Imposed Poles

This work investigates the identification of reduced-order state-space models from aeroelastic simulations of the interaction of a built-in structural finite element model and a linear aerodynamic model using unsteady potential theory. The objective is to propose and compare different new frequency-based identification methods operating on frequency response associated to the inputs and outputs of interest. The first methods considered are the Loewner interpolation method and a subspace algorithm. Subsequently, the paper introduces the possibility to apply stability constraints and to impose a certain number of poles estimated beforehand by the method in order to make the identified models closer to the true aeroelastic physics. To achieve this goal, new dedicated techniques are developed and subsequently validated on data generated by random state-space models of various orders, and on aeroelastic data obtained from structural and aerodynamic aircraft models.

Recursive identification of a nonlinear state space model

SummaryThe convergence of a recursive prediction error method is analyzed. The algorithm identifies a nonlinear continuous time state space model, parameterized by one right‐hand side component of the differential equation and an output equation with a fixed differential gain, to avoid over‐parametrization. The method minimizes the criterion by simulation using an Euler discretization. A stability analysis of the associated differential equations results in conditions for (local) convergence to a minimum of the criterion function. Simulations verify the theoretical analysis and illustrate the performance in the presence of unmodeled dynamics, by identification of the nonlinear drum boiler dynamics of a power plant model.

Further results on “System identification of nonlinear state-space models”

This note presents some further results concerning the identification of the nonlinear state-space model (NSSM) based on the meaningful conclusions in the above paper. We use the heavy-tailed Student’s t-distribution to model the system noises and the parameter estimation problem is solved via the expectation maximization (EM) algorithm wherein the decomposition of t-distribution as well as the particle smoother is applied, then a robust identification strategy is proposed. By using the mathematical decomposition of t-distribution, two major advantages are brought: (1) It facilitates the calculation of the desired Q-function efficiently; (2) It allows a more clear and evident explanation of the robustness of the proposed identification strategy.

Real-time temperature predictions via state-space model and parameters identification within rack-based cooling data centers

Current rack-based cooling architecture of data centers (DCs) is a promising method since it simplifies airflow distribution and provides fast cooling regulation. Real-time on-demand control of the cooling system is an effective way to improve its operational energy efficiency without sacrificing the thermal security of IT equipment. Accurate and fast temperature distribution prediction serves as one of the bases for ensuring the superior performance of advanced control algorithms. Thus, this study proposed a novel grey-box state-space model, to rapidly predict the dynamic temperature distribution for rack-based cooling DCs. Various heat transfer physics in the rack-based cooling DCs, including heat production caused by servers and heat movements by airflows, were modeled as a state-space structure using the zonal modeling approach. The coefficient matrices were identified through the prediction-error method (PEM), in order to avoid the extremely time-consuming process of obtaining accurate physical parameters regarding the system. This developed model was validated with an experimentally validated mechanistic model and computational fluid dynamics (CFD) simulations. Additionally, the impact of the prediction horizon's size and IT workload transient changes on the proposed model's prediction accuracy were investigated as well. Through simulation, the developed model achieves sufficient accuracy with an average root mean square error (RMSE) equal to 0.19 °C and less than 3% relative error for predicting 1-min dynamic temperature evolutions. Also, the developed model shows satisfying performances for the long-horizon prediction and transient scenario, which will facilitate advanced control techniques for DC cooling systems.

Direct identification of continuous-time LPV state-space models via an integral architecture

In this paper, we present a block-structured architecture for direct identification of continuous-time Linear Parameter-Varying (LPV) state-space models. The proposed architecture consists of an LPV model followed by an integral block. This structure is used to approximate the continuous-time LPV system dynamics. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate-descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV model, the optimization variables within each coordinate-descent step can be updated analytically via ordinary least squares. Furthermore, in order to handle large-size datasets, we discuss how to perform optimization based on short-size subsequences. The effectiveness of the proposed methodology is demonstrated via an academic example and two case studies. The first case study consists of identifying an LPV model describing the behaviour of an electronic bandpass filter from benchmark experimental data. The second case study involves identification of the plasma safety factor from a tokamak plasma simulator.

Low‐density polyethylene tubular reactor control using neural Wiener model predictive control

AbstractLow‐density polyethylene (LDPE) is a valued commodity plastic with versatile applications. However, controlling the LDPE polymerization reactor is a challenging task due to its nonlinear behavior and multivariable process and operates in a board operating region. This work aims to develop and explore the neural Wiener MPC (NWMPC) application in controlling the LDPE tubular reactor process. The motivation for NWMPC development originates from its advantage in terms of lower development effort, time, resource, and computational costs compared to nonlinear MPC (NMPC) using the first principle model (FPM). In order to develop the LDPE tubular reactor model, the Aspen Plus and Aspen Dynamic software are used to simulate the process in steady‐state and dynamic form. The neural Wiener (NW) model identification is performed using state space and neural network model identification using Matlab software. The identification result shows the ability of the NW model to identify the nonlinear LDPE tubular reactor process successfully. Furthermore, the NWMPC has outperformed the state space MPC (SSMPC) in controlling grade transition, feed pressure loss, feed impurity disturbance, and heat of polymerization change during the online closed‐loop performance tests. These results signify the ability of NWMPC to handle practical LDPE tubular reactor control scenarios.

An integral architecture for identification of continuous-time state-space LPV models

Abstract This paper presents an integral architecture for direct identification of continuous-time linear parameter-varying (LPV) state-space models. The main building block of the proposed architecture consist of an LPV model followed by an integral block, which is used to approximate the continuous-time state map of an LPV representation. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV models, the unknown parameters within each coordinate descent step can be computed analytically via ordinary least squares. The effectiveness of the proposed methodology is assessed via a numerical example.

Data-driven Modelling of Thermal Solid Sorption Storage Systems

An approach fofsr data-driven modelling of open sorption storage systems using zeolite as storage material is presented. The overall dynamic simulation model has the inflow air stream mass flow and absolute humidity as inputs and computes the outflow air temperature. The model is sub-divided into several components, where dynamic state space and process model identification techniques are applied. A comparison of the proposed modelling technique with simulated data from a validated model based on first principles shows that a reasonable accuracy − for a model application in temperature control systems design − can be obtained. It was found that using the proposed strategy, only a limited number of experiments are required, thus saving experimental time. Moreover, the computational requirements for a simulation using the proposed model are greatly reduced compared to a simulation model where differential equations discretised in time and space must be solved.

Learning latent dynamics for partially observed chaotic systems.

This paper addresses the data-driven identification of latent representations of partially observed dynamical systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications and long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely in general on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly reconstructing the latent states and learning an ordinary differential equation representation in this space. Through numerical experiments, we demonstrate the relevance of the proposed framework with respect to state-of-the-art approaches in terms of short-term forecasting errors and long-term behavior. We further discuss how the proposed framework relates to the Koopman operator theory and Takens' embedding theorem.

Epistemic Uncertainty Quantification in State-Space LPV Model Identification Using Bayesian Neural Networks

This letter presents a variational Bayesian inference Neural Network (BNN) approach to quantify uncertainties in matrix function estimation for the state-space linear parameter-varying (LPV) model identification problem using only inputs/outputs data. The proposed method simultaneously estimates states and posteriors of matrix functions given data. In particular, states are estimated by reaching a consensus between an estimator based on past system trajectory and an estimator by recurrent equations of states; posteriors are approximated by minimizing the Kullback-Leibler (KL) divergence between the parameterized posterior distribution and the true posterior of the LPV model parameters. Furthermore, techniques such as transfer learning are explored in this letter to reduce computational cost and prevent convergence failure of Bayesian inference. The proposed data-driven method is validated using experimental data for identification of a control-oriented reactivity controlled compression ignition (RCCI) engine model.

State-space system identification with physically motivated residual states and throughput rank constraint

It has been observed that energy conjugate input-output pair transfer functions with strongly participating outside-band modes of mechanical systems often render identified state-space models with poor fit to data. That holds even after common practice inclusion of mass and stiffness residual states. The inclusion of a particular form of extra residual states are suggested to improve the model fit for such pairs. A pole placement strategy for the extra states is derived. Furthermore, for identification of state-space models with force input and acceleration output, the system direct throughput matrix relating the two is modelled. For flexible structures with rigid body motion, it is shown that the direct throughput matrix can be decomposed into a rigid body and flexible motion part. In test situations with more inputs and outputs than rigid body modes, the rigid body partition of the direct throughput matrix of the identified model must be rank constrained for physical consistency. The constraint is enforced using a singular value decomposition during iterations of the state-space matrices used to further improve the identified model fit. The procedures are illustrated on simulated finite element data from an industrial component with known model order. A successful application to real experimental data is also shown.

Hierarchical parameter and state estimation for bilinear systems

ABSTRACTThe identification of state-space models of bilinear systems is studied in this paper. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem more difficult than that of the linear state-space model. For the coupled variables, this paper introduces the interaction estimation theory to study an on-line algorithm for joint state-parameter estimation. To be more specific, a state observer in the bilinear form is established by minimising the state estimation error covariance matrix in the same way of a Kalman filter on the condition that the parameters are known. Then, a bilinear state observer based recursive least squares algorithm is developed using the least squares method. Moreover, for the purpose of improving the computational efficiency, a bilinear state observer based two-stage recursive least squares algorithm and a bilinear state observer based multi-stage recursive least squares algorithm are proposed by decomposing the system into several subsystems based on the hierarchical identification. Finally, a numerical simulation is employed to show the specific performance of the proposed approaches.

On the vanishing and exploding gradient problem in Gated Recurrent Units

Recurrent Neural Networks are applied in areas such as speech recognition, natural language and video processing, and the identification of nonlinear state space models. Conventional Recurrent Neural Networks, e.g. the Elman Network, are hard to train. A more recently developed class of recurrent neural networks, so-called Gated Units, outperform their counterparts on virtually every task. This paper aims to provide additional insights into the differences between RNNs and Gated Units in order to explain the superior perfomance of gated recurrent units. It is argued, that Gated Units are easier to optimize not because they solve the vanishing gradient problem, but because they circumvent the emergence of large local gradients.

Temperature control of low density polyethylene (LDPE) tubular reactor using Model Predictive Control (MPC)

Application of advanced process control has become demanding in order to save energy and reduce operating cost, while attaining excellent controllability of the process. This situation can be achieved via better controller action performance compared to conventional control scheme such as PID controller. Model Predictive Control (MPC) has a wide application in the industry due to its ability to handle multivariable control and optimized process performance. In this study, a linear based MPC was implemented to control Low Density Polyethylene (LDPE) tubular reactor temperature. The control of LDPE tubular reactor is challenging due to the complexity of the polymerization process and the nature of the reactor itself. The steady state polymerization reactor model was simulated using Aspen Plus software. The validated steady state reactor model was then exported to Aspen Dynamic software for dynamic simulation. In order to implement online control of the process, the dynamic model was linked with Matlab Simulink environment. The linear model of the process was estimated using State-space model identification technique. Sequential Quadratic programming (SQP) method was adopted by the MPC to calculate the controller action. The performance of MPC was compared to a PID controller. Based on the results, MPC had overcome PID performance in set point tracking and disturbance rejection test despite its low accuracy process model. The linear model low accuracy drawback was compensated by proper tuning of the MPC. In overall, MPC had demonstrated its capability to control the process with optimized control action, which can lead to production cost saving in the long run.

Constrained Subspace Method for the Identification of Structured State-Space Models (COSMOS)

In this article, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user-specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the system-parameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The nonconvex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.

Combining Linear Algebra and Numerical Optimization for Gray-Box Affine State-Space Model Identification

Accurately estimating the parameters of a gray-box linear time-invariant state-space representation is still a challenging problem especially if the number of unknowns exceeds ten. The standard nonlinear optimization-based procedures often fail because the initial guesses are not in the domain of attraction of the user-defined cost function global minimum. Herein, a new solution is developed to give access to estimated parameters which are accurate estimates of the unknown parameters directly or, at worst, good initial guesses for any standard nonlinear optimization-based method. By assuming that 1) the gray-box model to identify is minimal and structurally identifiable, 2) the parameter dependency is affine, and 3) the available datasets have been transformed into a reliable and accurate black-box state-space model, our procedure consists in determining the unique similarity transformation between the black-box and gray-box representations of the system to identify. More specifically, we introduce a technique which first extracts a system of equations linear in terms of the similarity transformation; second, it solves this system by using standard linear algebra tools; finally, completes this two-step procedure by a numerical optimization solution (dedicated now to a very small number of unknowns) if the second step does not give access to all the similarity transformation parameters effectively. In this contribution, we first describe our new procedure, prove its capabilities of giving accurate estimates under specific practical constraints, and finally demonstrates its effectiveness with simulation examples.

Prior-knowledge-based subspace identification for batch processes

In this paper, a prior-knowledge-based subspace identification method (SIM) is proposed for batch processes subject to repeatable disturbances. The proposed method is a two-step procedure for state-space model identification: in the first step, the extended observability and triangular Toeplitz matrices are estimated simultaneously from a parity space of the experimental data and, based on which, the corresponding system matrices are retrieved in the second step. More specifically, A and C are retrieved from the estimated extended observability matrix, while B and D are retrieved from the estimated triangular Toeplitz matrix. The proposed method shows several superiorities in the following aspects. Firstly, it is able to provide unbiased parameter estimation in the presence of repeatable disturbances, thanks to the proposed difference operator which eliminates the disturbance effect. Secondly, it shows better robustness to measurement noise compared with the existing SIMs using parity space, due to the inherent instrumental variable mechanism and the new technique to build the instrument, which greatly enhance the estimated model efficiency/accuracy. Lastly, by taking the auxiliary static-gain information into account in the identification procedure, the variance properties of the parameters can be improved, especially for the system matrices B and D. All the above-mentioned developments are analyzed with strict mathematical proofs, along with two illustrative examples to confirm the effectiveness and merits.

Research on unmanned aerial vehicle modeling and control based on intelligent algorithms

This article designs an automatic flight control system for an unmanned aerial vehicle helicopter. The differential evolution intelligent algorithm is used for a state-space model identification; the differential evolution method has an advantage of choosing initial point randomly. The accuracy of the identified model is verified by comparing the model-predicted responses with the responses collected during flight experiments. The reliability and efficiency of the differential evolution algorithm are demonstrated by the experimental results. A robust controller is designed based on the identified model for the unmanned aerial vehicle helicopter with two-loop control frame: the outer-loop is used to obtain the expected attitude angles through reference path and speed with guidance-based path-following control, and the inner-loop is used to control the attitude angles of helicopter tracking the expected ones with H∞ loop-shaping method. The greatest common right divisor method is used to choose the weighting matrix in loop shaping, in which the stability margin is larger and has a greater bandwidth of the unmanned aerial vehicle system. Finally, a space spiral curve trajectory tracking simulation is conducted to illustrate the efficiency of the proposed control systems, and the simulation results prove that the unmanned helicopter system achieves a top-level control performance.