Hierarchical Identification Research Articles

Iterative parameter identification for Hammerstein systems with ARMA noises by using the filtering identification idea

SummaryIn practical applications, many processes have nonlinear characteristics that require nonlinear models for accurate description. However, constructing such models and determining their parameters are a challenging task. This article explores filtered identification methods for estimating the parameters of a particular type of nonlinear Hammerstein systems with ARMA noise. An auxiliary model‐based least squares algorithm is developed for such systems based on the auxiliary model identification idea. A hierarchical least squares algorithm that utilizes the hierarchical identification principle is proposed to enhance computational efficiency. Additionally, a key term separation technique is employed to express the system output as a linear combination of parameters, allowing the system to be decomposed into smaller subsystems for more efficient estimation of parameters. Simulation results demonstrate the effectiveness of these proposed algorithms.

Highly-efficient filtered hierarchical identification algorithms for multiple-input multiple-output systems with colored noises

Multiple-input multiple-output (MIMO) systems have extensive applications in industrial processes and systems engineering. This letter applies the filtering identification idea to establish a filtered identification model and investigate a filtered auxiliary model-based recursive least squares (F-AM-RLS) algorithm for parameter identification of MIMO systems with colored noises. To improve the computational efficiency, this work further proposes a four-stage filtered auxiliary model-based recursive least squares (4S-F-AM-RLS) algorithm by means of the hierarchical identification principle. Then, by incorporating the forgetting factor, a four-stage filtered auxiliary model-based forgetting factor recursive least squares (4S-F-AM-FF-RLS) algorithm is given to improve the convergence speed and the estimation accuracy. Additionally, the computational complexity analysis of the proposed algorithms indicates that the 4S-F-AM-RLS algorithm effectively reduces the computational burden and improves computational efficiency. Finally, the effectiveness of the F-AM-RLS, 4S-F-AM-RLS and 4S-F-AM-FF-RLS algorithms is validated through a numerical example.

Auxiliary model-based hierarchical stochastic gradient methods for multiple-input multiple-output systems

This paper presents a hierarchical identification model for multiple-input multiple-output (MIMO) systems. An auxiliary model-based hierarchical stochastic gradient (AM-HSG) algorithm is derived by means of the auxiliary model identification idea and the hierarchical identification principle. Furthermore, an auxiliary model-based hierarchical multi-innovation stochastic gradient (AM-HMISG) algorithm is derived by utilizing the multi-innovation identification theory. In order to compare the computational efficiency of the AM-HSG and AM-HMISG algorithms for identifying MIMO systems, this paper gives the existing traditional gradient algorithms and discusses the complexity of these algorithms in detail. Finally, the simulation example tests the effectiveness of all four algorithms.

Research on partition control of direct air‐cooling condenser based on multivariable Hammerstein CARMA model predictive control

AbstractPartition control of the fan array within a direct air‐cooling condenser (DACC) is recognized as a highly effective energy‐saving measure and a means to mitigate the adverse effects of ambient winds. This study focuses on the development of a dynamic partition model, which establishes the relationship between mass flow rate and fan array speed under windy conditions. The model is grounded in multivariable Hammerstein controlled autoregressive moving average (H‐CARMA) systems. Additionally, an innovative extended stochastic gradient algorithm, founded on the hierarchical identification principle, is introduced to estimate the model's unknown parameters. The recursive least square is employed as a benchmark to verify the accuracy and efficiency of the approach. Subsequently, leveraging the identified model, the model predictive controller based on the differential evolution method is designed to derive the optimal control law. Finally, simulation test and analysis are carried out to testify the effectiveness of our control strategy. The experiment result shows that the dynamic characteristics of the system have been significantly improved and the fan power consumption is reduced by 3.5% compared to the PID controller.

Maximum likelihood gradient‐based iterative estimation for closed‐loop Hammerstein nonlinear systems

AbstractThis article studies a new iterative method for a class of closed‐loop Hammerstein systems. The new iterative method solves the crossproducts between the parameters of the linear block and the nonlinear block by using the key term separation technique, decomposes a system into two subidentification models by utilizing the hierarchical identification principle for reduced computational complexity, and maximizes the maximum likelihood cost function by using the input and output data with a data window for improved parameter estimation accuracy. A numerical simulation example and a continuous stirred tank reactor experiment are presented to demonstrate that the proposed algorithm can work effectively.

Decomposition and composition modeling algorithms for control systems with colored noises

SummaryThis article proposes a novel identification framework for estimating the parameters of the controlled autoregressive autoregressive moving average (CARARMA) models with colored noise. By means of building an auxiliary model and using the hierarchical identification principle, this article investigates a highly‐efficient parameter estimation algorithm. In order to meet the need for identifying the systems with large‐scale parameters, the whole parameters of the CARARMA system is separated into two parameter sets and a decomposition and composition recursive identification algorithm (i.e., hierarchical generalized extended least squares algorithm or decomposition‐based recursive generalized extended least squares algorithm) is presented. Moreover, this article analyzes the convergence of the proposed decomposition and composition recursive identification algorithm. The performance analysis shows that the proposed decomposition and composition identification algorithm can reduce the complexity of the identification algorithm compared with the algorithm without decomposition.

Hierarchical gradient‐ and least‐squares‐based iterative estimation algorithms for input‐nonlinear output‐error systems from measurement information by using the over‐parameterization

AbstractThis article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms.

Two‐stage and three‐stage recursive gradient identification of Hammerstein nonlinear systems based on the key term separation

AbstractThis article explores recursive algorithms for parameter identification issues of Hammerstein output‐error systems. The proposed approach includes the key term separation auxiliary model recursive gradient algorithm, which utilizes the gradient search and the key term separation. To enhance computational efficiency, the system is decomposed into two or three subsystems through the hierarchical identification principle. Based on this, a key term separation based auxiliary model two‐stage recursive gradient algorithm and a key term separation based auxiliary model three‐stage recursive gradient algorithm are presented. The simulation results verify the validity of the obtained algorithms.

Hierarchical recursive least squares parameter estimation methods for multiple‐input multiple‐output systems by using the auxiliary models

SummaryMultiple‐input multiple‐output (MIMO) models are widely used in practical engineering. This article derives a new identification model of the MIMO system by decomposing the MIMO system into several multiple‐input single‐output subsystems. By means of the auxiliary model identification idea, an auxiliary model‐based recursive least squares (AM‐RLS) algorithm is derived for identifying the MIMO systems. In order to reduce the computational burden for identifying MIMO systems, this article presents a hierarchical identification model for the MIMO systems. By applying the hierarchical identification principle, an auxiliary model‐based hierarchical least squares (AM‐HLS) algorithm is proposed for improving the computational efficiency. The computational efficiency analysis indicates that the AM‐HLS algorithm is effective in reducing the calculation amount compared with the AM‐RLS algorithm. Moreover, this article analyzes the convergence of the AM‐HLS algorithm. The simulation example shows that the AM‐RLS and AM‐HLS algorithms studied in this article are effective.

On Recovery of a Non-Negative Relaxation Spectrum Model from the Stress Relaxation Test Data.

The relaxation spectra, from which other material functions used to describe mechanical properties of materials can be uniquely determined, are important for modeling the rheological properties of polymers used in chemistry, food technology, medicine, cosmetics, and many other industries. The spectrum, being not directly accessible by measurement, is recovered from relaxation stress or oscillatory shear data. Only a few models and identification methods take into account the non-negativity of the real spectra. In this paper, the problem of recovery of non-negative definite relaxation spectra from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test is considered. A new hierarchical identification scheme is developed, being applicable both for relaxation time and frequency spectra. Finite-dimensional parametric classes of models are assumed for the relaxation spectra, described by a finite series of power-exponential and square-exponential basis functions. The related models of relaxation modulus are given by compact analytical formula, described by the products of power of time and the modified Bessel functions of the second kind for the time spectrum, and by recurrence formulas based on products of power of time and complementary error functions for frequency spectrum. The basis functions are non-negative. In result, the identification task was reduced to a finite-dimensional linear-quadratic problem with non-negative unknown model parameters. To stabilize the solution, an additional smoothing constraint is introduced. Dual approach was used to solve the stated optimal identification task resulting in the hierarchical two-stage identification scheme. In the first stage, dual problem is solved in two levels and the vector of non-negative model parameters is computed to provide the best fit of the relaxation modulus to experiment data. Next, in second stage, the optimal non-negative spectrum model is determined. A complete scheme of the hierarchical computations is outlined; it can be easily implemented in available computing environments. The model smoothness is analytically studied, and the applicability ranges are numerically examined. The numerical studies have proved that using developed models and algorithm, it is possible to determine non-negative definite unimodal and bimodal relaxation spectra for a wide class of polymers. However, the examples also demonstrated that if the basis functions are non-negative and the model is properly selected for a given type of the real spectrum (unimodal, multimodal), the optimal model determined without non-negativity constraint can be non-negative in the dominant range of its arguments, especially in the wide neighborhood of the spectrum peaks.

Highly‐computational hierarchical iterative identification methods for multiple‐input multiple‐output systems by using the auxiliary models

AbstractThe identification of multiple‐input multiple‐output (MIMO) systems is an important part of designing complex control systems. This article studies an auxiliary model least squares iterative (AM‐LSI) algorithm for MIMO systems. With the expansion of the system scale and limitations of the computer resources, there is an urgent need for an identification algorithm that provides higher computational efficiency. To address this issue, this article further derives a hierarchical identification model and proposes a new auxiliary model hierarchical least squares iterative (AM‐HLSI) algorithm for MIMO systems by applying the hierarchical identification principle. Through the analysis of the computational efficiency, the AM‐HLSI algorithm has higher computational efficiency than the AM‐LSI algorithm. Additionally, the feasibility of the AM‐LSI and AM‐HLSI algorithms is validated by a simulation example.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

Two-input one-output Hammerstein model consists of two parallel nonlinear static blocks followed by a linear dynamic part. By using Hammerstein structure to map relation between a battery State of Charge (SOC) and its terminal voltage/current, a hierarchical stochastic gradient algorithm is studied to estimate parameters of Hammerstein SOC model, so as to predict battery SOC. Firstly, the Hammerstein model is transformed into a bilinear parameter system with the least number of required parameters. Then, a hierarchical stochastic gradient algorithm with a forgetting factor is used to update the two sets of model parameters of the bilinear parameter system, so as to realize SOC estimation. Furthermore, the experiment platform of lithium-ion battery was built and the data of the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile were collected. Finally, the MATLAB simulation results show that the proposed parameter optimized method based Hammerstein model has the advantages of fast convergence speed and high SOC estimation accuracy.

Parameter estimation of fractional‐order Hammerstein state space system based on the extended Kalman filter

SummaryThis paper addresses the combined estimation issues of the parameters and states for fractional‐order Hammerstein state space systems with colored noises. An extended state estimator is derived by using the parameter estimates to replace the unknown system parameters in Kalman filter. The hierarchical identification principle is introduced to solve the unknown parameters of measurement noises. By introducing the forgetting factor, an extended Kalman filtering‐based hierarchical forgetting factor stochastic gradient algorithm is presented to estimate the unknown states, parameters and fractional‐order. A numerical example is respectively presented to demonstrate the feasibility of the proposed identification algorithm. It can be seen that the estimation errors are relatively small, which reflects the proposed algorithms have good identification effect.

Hierarchical iterative identification algorithms for a nonlinear system with dead‐zone and saturation nonlinearity based on the auxiliary model

SummaryThis paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea, an auxiliary model hierarchical least squares‐based iterative algorithm is proposed for estimating the parameters of the nonlinear system. Based on the hierarchical identification model, an auxiliary model hierarchical gradient‐based iterative algorithm is presented for the nonlinear system by utilizing the gradient search. In order to take full advantage of the system data, an auxiliary model hierarchical multi‐innovation gradient‐based iterative algorithm is derived for the nonlinear system according to the multi‐innovation identification theory. Finally, the numerical simulation results illustrate the effectiveness of the proposed algorithms.

Hierarchical maximum likelihood identification based on Levenberg–Marquardt and particle swarm optimization for feedback nonlinear systems

This article covers the identification of the feedback nonlinear systems. The parameterized nonlinear identification model involves products of system nonlinear part parameters and system linear part parameters. To deal with these product terms, the hierarchical identification based on maximum likelihood is used to decompose the system into two subsystems. The Levenberg–Marquardt and particle swarm optimization methods are applied for identifying the two subsystems, respectively. For the purpose of enhancing the optimization capability of the basic particle swarm optimization method, some improvement strategies are constructed. Thus, the improved particle swarm optimization algorithm which combines the adaptive feedback, the linearly decreasing method and the mutational operator is applied to adaptively adjust the search strategy and improve the ergodicity. The simulation indicates that the derived estimation is effective because it can obtain high identification accuracy and fast convergence speed when identifying the feedback systems. Besides, the case study demonstrates that the proposed method can be well used to identify the electro-hydraulic-servo position system.

Sound of Daily Living Identification Based on Hierarchical Situation Audition.

One of the key objectives in developing IoT applications is to automatically detect and identify human activities of daily living (ADLs). Mobile phone users are becoming more accepting of sharing data captured by various built-in sensors. Sounds detected by smartphones are processed in this work. We present a hierarchical identification system to recognize ADLs by detecting and identifying certain sounds taking place in a complex audio situation (AS). Three major categories of sound are discriminated in terms of signal duration. These are persistent background noise (PBN), non-impulsive long sounds (NILS), and impulsive sound (IS). We first analyze audio signals in a situation-aware manner and then map the sounds of daily living (SDLs) to ADLs. A new hierarchical audible event (AE) recognition approach is proposed that classifies atomic audible actions (AAs), then computes pre-classified portions of atomic AAs energy in one AE session, and finally marks the maximum-likelihood ADL label as the outcome. Our experiments demonstrate that the proposed hierarchical methodology is effective in recognizing SDLs and, thus, also in detecting ADLs with a remarkable performance for other known baseline systems.

ScROSHI: robust supervised hierarchical identification of single cells.

Identifying cell types based on expression profiles is a pillar of single cell analysis. Existing machine-learning methods identify predictive features from annotated training data, which are often not available in early-stage studies. This can lead to overfitting and inferior performance when applied to new data. To address these challenges we present scROSHI, which utilizes previously obtained cell type-specific gene lists and does not require training or the existence of annotated data. By respecting the hierarchical nature of cell type relationships and assigning cells consecutively to more specialized identities, excellent prediction performance is achieved. In a benchmark based on publicly available PBMC data sets, scROSHI outperforms competing methods when training data are limited or the diversity between experiments is large.

Data filtering‐based parameter estimation algorithms for a class of nonlinear systems with colored noises

AbstractThis article studies the data filtering‐based identification algorithms for a class of nonlinear system with autoregressive noise. By means of the data filtering technique and the hierarchical identification principle, the identification model is transformed into two sub‐identification models, and a filtering hierarchical gradient‐based iterative algorithm is proposed for improving parameter estimation accuracy and reducing computational burden. Meanwhile, to further improve the identification performance, the multi‐innovation identification theory is used to derived the filtering hierarchical multi‐innovation gradient‐based iterative algorithm. The gradient‐based iterative algorithm is given for comparison. The analysis shows that the filtering hierarchical gradient‐based iterative algorithm has smaller computational burden and can give more accurate parameter estimates than the gradient‐based iterative algorithm, and the filtering hierarchical multi‐innovation gradient‐based iterative algorithm can track time‐varying parameters based on the dynamical window data. Finally, the example part is provided to verify the effectiveness of the proposed algorithms.

Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data

Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least squares methods and the multi-innovation least squares methods. It demonstrates lemmas and theorems about the least squares and multi-innovation least squares parameter estimation algorithms after reviewing and surveying some important contributions in the area of system identification, such as the auxiliary model identification idea, the multi-innovation identification theory, the hierarchical identification principle, the coupling identification concept and the filtering identification idea. The results of the least squares and multi-innovation least squares algorithms for linear regressive systems with white noises can be extended to other systems with colored noises.

L-АЛГОРИТМ МОДЕЛИРОВАНИЯ ПЕРЕМЕННЫХ СОСТОЯНИЯ СТАДИИ ДИФФУЗИИ ПРОИЗВОДСТВА САХАРА

The article describes an algorithm for recurrent hierarchical identification of a regression model for the diffusion stage temperature mode in sugar production based on the trichotomy of residuals of intermediate models (L-algorithm). The algorithm uses a scheme that makes it possible to develop a neighborhood model while identifying the hierarchical partitioning of input data. This algorithm makes it possible to improve the approximation quality of some initial analytical model based on the analysis of its residuals and subsequent recurrent identification of additional terms corresponding to the hierarchical partitioning of the domain of model input definition (input tuples).