Proposed Identification Technique Research Articles

On soft measurement modeling for predicting photovoltaic power with uncertainty based on the Takagi–Sugeno model

Abstract Accurate solar power forecast is becoming more essential for safe and reliable power grid operation with the increasing number of grid-connected photovoltaic (PV) power production units. However, PV power exhibits significant output fluctuation due to both external inputs and intrinsic stochasticity in system dynamics. Therefore, an efficient and reliable soft measurement model of PV power with uncertainty is demanded in practice applications. The technique described in this paper captures the impacts produced by the fundamental uncertainty observed in the data, instead of relying on unrealistic assumptions about uncertainty. A soft measurement model using the Takagi-Sugeno (TS) Fuzzy Logic System (FLS) based on several input-output time series of PV plants is presented in this study. Chebyshev's inequality from probability theory and statistics is adopted to create the confidence interval-based response envelopes for these time series at each moment. An envelope-based measure of output uncertainty and a center-valued response forecasting model can be obtained by the proposed identification technique. PV datasets are employed to demonstrate the concept, which indicates the proposed soft measurement may outperform existing methods in terms of prediction accuracy. The average values of Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the Correlation Coefficient (R) are only 0.0787, 0.1113, and 0.9979. The average values of the prediction interval coverage probability (PICP) and the prediction interval normalized average width (PINAW) are 0.9806 and 0.1051.

Linear modeling techniques for liquid height regulation in two tank - Two variable system

In this paper, two linear modeling techniques are presented for regulating the liquid height in two tank - two variable system (TT-TVS). Initially, the nonlinear dynamics of TT-TVS are linearized using the Taylor series linearization technique. However, this method reveals that some parameters of TT-TVS are inexact, necessitating the adoption of system identification techniques or mathematical approaches to accurately identify the linear dynamics. To address this, two new approaches are proposed: (i) a mathematical approach utilizing real-time input-output data, and (ii) a Linear Variable Parameter Transfer Function (LVPTF) model identification approach, which employs real-time data and MATLAB curve fitting tool. A comparative analysis between the proposed identification techniques and existing methods from the literature is also presented. The results indicate that the LVPTF modeling technique offers superior accuracy in identifying the linear dynamics of TT-TVS.

Identification of Wiener state–space models utilizing Gaussian sum smoothing

In this paper, we address the problem of system identification for Wiener state–space models. Our approach is based on the Maximum Likelihood method and the Expectation–Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation–Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state–space systems in which the output is produced by a known quantizer. We present numerical examples to illustrate the benefits of the proposed identification technique.

A Nonparametric Regularization for Spectrum Estimation of Time-Varying Output-Only Measurements

In this work, an advanced 2D nonparametric correlogram method is presented to cope with output-only measurements of linear (slow) time-varying systems. The proposed method is a novel generalization of the kernel function-based regularization techniques that have been developed for estimating linear time-invariant impulse response functions. In the proposed system identification technique, an estimation method is provided that can estimate the time-varying auto- and cross-correlation function and indirectly, the time-varying auto- and cross-correlation power spectrum estimates based on real-life measurements without measuring the perturbation signals. The (slow) time-varying behavior means that the dynamic of the system changes as a function of time. In this work, a tailored regularization cost function is considered to impose assumptions such as smoothness and stability on the 2D auto- and cross-correlation function resulting in robust and uniquely determined estimates. The proposed method is validated on two examples: a simulation to check the numerical correctness of the method, and a flutter test measurement of a scaled airplane model to illustrate the power of the method on a real-life challenging problem.

Automated multi-objective system identification using grammar-based genetic programming

In order to use existing identification tools effectively, a user must make critical choices a priori that ultimately determine the quality of estimated models. Furthermore, while estimated models are typically optimized for a single identification criterion, engineering applications typically impose multiple performance specifications that may contradict each other. In this contribution, we develop a system identification methodology that automatically selects parametric model structures from a wide range of dynamic system models based on measured data. The problem of inferring model structures and estimating model parameters within these structures is encapsulated in a bi-level optimization problem. The optimization problem is formulated for multiple user-specified identification objectives. Finally, the range of dynamical systems considered for the optimization problem is specified using Tree Adjoining Grammar. A solution approach based on genetic programming is developed, and its asymptotic properties and computational complexity is analysed. The empirical performance of the proposed identification techniques is studied using a simulation example.

Identification of the extended standard linear solid material model by means of experimental dynamical measurements

A novel algebraic procedure for the non-parametric identification of the material model by means of dynamical test measurements is proposed. An extended Standard Linear Solid (SLS) material model is taken into account to model the material linear visco-elastic behavior. It consists of the series arrangement of fractional Kelvin model elements adopting real parameters and integer and non-integer order time differential operators, and of hysteretic Kelvin model elements adopting complex parameters and integer order time differential operators. Hysteretic Kelvin model elements are introduced to take account of the material hysteretic behavior. The material E(j⋅ω) complex modulus, is analytically modeled as the ratio of pseudo polynomials (non-integer power terms) in the j⋅ω Fourier variable. A multi-step, iterative, material model identification technique is here proposed to identify the unknown polynomial coefficients and the non-integer exponent values starting from E(j⋅ω) material discrete estimates from input-output dynamical measurements made on a beam specimen at different ω frequency values. Computational, nonphysical SLS elements resulting from the application of the identification procedure can be found and eliminated, so that a low order optimal model result. Some results obtained by applying the proposed identification technique with real experimental measurements are shown and discussed.

Output-only identification of self-excited systems using discrete-time Lur'e models with application to a gas-turbine combustor

A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimisation to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimisation to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor.

Structural and Parametric Identification of Knowm Memristors.

This paper proposes a novel identification method for memristive devices using Knowm memristors as an example. The suggested identification method is presented as a generalized process for a wide range of memristive elements. An experimental setup was created to obtain a set of intrinsic I–V curves for Knowm memristors. Using the acquired measurements data and proposed identification technique, we developed a new mathematical model that considers low-current effects and cycle-to-cycle variability. The process of parametric identification for the proposed model is described. The obtained memristor model represents the switching threshold as a function of the state variables vector, making it possible to account for snapforward or snapback effects, frequency properties, and switching variability. Several tools for the visual presentation of the identification results are considered, and some limitations of the proposed model are discussed.

Modal identification in the case of complex modes – Use of the wavelet analysis applied to the after-shock responses of a masonry wall during shear compression tests

In real structures, the proportional damping assumption is never strictly verified. Indexes of non-proportionality are then necessary to determine if this assumption leading to real modes still remains valid. If not, complex modes will appear and moreover, if their corresponding natural frequencies are close, their imaginary part can become large. In this paper, a new non-proportionality index, quantifying the “complexity” of mode shapes, is presented, derived from the notion of optimal complex modes introduced by Adhikari. This new index is designed for experimental results, for which the system’s parameters are not known, and proven to be equal to the previous one up to the first order on damping. Modal identification based on wavelet analysis is considered promising in this study for processing free responses of non-proportionally damped systems, integrated in noise, to directly obtain complex modes. A procedure for choosing an appropriate quality factor for the time-frequency resolution, necessary to get correct identification results in the case of free responses combined with responses to ambient excitation and/or to additive noise, is detailed. The proposed identification technique based on Continuous Wavelet Transform (CWT) is finally applied on different transient responses of a masonry wall specimen during an experimental campaign comprising simultaneous vibrations and shear-compression tests. The results of the CWT method for modal identification are compared with those obtained by a classical modal analysis technique, called Least Squares Complex Frequency method, by means of the Modal Assurance Criterion and the proposed non-proportionality index.

A single-step identification strategy for the coupled TITO process using fractional calculus

The reliable performance of a complete control system depends on accurate model information being used to represent each subsystem. The identification and modelling of multivariable systems are complex and challenging due to cross-coupling. Such a system may require multiple steps and decentralized testing to obtain full system models effectively. In this paper, a direct identification strategy is proposed for the coupled two-input two-output (TITO) system with measurable input–output signals. A well-known closed-loop relay test is utilized to generate a set of inputs–outputs data from a single run. Based on the collected data, four individual fractional-order transfer functions, two for main paths and two for cross-paths, are estimated from single-run test signals. The orthogonal series-based algebraic approach is adopted, namely the Haar wavelet operational matrix, to handle the fractional derivatives of the signal in a simple manner. A single-step strategy yields faster identification with accurate estimation. The simulation and experimental studies depict the efficiency and applicability of the proposed identification technique. The demonstrated results on the twin rotor multiple-input multiple-output (MIMO) system (TRMS) clearly reveal that the presented idea works well with the highly coupled system even in the presence of measurement noise.

Entropy Fuzzy System Identification for the Heave Flight Dynamics of a Model-Scale Helicopter

This article studies nonlinear system identification of a small scale and flybar-free unmanned helicopter, the Trex450 chopper, built using commercial off-the-shelf components. We employ the real-time input-output data, obtained from human-controlled flight tests, operating the aircraft under severe ground effects during the vertical flight maneuvers. We highlight the efficacy of the entropy fuzzy system identification method with respect to the performance of several well-known nonlinear system identification techniques (i.e., a Takagi-Sugeno Fuzzy system, an adaptive neuro-fuzzy inference system (ANFIS), and a nonlinear autoregressive with exogenous (NARX) model) as our benchmarks. Our research confirms the benefits of the entropy fuzzy identification technique. Despite being nonlinear, the proposed fuzzy model is relatively simple, transparent, and highly accurate to represent the complex non-linear dynamic behaviors of our unmanned helicopter under severe ground effects. Another major advantage of the proposed system identification technique is its ability to avoid overfitting, an essential requirement in modeling. Overall, the fuzzy system is also capable of achieving a delicate balance between maximizing the accuracy while minimizing the complexity of the acquired model.

PRBS-based loop gain identification and output impedance shaping in DC microgrid power converters

Due to potential dynamic interactions among dc microgrid power converters, the performance of some of their control loops can vary from the designed behavior. Thus, online monitoring of different control loops within a dc microgrid power converter is highly desirable. This paper proposes the simultaneous identification of several control loops within dc microgrid power converters, by injecting orthogonal pseudo-random binary sequences (PRBSs), and measuring all the loop gains in one measurement cycle. The identification results can be used for different purposes such as controller autotuning, impedance shaping, etc. Herein, an example of output impedance estimation and shaping based on locally-measured loop gains is presented. The proposed identification technique and its application in output impedance shaping are validated on an experimental dc microgrid prototype, composed of three droop-controlled power converters.

Evaluation of natural periods and modal damping ratios for seismic design of building structures

A comprehensive technique for identification of modal properties (i.e. natural periods and equivalent modal damping ratios) of building structures is presented. The proposed identification technique employs a combination of multiple system identification methods; it utilizes the benefits and suppresses the shortcomings of each method to provide a succinct set of modal properties for building structures. Using the proposed modal identification technique, modal properties of 80 buildings with a total of 896 distinct seismic event and building direction records were identified. Simplified and practical equations for modal quantities along with the variation of such parameters for different structural system types, building height, and amplitude of excitation are studied and presented. A critical assessment of other similar studies and results are presented.

T2-ETS-IE: A Type-2 Evolutionary Takagi–Sugeno Fuzzy Inference System With the Information Entropy-Based Pruning Technique

We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi–Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.

Two-Layer On-line Parameter Estimation for Adaptive Incremental Backstepping Flight Control for a Transport Aircraft in Uncertain Conditions

Abstract Presence of uncertainties caused by unforeseen malfunctions of the actuator or changes in aircraft behavior could lead to aircraft loss of control during flight. The paper presents two-layer parameter estimation procedure augmenting Incremental Backstepping (IBKS) control algorithm designed for a large transport aircraft. IBKS uses angular accelerations and current control deflections to reduce the dependency on the aircraft model. However, it requires knowledge of the control effectiveness. The proposed identification technique is capable to detect possible problems such as a failure or presence of unknown actuator dynamics even in case of redundancy of control actuation. At the first layer, the system performs monitoring of possible failures. If a problem in one of the control direction is detected the algorithm initiates the second-layer identification determining the individual effectiveness of the each control surface involved in this control direction. Analysis revealed a high robustness of the IBKS to actuator failures. However, in severe conditions with a combination of multiple failures and presence of unmodelled actuator dynamics IBKS could lost stability. Meanwhile, proposed control derivative estimation procedure augmenting the IBKS control helps to sustain stability.

Reconfigurable Fault Tolerant Flight Control for UAV with Pseudo-Inverse Technique

Abstract In this study, the parameter identification based fault tolerant control of an unmanned aerial vehicle (UAV) dynamics is presented. When faults occur in the actuator, then the elements of the control distribution matrix (control derivatives) change. The augmented Kalman filter (KF) is used in order to identify the control distribution matrix elements; thus, the control reconfiguration is carried out using this identified control distribution matrix. A reconfigurable pseudo-inverse controller is designed for the modeled UAV. The control derivatives are identified by the augmented KF and pseudo-inverse controller is reconfigured for the identified control distribution matrix. In simulations, the linearized model of longitudinal dynamics of ZAGI UAV is considered, and the performance of the proposed system identification and reconfigurable control techniques are examined for this model. For this purpose the control derivatives related to elevator and thrust are changed in accordance with faulty system condition and the augmented KF based reconfigurable control algorithm using pseudo-inverse technique is investigated.

Parameter estimation algorithms for dynamical response signals based on the multi‐innovation theory and the hierarchical principle

In this study, the authors consider the parameter estimation problem of the response signal from a highly non-linear dynamical system. The step response experiment is taken for generating the measured data. Considering the stochastic disturbance in the industrial process and using the gradient search, a multi-innovation stochastic gradient algorithm is proposed through expanding the scalar innovation into an innovation vector in order to obtain more accurate parameter estimates. Furthermore, a hierarchical identification algorithm is derived by means of the decomposition technique and interaction estimation theory. Regarding to the coupled parameter problem between subsystems, the authors put forward the scheme of replacing the unknown parameters with their previous parameter estimates to realise the parameter estimation algorithm. Finally, several examples are provided to access and compare the behaviour of the proposed identification techniques.

Damping for large-amplitude vibrations of plates and curved panels, part 2: Identification and comparisons

A non-linear identification technique based on the harmonic balance method is presented to obtain the damping ratio and non-linear parameters of isotropic and laminated sandwich rectangular plates and curved panels, subjected to harmonic excitation orthogonal to the surface. The response of structures under consideration is approximated by a single-degree of freedom Duffing oscillator accounting for viscous damping, quadratic and cubic non-linear stiffness. The method uses experimental frequency-amplitude data and a least-squares technique to identify parameters and reconstruct frequency-response curves by spanning the excitation frequency in the neighborhood of the lowest natural frequencies. In particular, an iterative procedure is implemented to construct the mean displacement and identify the damping ratio. Close agreement is seen between the reconstructed non-linear frequency-amplitude curves, the experimental data and the results of the reduced-order model obtained in part 1 of the present study (Alijani et al., 2015 [1]). The proposed identification technique confirms the very large increase of damping during large-amplitude vibrations, as observed in part 1 of the present study, and demonstrates a non-linear correlation between damping, vibration amplitude and excitation level.

Identification and Modeling of Contact Dynamics of Precise Direct Drive Stages

The aim of this paper is to develop identification that is capable of capturing the characteristics of nonlinear tangential elastic and friction forces arising in submicron motions. Using novel Hilbert transform based signal processing and making use of the intimate relations between internal elastic and friction forces, the latter can be simultaneously recovered from measured data. The experiments were performed on a stage equipped with linear motors, while being driven by slow, quasi-harmonic excitation at frequencies of 1–40 Hz. The identified elastic force incorporates the inevitable nonlinear nature of the stage. The proposed identification technique can be useful for the analysis of modeling contact dynamics between moving and sliding parts in situ. This technique can possibly develop improved closed-loop control algorithms.

Crack identification for rotating machines based on a nonlinear approach

In a previous contribution, a crack identification methodology based on a nonlinear approach was proposed. The technique uses external applied diagnostic forces at certain frequencies attaining combinational resonances, together with a pseudo-random optimization code, known as Differential Evolution, in order to characterize the signatures of the crack in the spectral responses of the flexible rotor. The conditions under which combinational resonances appear were determined by using the method of multiple scales. In real conditions, the breathing phenomenon arises from the stress and strain distribution on the cross-sectional area of the crack. This mechanism behavior follows the static and dynamic loads acting on the rotor. Therefore, the breathing crack can be simulated according to the Mayes׳ model, in which the crack transition from fully opened to fully closed is described by a cosine function. However, many contributions try to represent the crack behavior by machining a small notch on the shaft instead of the fatigue process. In this paper, the open and breathing crack models are compared regarding their dynamic behavior and the efficiency of the proposed identification technique. The additional flexibility introduced by the crack is calculated by using the linear fracture mechanics theory (LFM). The open crack model is based on LFM and the breathing crack model corresponds to the Mayes׳ model, which combines LFM with a given breathing mechanism. For illustration purposes, a rotor composed by a horizontal flexible shaft, two rigid discs, and two self-aligning ball bearings is used to compose a finite element model of the system. Then, numerical simulation is performed to determine the dynamic behavior of the rotor. Finally, the results of the inverse problem conveyed show that the methodology is a reliable tool that is able to estimate satisfactorily the location and depth of the crack.