System Identification Results Research Articles

A PINN approach for identifying governing parameters of noisy thermoacoustic systems

Identifying the governing parameters of self-sustained oscillation is crucial for the diagnosis, prediction and control of thermoacoustic instabilities. In this paper, we propose and validate a novel method for computing the parameters of thermoacoustic oscillation in a stochastic environment, which exploits a physics-informed neural network (PINN). Specifically, we introduce a negative log-likelihood loss function that integrates the stochastic samples and the solution of the Fokker–Planck equation. The proposed framework is validated using the numerically generated signal and the experimental data obtained from an annular combustor, both before and after the supercritical Hopf bifurcation. The results of PINN-based system identification show good agreement with the actual system parameters and the original stochastic signal, with improved accuracy compared to established methods. To the best of our knowledge, this study constitutes the first demonstration of the PINN-inverse approach that uses the noise-induced dynamics of thermoacoustic systems, opening up new pathways for diagnosing and predicting the thermoacoustic behaviour of various combustion systems.

Operational modal analysis, seismic vulnerability assessment and retrofit of a degraded RC bell tower

This paper presents damage assessment through Operational Modal Analysis (OMA) and Finite Element (FE) model updating of the bell tower of the church of Castro in Bergamo, Italy. The tower is a 39 m high reinforced concrete structure with hollow cross-section and double-curved shape. The research was dictated by the need to identify the actual damage state of the structure, which was found through visual inspections. Piezoelectric accelerometers were used to record the ambient vibrations in subsequent test setups, using the roving technique for system identification. A detailed FE model was created with shell elements and calibrated to match the system identification results. A simplified beam model was then developed based on the modal analysis results of the detailed model. A sensitivity analysis was performed to identify the most influential model parameters on the modal characteristics of the system. Subsequently, the optimal values of these parameters were determined by an optimisation procedure carried out using a typical global optimization algorithm. The updating results allowed assessment of the actual condition of the bell tower and its seismic vulnerability. Finally, a seismic strengthening solution was recommended.

Asymptotic Theory for Regularized System Identification Part I: Empirical Bayes Hyperparameter Estimator

Regularized techniques, also named as kernel-based techniques, are the major advances in system identification in the last decade. Although many promising results have been achieved, their theoretical analysis is far from complete and there are still many key problems to be solved. One of them is the asymptotic theory, which is about convergence properties of the model estimators as the sample size goes to infinity. The existing related results for regularized system identification are about the almost sure convergence of various hyper-parameter estimators. A common problem of those results is that they do not contain information on the factors that affect the convergence properties of those hyper-parameter estimators, e.g., the regression matrix. In this paper, we tackle problems of this kind for the regularized finite impulse response model estimation with the empirical Bayes (EB) hyper-parameter estimator and filtered white noise input. In order to expose and find those factors, we study the convergence in distribution of the EB hyper-parameter estimator, and the asymptotic distribution of its corresponding model estimator. For illustration, we run Monte Carlo simulations to show the efficacy of our obtained theoretical results.

Closed-loop Aspects of Data-Enabled Predictive Control

In recent years, the amount of data available from systems has drastically increased, motivating the use of direct data-driven control techniques that avoid the need of parametric modeling. The aim of this paper is to analyze closed-loop aspects of these approaches in the presence of noise. To analyze this, a unified formulation of several approaches, including Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC) is obtained and the influence of noise on closed-loop predictors is analyzed. The analysis reveals potential closed-loop correlation problems, which are closely related to well-known results in closed-loop system identification, and consequent control issues. A case study reveals the hazards of noise in data-driven control.

Robust Frequency Domain Spline Adaptive Filtering Based on the Half-Quadratic Criterion: Performance Analysis and Applications

Frequency domain spline adaptive filters (FDSAF) have attracted a great deal of attention because of their enhanced computational efficiency. However, their performance will be extremely degraded in practical environments where non-Gaussian phenomena exist. In order to attain good robustness to non-Gaussian noises while ensuring a low computational burden, this paper proposes a frequency domain spline adaptive filtering algorithm based on the half-quadratic criterion (HQC), named FDSAF-HQC. Further, to offer a theoretical foundation for the proposed FDSAF-HQC, a detailed performance analysis based on the principle of energy conservation is conducted and then validated by simulations. Moreover, the computational complexity of FDSAF-HQC is evaluated and compared with other similar algorithms. Simulation results of nonlinear system identification corroborate the outstanding performance of the proposed FDSAF-HQC, i.e., better robustness and computational efficiency. The superiority of the proposed FDSAF-HQC is also supported by practical applications of echo cancellation and biological signal denoising.

System Identification and Control Using Quadratic Neural Networks

This paper proposes convex formulations of system identification and control for nonlinear systems using two layer quadratic neural networks. The results in the paper cast system identification, stability and control design as convex optimization problems, which can be solved efficiently with polynomial-time algorithms. The main advantage of using quadratic neural networks for system identification and control as opposed to other neural networks is the fact that they provide a smooth (quadratic) mapping between the input and the output of the network. This allows one to cast stability and control for quadratic neural network models as a Sum of Squares (SOS) optimization, which is a convex optimization program that can be efficiently solved. Additionally, these networks offer other advantages, such as the fact that the architecture is a by-product of the design and is not determined a-priori, and the training can be done by solving a convex optimization problem so that the global optimum of the weights is achieved. It also appears from the examples in this paper that quadratic networks work extremely well using only a small fraction of the training data.

Vision‐based seismic damage detection and residual capacity assessment for an RC shaking table test structure

AbstractIn this paper, the existing postearthquake performance assessment framework for reinforced concrete (RC) building structures is improved by adding a new feature of the computer vision‐based damage detection. In this framework, visible seismic damage is classified and quantified from photographs of damaged RC components using the developed deep convolutional network (CNN) Damage‐Net of semantic segmentation, and then the mechanical property degradation factors of components determined from the detected damage states are used to update the numerical model. Pushover analysis of the updated model assesses the residual capacity of the damaged structure. Large‐scale shaking table tests of a three‐story RC building structure, which was heavily instrumented with sensors and recorded with a large volume of photographs, were used as a case study to demonstrate the improved postearthquake performance assessment framework. The vision‐based approach accurately detected multicategory seismic damage of the test structure and effectively estimated the residual crack widths and angles under various lighting, image acquisition, and surface conditions. The updated model, which incorporated the mechanical property degradation of the damaged components, provided accurate estimate on the fundamental vibrational frequencies of the damaged structure after various levels of seismic motion shaking, which matched well with the system identification results. Using the mechanical property reduction factor values recommended by FEMA 306 & Chiu et al., pushover analysis of the updated models provided residual capacity curves that reasonably captured the measured hysteretic responses of the structure. In addition, the damage states of components as estimated by the vision‐based methods were also compared with the measured plastic hinge rotation data. The successful implementation of the vision‐based assessment in this test case indicates its potential for application in the postearthquake evaluation of buildings.

Bias-compensated augmented complex-valued NSAF algorithm and its low-complexity implementation

The performance of traditional adaptive filtering algorithms will be degraded when the input signal contains noise. To handle colored noisy input and output measurements in the complex domain, this paper proposes an augmented complex-valued estimation-input NSAF (ACEI-NSAF) algorithm, derived by using estimated noiseless input, which is obtained by the minimization of an instantaneous perturbation with both input and output data, to update the weight vectors. Benefiting from this, the proposed algorithm can achieve unbiased estimation of the unknown system in the presence of noisy inputs, thereby surpassing the augmented complex-valued NSAF (ACNSAF) algorithm. The mean stability, excess mean-square error, and computational complexity are investigated, and the unbiasedness condition of the proposed algorithm is presented. Subsequently, a low-complexity ACEI-NSAF (SACEI-NSAF) algorithm is introduced by using the subband selection approach. Experimental results in system identification demonstrate the effectiveness of the proposed algorithms and analysis.

System response modeling of HMCVT for tractors and the comparative research on system identification methods

The HMCVT (Hydro-mechanical Continuously Variable Transmission) is widely applied in agricultural and engineering machinery such as tractors. Getting a correct system response model is the key to HMCVT control strategy implementation and controller design. The study decomposes and analyzes the HMCVT system and builds response models. The study proposes to decompose the HMCVT system into three dynamic response stages including the electronic proportional pressure relief valve response, the variable plunger displacement response and the pump-motor system speed ratio response, and builds the response models of three stages respectively and then obtains the general form of transfer function of HMCVT system using a tandem method. The study proposes a system identification method based on the prior-model-heuristic-intelligent-optimization algorithm, and makes a comparative analysis between the classical system identification method (the area method) and the three heuristic intelligent optimization algorithms (the FI-SA, the I-SA and the I-AFSA) in terms of system identification result. The study compares the results of identification methods through a step response test of a model of HMCVT for tractors, and verifies the correctness of the transfer function model of HMCVT system proposed. Research results show that the general form of HMCVT system response model should be a 4-order denominator 1-order numerator transfer function model (the mean identification precision of 15 groups of measurement tests is about 0.9849). The area method is affected by the sampling frequency in the response measurement and requires a complete response process measured. The system identification based on heuristic intelligent optimization algorithm has low dependence on sampling frequency and time consumed and high precision. According to the results of the calculation example in the study, the coefficient of determination about the identified model is 1 under the measurement frequency of 4 Hz and the measurement duration of 4 s by using the FI-SA, the I-SA, and the I-AFSA. The precision is improved by 4.93 % compared with using the area method. According to the actual test results, the coefficients of determination about the FI-SA and the area method are 0.9939 and 0.9834, respectively. Comparing the three heuristic intelligent optimization algorithms, the FI-SA proposed has the fastest identification speed. The results of 20 groups measurement tests show that the average iteration number of FI-SA are 43.58 % and 17.95 % lower than those of I-SA and I-AFSA, and the average time consumption of FI-SA is 43.36 % and 84.76 % lower than that of I-SA and I-AFSA.

Statistical analysis of the modal properties of a seismically-damaged five-story RC building identified using ambient vibration data

Damage detection (DD) is one of the primary goals of health monitoring of civil structures. Vibration-based techniques aim to identify the modal properties (or vibration characteristics) of structures and are one of the most popular approaches for structural damage detection. The use of vibration characteristics (natural frequencies, damping ratios, and mode shapes) for DD purposes is based on the premise that these characteristics change when the structure suffers damage, since the modal properties depend on the physical properties (mass, stiffness, and damping) of the structure. The use of output-only measurements (e.g., ambient vibration or AV) is the most popular approach for damage detection of civil structures. AV data recorded before and after the structure has potentially suffered damage can be used for DD. However, application of vibration-based DD using AV requires an accurate and reliable estimation of the modal properties and their variability (or uncertainty) in order to genuinely determine the existence of damage. This study presents a comprehensive statistical analysis of the identified modal properties of a full-scale five-story reinforced concrete building using AV data. The building specimen was tested on the NHERI@UCSD shake table in base-isolated and fixed-base configurations. On April 6, 2012, about two weeks before the start of the seismic tests in the base-isolated configuration, a dense array of twenty accelerometers was deployed on the structure and AV data were recorded continuously until May 18, 2012, three days after completion of the seismic tests in the fixed-base configuration. In its fixed-base configuration, the building was subjected to a sequence of six earthquake motions that progressively damaged the structure. Two popular methods of operational modal analysis are used to automatically identify the modal properties of the fixed-base building at different damage states using the recorded AV data. A statistical analysis of the identified modal parameters is performed to investigate the statistical variability and accuracy of the system identification results. The variability of the identified modal parameters due to environmental conditions is also investigated.

One optimized LMF algorithm in low SNR

There is a need to improve the capability of the adaptive filtering algorithm against Gaussian or multiple types of non-Gaussian noises, time-varying system, and systems with low SNR. In this paper, we propose an optimized least mean absolute fourth (Optimized-LMF) algorithm, especially for a time-varying unknown system with low signal-noise-rate (SNR). The optimal step-size of LMF is obtained by minimizing the mean-square deviation (MSD) at any given moment in time. In addition, the mean convergence and steady-state error of Optimized-LMF are derived. Also the theoretical computational complexity of Optimized-LMF is analyzed. Furthermore, the simulation experiment results of system identification are used to illustrate the principle and efficiency of the Optimized-LMF algorithm. The performance of the algorithm is analyzed mathematically and validated experimentally. Simulation results demonstrate that the proposed Optimized-LMF is superior to the normalized LMF (NLMF) and variable step-size of LMF using quotient form (VSSLMFQ) algorithms.

Development of a structural identification methodology with uncertainty quantification through the SSI and bootstrap techniques

In the last few years, increasing attention has been given to obtaining reliable results in system identification as a key step in performing model updating, damage detection and structural health monitoring. Many methods have been developed to measure the uncertainty in modal estimates. Some techniques are based on signal resampling to obtain a larger sample space and consequently better process statistics. Thus, this study proposes a new method to quantify uncertainties using the stochastic subspace identification (SSI) technique combined with bootstrap resampling. To validate and compare the performance of the proposed algorithm, two algorithms previously mentioned in the literature were implemented. The first is based on the “moving block method”, and the second is based on blocks of the projection matrix. The proposed method initially generates random decrement functions from signal segments and later uses these functions as bootstrap resampling blocks in SSI. To validate and compare the performance of the proposed algorithm, numerical simulations and two experimental analyses are performed. The first analysis involves a simply supported steel beam subjected to vibration tests through random impacts, and the second involves a three-dimensional four-story frame subjected to vibrations from random signals generated by an electrodynamic exciter. The results of the proposed technique were more robust and accurate than those of the other methods.

Identification and uncertainty quantification of structural flexibility for reliability analysis

In recent years, research on the effect of uncertainty on the results of structural system identification in order to effectively enhance structural safety has been rarely conducted. This paper studies identification and uncertainty quantification of structural flexibility from ambient vibration measurements to develop an efficient reliability analysis. The structural deflection with a confidence interval can be predicted under static loads via the uncertainty quantification on structural flexibility, and can then be used for the reliability analysis of the deflection serviceability limit state. First, the evaluation method for the uncertainty bounds of the modal parameters by a first-order perturbation analysis is reviewed. Then, the perturbation analysis method is extended to structural flexibility identification with considering the uncertainty in the identified modal parameters and the uncertainty in the reduced mass matrix. In addition, the structural deflection and its confidence interval under static load can be simultaneously derived with the identified structural flexibility. Eventually, by combining fuzzy criteria with the confidence intervals of the deflection prediction under the ultimate design load, the reliability index of the deflection serviceability limit state can be formulated. Both numerical and experimental examples were conducted to verify the efficiency of the proposed method. This study provides a scheme to directly link the structural identification with the structural safety evaluation.

Virtual flight test techniques to predict a blended-wing-body aircraft in-flight departure characteristics

As one of the promising configurations of the next generation of commercial aircraft, research on departure characteristics of the Blended-Wing-Body (BWB) is of great signification to safe flight limits. A three-degree-of-freedom (3-DOF) virtual flight test in a wind tunnel has been implemented for a candidate configuration to predict the departure characteristics. The support mechanism, the test model and the control law of the virtual flight test are introduced. In order to show the relationship between virtual flight test and actual flight test, the similarity criterion is also given. In open loop, the model has mild oscillations in the longitudinal and lateral directions, which are stable in closed-loop. The effect of flight control has been verified in virtual flight and actual subscale flight test. The analysis of system identification results indicate that the model has a good response to the excitation signal, and the response is in reasonable agreement with the flight test. Finally, the virtual flight departure test results are compared with the flight test. It shows that there is a good correspondence between the angle of attack and the elevator deflection at departure. This gives promising evidence of the practicability of virtual flight testing to predict departure of a BWB.

Data-driven machine learning for accurate prediction and statistical quantification of two phase flow regimes

Two different two-phase flow regimes including slug and dispersed flows are examined through the implementation of system identification methods to attain reduced-order models. The obtained models accurately capture the flow dynamics of the studied regimes. The models also provide state-space frequency by defining the transfer functions. The system identification results are compared with those of the bidirectional neural network to predict the phase fraction of the considered two-phase flows. The result of long short-term memory shows correlations of 91% between the real and predicted phase fractions.

An RF-PCE Hybrid Surrogate Model for Sensitivity Analysis of Dams

Quantification of structural vibration characteristics is an essential task prior to perform any dynamic health monitoring and system identification. Anatomy of vibration in concrete arch dams (especially tall dams with un-symmetry shape) is very complicated and requires special techniques to solve the eigenvalue problem. The situation becomes even more complicated if the material distribution is assumed to be heterogeneous within the dam body (as opposed to conventional isotropic homogeneous relationship). This paper proposes a hybrid Random Field (RF)–Polynomial Chaos Expansion (PCE) surrogate model for uncertainty quantification and sensitivity assessment of dams. For different vibration modes, the most sensitive spatial locations within dam body are identified using both Sobol’s indices and correlation rank methods. Results of the proposed hybrid model is further validated using the classical random forest regression method. The outcome of this study can improve the results of system identification and dynamic analysis by properly determining the vibration characteristics.

System Identification and Seismic Performance Assessment of Representative RC Buildings in Kathmandu Valley

To identify dynamic characteristics of representative reinforced concrete frame buildings with brick infills, ambient vibration measurements were taken in two four-storied buildings—one situated in soft soil and the another in stiff soil. Non-parametric as well as parametric system identification (SID) algorithms were used to estimate vibration frequencies and damping of the two buildings. The numerical models of the buildings were created using the finite element method. The modal frequencies and damping ratios obtained from ambient measurements were used to calibrate and tune the finite element models. The comparison between measured vibration frequencies and those obtained from finite element model highlights the need for accuracy in modeling assumptions, in particular, consideration of the stiffness of infill walls and the flexibility of foundation soil. The finite element models calibrated with SID results were used to estimate the response of the two buildings when subjected to strong ground motion recorded at different places in the Kathmandu Valley during the 2015 Gorkha earthquake. The results show that not considering flexibility of foundation and stiffness of infill walls, as is commonly done in engineering practice, can lead to inaccurate estimates of seismic demand.

Bias-Compensated Sparsity-Aware NLMM Algorithms for Robust Adaptive Echo Cancellation

For adaptive echo cancellation in hands-free communication systems, a family of bias-compensated sparsity-aware normalized least mean M-estimate (NLMM) algorithms is proposed that are robust to both impulsive noise and noisy inputs. First, we define a new cost function that integrates the M-estimate function of the a posteriori error, the Riemannian distance between the current and previous weight vectors, and the $L_{0}$ norm of the weighted current weight vector. By minimizing the defined cost function, we develop the sparsity-aware NLMM algorithms to achieve robustness against the impulsive noise. Then, an improved cost function is developed and proved to be unbiased in the presence of input noise. This leads to the development of the bias-compensated sparsity-aware NLMM algorithms that can deal with noisy inputs. The stability and computational complexity of the proposed algorithms are analyzed as well. Experimental results for system identification and adaptive echo cancellation demonstrate that the proposed algorithms outperform the existing ones in terms of convergence rate and steady-state misalignment.

Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders

The paper presents the experimental and numerical results of the dynamic system identification and verification of the behavior of two footbridges in Poland. The experimental part of the study involved vibration testing under different scenarios of human-induced load, impulse load, and excitations induced by vibration exciter. Based on the results obtained, the identification of dynamic parameters of the footbridges was performed using the peak-picking method. With the impulse load applied to both structures, determination of their natural vibration frequencies was possible. Then, based on the design drawings, detailed finite element method (FEM) models were developed, and the numerical analyses were carried out. The comparison between experimental and numerical results obtained from the modal analysis showed a good agreement. The results also indicated that both structures under investigation have the first natural bending frequency of the deck in the range of human-induced excitation. Therefore, the risk of excessive structural vibrations caused by pedestrian loading was then analysed for both structures. The vibration comfort criteria for both footbridges were checked according to Sétra guidelines. In the case of the first footbridge, the results showed that the comfort criteria are fulfilled, regardless of the type of load. For the second footbridge, it was emphasized that the structure meets the assumptions of the guidelines for vibration severability in normal use; nevertheless, it is susceptible to excitations induced by synchronized users, even in the case of a small group of pedestrians.

A new full‐scale testbed for structural health monitoring and soil–structure interaction studies: Kunming 48‐story office building in Yunnan province, China

This paper introduces a new and unique full-scale testbed site for structural health monitoring and soil–structure system identification studies being developed in southwest China. The site is a 48-story skyscraper with an extended four-level basement, supported by piles, located in Kunming, the capital of Yunnan Province. Located in the diffused zone of collision of the Indian and Eurasian tectonic plates, Yunnan is one of the most active seismic areas in mainland China. The final sensor deployment will consist of 43 triaxial accelerometers (129 channels) and one weather station. The accelerometer array comprises (a) a structural array of 25 accelerometers installed at 10 levels aboveground, (b) a basement array of 14 accelerometers distributed in the first and fourth basements, and (c) two borehole arrays installed close to the basement perimeter wall, each with one accelerometers at the surface and another one at 50-m depth, which is the depth reached by the piles. With such dense instrumentation of structure, basement, and pile foundation, this site will be the first permanently instrumented full-scale testbed to enable identification of a soil-foundation–basement-structure system and validation of many assumptions commonly made in the prediction of the soil–structure interaction effects. A high-performance wired local area network has been installed in the building, featuring a Precision Time Protocol-enabled time synchronization and real-time remote access over the Internet. The site will be fully operational in late spring of 2020. Results of preliminary system identification of the structure from ambient vibration test data are presented.