Domain System Identification Method Research Articles

Advancements in the Theory and Practice of Flight Vehicle System Identification

System identification methods have played an essential role in the research and industry projects at the Institute of Flight System Dynamics of the Technical University of Munich. Besides the application of the established system identification approaches to multiple aircraft, novel methods have been developed at the institute to deal with the challenges associated with fixed- and rotary-wing aircraft system identification in the time and frequency domains. This paper provides an overview of these new developments, as well as practical application examples from the past and ongoing projects at the institute. After a brief introduction to the work at the institute, the paper describes the new advancements in the fields of time domain system identification and optimal input design by introducing optimal control methods. It continues with an alternative problem formulation for applying frequency domain system identification and parameter estimation methods to a novel flight control design and tuning approach. Additional topics from the past and ongoing research at the institute such as novel methods and practical findings in rotorcraft system identification and flight path reconstruction for different applications will be discussed and referenced.

An efficient coupled-mode flutter analysis method for turbomachinery

An efficient aeroelastic eigenvalue method based on time domain system identification has been developed to analyze coupled-mode flutter in turbomachinery. The aeroelastic stability problem is transformed into a generalized eigenvalue problem (GEP) by incorporating the aeroelastic equation and an aerodynamic modal force model. The aerodynamic modal force model correlates the generalized aerodynamic modal force with generalized motion variables by influence coefficient matrices which are calculated through a time domain system identification method. The aerodynamic damping ratios and the corresponding eigenfrequencies for all interblade phase angles (IBPA) can be obtained conveniently from a single time domain aerodynamic computation. The proposed method has been validated and demonstrated by presenting results for NASA Rotor 67 flutter cases in this paper.

Structural Damage Identification with a Tuning-free Hybrid Extended Kalman Filter

As a time domain system identification method, the extended Kalman filter (EKF) has been continuously used for structural damage identification. The performance of the EKF varies greatly depending on the selection of the initial parameters’ values and their combinations. In this paper, to improve the convergence performance of the EKF and to overcome the dependence on the setting parameter values, a hybrid extended Kalman filter (HEKF) for structural damage identification is proposed. As significant properties of the EKF, the structural damage identification, global convergence, stability, and robustness of the HEKF are guaranteed by integrating a genetic algorithm and the EKF. The performance of the HEKF in structural damage identification was investigated in experiments with four 3-story steel frame test models, which were designed for four different damage scenarios.

Modal parameter identification of a multiple-span post-tensioned concrete bridge using hybrid vibration testing data

The paper describes and evaluates application of output-only system identification to an eleven-span post-tensioned concrete bridge using hybrid excitation. A linear chirp sweeping force, induced by two light-weight electro-dynamic shakers, augmented environmental sources to excite the bridge during the hybrid testing exercise. To obtain the modal characteristics of the structure, two output-only time domain system identification methods were employed, namely auto-regressive (AR) time series model and eigensystem realization algorithm with observer/Kalman identification (ERA-OKID), with the traditional data-driven stochastic subspace identification method (SSI-data) providing a comparative benchmark. The accuracy and efficiency of both system identification algorithms when used on hybrid testing data are investigated and compared to the results from purely ambient vibration testing data. The study demonstrates that using both output-only identification algorithms the collected vibration responses induced by the proposed hybrid vibration testing methodology can be used for extracting modal parameters with enhanced accuracy and reliability (i.e. more identified modes) for the large-scale post-tensioned concrete bridge due to the increase in the excitation strength and better coverage of the relevant frequency bands. Compared to the classical SSI-data, the AR and ERA-OKID techniques were able to identify more modes at reduced computational cost when applied to voluminous data from multi-channel measurements.

Dynamic behaviour of a 13-story reinforced concrete building under ambient vibration, forced vibration, and earthquake excitation

This paper presents a unique study of dynamic behaviour of a full-scale 13-story reinforced concrete building under forced vibration, ambient vibration, and distal earthquake-induced excitation. Initially, an eccentric mass shaker located on the upper floor of the building was used to excite the building while instrumented with eight accelerometers. Then, ambient vibrations induced by traffic and wind were recorded over a period of two weeks, utilizing over 40 tri-axial accelerometers. During the sampling period, the building was excited by a M6.5 earthquake and high-quality vibration data sets were recorded. Modal parameters of the building were identified with a range of frequency and time domain system identification (SI) methods, and the influence of excitation force characteristics on performance of various techniques was also investigated. A finite element model of the building was developed using SAP2000 to compare modal properties to the identified counterparts from experiments. Results showed a strong correlation between modal parameters identified by different SI methods, and all techniques provided accurate estimation of modal parameters when used with output-only data. Modal parameters determined from ambient vibrations were comparable to their forced vibration counterparts, providing evidence that ambient vibration testing can be as effective as forced vibration testing in determining modal parameters for similar size structures. The near stationary vibration data can produce accurate estimation of modal parameters. However, further study is required to facilitate application of output-only SI techniques with non-stationary data. There was a good match between peak displacement amplitudes obtained by the numerical model and those experimentally measured at different excitation frequencies. This match demonstrated the accuracy of the finite element model to predict realistic dynamic behaviour of the building under various harmonic excitation forces.

Initial investigation into the complementary use of black box and physics-based techniques in rotorcraft system identification

Accurate linear helicopter models are needed for control system development and simulation and can be determined by system identification when appropriate test data are available. Standard methods for rotorcraft system identification are the frequency domain maximum likelihood method and the frequency response method that are used to derive physics-based linear state-space models. Also the optimized predictor-based subspace identification method (PBSIDopt), a time domain system identification method that yields linear black box state-space models, has been successfully applied to rotorcraft data. As both methods have their respective strengths and weaknesses, it was tried to combine both techniques. The paper demonstrates the successful complementary use of physics-based frequency domain methods and the black box PBSIDopt method in the areas of database requirements, accuracy metrics, and model structure development using flight test data of DLR’s ACT/FHS research rotorcraft.

First Results on Regularized Time-Varying Operational Modal Analysis

This paper presents an efficient nonparametric time-varying time domain system identification method for the Operational Modal Analysis (OMA) framework. OMA tackles industrial measurements of vibrating structures in real-life operating conditions without the exact knowledge of the excitation signal. In case of time-varying Operational Modal Analysis it is desired to carefully verify and track the vibration behavior, since during flutter appearance, system destruction can occur. In this work a method is provided to estimate the time-varying output autocorrelation function of vibrating structures and applied to a measurement of wind tunnel testing of an airplane. The proposed method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time-invariant systems. Using the proposed methodology, the estimated time-varying two-dimensional output autocorrelation model provides a good data-fit with respect to tracking of varying resonances.

청음용 자동차 로드노이즈 추출 방법 연구

This study pertains to the extraction of the road noise component of signals from a vehicle's interior noise via the traditional frequency domain and time domain system identification methods. For road noise extraction based on the frequency domain system identification method, the appropriate matrix inversion strategy is investigated and causal and non-causal impulse response filters are compared. Furthermore, appropriate data lengths for the frequency domain system identification method are investigated. In addition to the traditional road noise extraction methods based on frequency domain system identification, a new approach to extract road noise via the time domain system identification method based on a parametric input-output model is proposed and investigated in the present study. In this approach, instead of constructing a higher order model for the full-band road noise, input and output signals are processed in the subband domain and lower order parametric models optimal to each subband are determined. These parametric models are used to extract road noises in each subband; the full band road noise is then reconstructed from the subband road noises. This study shows that both the methods in the frequency domain and the time domain successfully extract the road noise from the vehicle's interior noise.

An experimental validation of time domain system identification methods with fusion of heterogeneous data

SummaryRecent events of significant seismic activity (L' Aquila 2009, Christchurch 2011), have highlighted the importance of accurately assessing the properties of structures, for estimating their risk in future earthquakes as well as detecting and quantifying damage following an event. This demand may be fulfilled through implementation of SHM methodologies, which offer a means of assessing structural condition through the use of sensor data. Furthermore, the emergence of various sensor technologies has improved the quality of collected signals and made the idea of fusing heterogeneous data more appealing. Similar steps were achieved in advancing system identification algorithms. Several methods such as the Autoregressive Moving Average, Least Squares Estimation, Eigensystem Realization Algorithm, and Subspace State‐Space System Identification (SSID) perform well in identifying elastic properties. However, the resulting matrices are often not obtained with respect to the physical basis, which is often desirable. Such a representation is obtained by default in Bayesian estimation methods, as the Unscented Kalman Filter and Particle Filters, which have recently been applied in the literature for data fusion problems. In this work, an experimental structure mounted on a shake table is monitored using accelerometers and displacement sensors. A method is developed (T‐SSID) to transform the results of the SSID onto the physical basis. The introduced method and the Unscented Kalman Filter are employed identifying the structural properties and detecting an artificially induced in the original system damage. The performance of various sensor setups, which include fusion of heterogeneous sensors, are investigated to illustrate the performance of both methods, their ability to localize damage, and the benefits of data fusion. Copyright © 2014 John Wiley & Sons, Ltd.

A dynamic thermal modelling of solar panels using frequency-domain method

A frequency-domain method for a dynamic thermal modelling of solar panels is presented in this paper. Different from the prevailing static models which assume the heat balance always holds between PV modules and local environments, the proposed method also considers the thermal dynamics before the heat balance is reached. To that end, time domain differential equations are established to describe the thermal dynamics using the standard heat transfer model in physics. With Laplace transform (F(s)≔L[f(t)]=∫0∞f(t)e-stdt), these differential equations are then converted equivalently into the frequency domain 2nd-order transfer function model with time delay, i.e., H(s)=(b1s+b0)e-Ls/(s2+a1s+a0), so that many mature frequency domain system identification methods can be utilised to determine the unknown model parameters of ai, bi (i=0,1), and L. Recursive square algorithm is also applied to minimise the modelling error. The proposed method is applied to both c-Si and a-Si PV modules from Photon Lab module test facility at Aachen, Germany, and compared with the measurement data of module temperatures for the full year of 2012. Both case studies consistently show significant improvements in accuracy, as compared to the existing thermal models. Physical meanings of the proposed model parameters are further discussed.

Linear Modeling of Human Hand-Arm Dynamics Relevant to Right-Angle Torque Tool Interaction

A new protocol was evaluated for identification of stiffness, mass, and damping parameters employing a linear model for human hand-arm dynamics relevant to right-angle torque tool use. Powered torque tools are widely used to tighten fasteners in manufacturing industries. While these tools increase accuracy and efficiency of tightening processes, operators are repetitively exposed to impulsive forces, posing risk of upper extremity musculoskeletal injury. A novel testing apparatus was developed that closely mimics biomechanical exposure in torque tool operation. Forty experienced torque tool operators were tested with the apparatus to determine model parameters and validate the protocol for physical capacity assessment. A second-order hand-arm model with parameters extracted in the time domain met model accuracy criterion of 5% for time-to-peak displacement error in 93% of trials (vs. 75% for frequency domain). Average time-to-peak handle displacement and relative peak handle force errors were 0.69 ms and 0.21%, respectively. Model parameters were significantly affected by gender and working posture. Protocol and numerical calculation procedures provide an alternative method for assessing mechanical parameters relevant to right-angle torque tool use. The protocol more closely resembles tool use, and calculation procedures demonstrate better performance of parameter extraction using time domain system identification methods versus frequency domain. Potential future applications include parameter identification for in situ torque tool operation and equipment development for human hand-arm dynamics simulation under impulsive forces that could be used for assessing torque tools based on factors relevant to operator health (handle dynamics and hand-arm reaction force).

A new frequency domain system identification method

A new frequency domain system identification method based on a multi-frequency input signal is proposed. Frequency contents of the oscillating signal are estimated using a modified Kaczmarz algorithm proposed in this paper. Lyapunov stability analysis is performed for this new Kaczmarz algorithm and transient bounds for estimation error are established. Moreover, a new method for estimation of the variance of the measurement noise in Kaczmarz algorithms is also described. A comparison of a transient performance of modified Kaczmarz algorithm and a recursive least-squares algorithm is presented. The results are applied to a frequency domain identification of a DC motor.

Identification of flutter derivatives from full-scale ambient vibration measurements of the Clifton Suspension Bridge

The estimated response of large-scale engineering structures to severe wind loads is prone to modelling uncertainties that can only ultimately be assessed by full-scale testing. To this end ambient vibration data from full-scale monitoring of the historic Clifton Suspension Bridge has been analysed using a combination of a frequency domain system identification method and a more elaborate stochastic identification technique. There is evidence of incipient coupling action between the first vertical and torsional modes in strong winds, providing unique full-scale data and making this an interesting case study. Flutter derivative estimation, which has rarely previously been attempted on full-scale data, was performed to provide deeper insight into the bridge aerodynamic behaviour, identifying trends towards flutter at higher wind speeds. It is shown that, as for other early suspension bridges with bluff crosssections, single-degree-of-freedom flutter could potentially occur at wind speeds somewhat below requirements for modern designs. The analysis also demonstrates the viability of system identification techniques for extracting valuable results from full-scale data.

A New Frequency Domain System Identification Method

AbstractA new frequency domain system identification method based on a multi-frequency input signal is proposed. Frequency contents of the oscillating signal are estimated using a modified Kaczmarz algorithm proposed in this paper. Lyapunov stability analysis is performed for this new Kaczmarz algorithm and transient bounds for estimation error are established. Moreover, a new method for estimation of the variance of the measurement noise in Kaczmarz algorithms is also described. A comparison of a transient performance of modified Kaczmarz algorithm and a recursive least-squares algorithm is presented. The results are applied to a frequency domain identification of a DC motor.

A Linear Domain System Identification for Small Unmanned Aerial Rotorcraft Based on Adaptive Genetic Algorithm

This paper proposes a new adaptive linear domain system identification method for small unmanned aerial rotorcraft. By using the flash memory integrated into the micro guide navigation control module, system records the data sequences of flight tests as inputs (control signals for servos) and outputs (aircraft's attitude and velocity information). After data preprocessing, the system constructs the horizontal and vertical dynamic model for the small unmanned aerial rotorcraft using adaptive genetic algorithm. The identified model is verified by a series of simulations and tests. Comparison between flight data and the one-step prediction data obtained from the identification model shows that the dynamic model has a good estimation for real unmanned aerial rotorcraft system. Based on the proposed dynamic model, the small unmanned aerial rotorcraft can perform hovering, turning, and straight flight tasks in real flight tests.

Roll-channel fractional order controller design for a small fixed-wing unmanned aerial vehicle

Low-cost small unmanned aerial vehicles (UAVs) attracted researchers and developers around the world for use in both military and civilian applications. However, there are challenges in designing stable and robust flight controllers that handle the UAV model and environmental uncertainties. This paper focuses on the design and implementation of a roll-channel fractional order proportional integral ( PI λ ) flight controller for a small fixed-wing UAV. Time domain system identification methods are used to obtain a simple auto-regressive with exogenous input (ARX) model of the UAV roll-channel. A new fractional order PI controller design method is introduced based on the identified simple model. The fractional order PI λ controller outperforms the optimized traditional integer order proportional integral derivative (PID) controller due to the fractional order introduced as a design parameter. The simulation results show the effectiveness of the proposed controller design strategy and the robustness of fractional order controller under conditions of wind gusts and payload variations. Further real flight test results are also provided to show the advantages of the proposed PI λ controller.

Determination of optimal accelerometer locations using modal sensitivity for identifying a structure

A new algorithm is proposed to determine optimal accelerometer locations (OAL) when a structure is identified by frequency domain system identification (SI) method. As a result, a guideline is presented for selecting OAL which can reflect modal response of a structure properly. The guideline is to provide a minimum number of necessary accelerometers with the variation in the number of measurable target modes. To determine OAL for SI applications effectively, the modal sensitivity effective independence distribution vector (MS-EIDV) is developed with the likelihood function of measurements. By maximizing the likelihood of the occurrence of the measurements relative to the predictions, Fisher Information Matrix (FIM) is derived as a function of mode shape sensitivity. This paper also proposes a statistical approach in determining the structural parameters with a presumed parameter error which reflects the epistemic paradox between the determination of OAL and the application of a SI scheme. Numerical simulations have been carried out to examine the proposed OAL algorithm. A two-span multi-girder bridge and a two-span truss bridge were used for the simulation studies. To overcome a rank deficiency frequently occurred in inverting a FIM, the singular value decomposition scheme has been applied.

Evaluation of dynamic characteristics of high-rise buildings using system identification techniques

Among many estimation methods of modal parameters of structures, system identification methods in the time domain have recently been spotlighted. System identification methods in the time domain have advantages over the methods in the frequency domain in such cases where the modal parameters are changed during the records or where the length of the record is very short. In this paper, dynamic characteristics, including natural frequencies and damping ratios, of twin high-rise buildings are estimated by applying time domain system identification methods to the records of their earthquake responses.

Stabilizing the helicopter

This paper proposes a new adaptive linear domain system identification method for small unmanned aerial rotorcraft. By using the flash memory integrated into the micro guide navigation control module, system records the data sequences of flight tests as inputs (control signals for servos) and outputs (aircraft's attitude and velocity information). After data preprocessing, the system constructs the horizontal and vertical dynamic model for the small unmanned aerial rotorcraft using adaptive genetic algorithm. The identified model is verified by a series of simulations and tests. Comparison between flight data and the one-step prediction data obtained from the identification model shows that the dynamic model has a good estimation for real unmanned aerial rotorcraft system. Based on the proposed dynamic model, the small unmanned aerial rotorcraft can perform hovering, turning, and straight flight tasks in real flight tests.