Frequency Domain System Identification Research Articles

Validation of the Flight Dynamics Engine of the X-Plane Simulator in Comparison with the Real Flight Data of the Quadrotor UAV Using CIFER

The vertical take-off and landing (VTOL) of unmanned aerial vehicles (UAVs) is extensively employed in various sectors. To ensure adherence to design specifications and mission requirements, it is vital to verify flight control and system performance using an accurate dynamic model specific to UAV configuration. Traditionally, engineers follow a sequential approach in UAV design, which involves multiple design iterations comprising CAD drawings, material collection, fabrication, flight tests, system identification, modifications, dynamic model extraction, checking if the results meet requirements, and then repeating the process. However, as UAVs become larger, heavier, and more enduring to meet complex system demands, the costs and time associated with each design iteration of creating a new UAV escalate exponentially. The bare-airframe dynamics of the UAV are crucial for engineers to design a controller and validate handling quality and performance. This paper proposes a novel method to accurately predict the dynamic model of the bare airframe for quadrotor UAVs without physically constructing them in the real world. The core concept revolves around converting the quadrotor UAV design from CAD software into a UAV model within an X-Plane simulator. Leveraging the CIFER software’s two key features—frequency domain system identification and parametric model fitting—the unstable bare-airframe dynamics are extracted for both the UAV model in X-Plane and a real-world DJI 450 UAV with the same physical configuration. This paper provides essential parameters and guidance for constructing a 92% high-fidelity dynamic model of the given UAV configuration in X-Plane. The flight test results demonstrate excellent alignment with the simulation outcomes, instilling confidence in the effectiveness of the proposed method for designing and validating new UAVs. Moreover, this approach significantly reduces the time and cost associated with the traditional design process, which requires an actual build of the UAV and many flight tests to verify the performance.

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.

NIXO-Based identification of the dominant terms in a nonlinear equation of motion of structures with geometric nonlinearity

The objective of this publication is to propose a novel technique for black-box identification of structures with geometric nonlinearity. The technique is based on a recently introduced frequency-domain system identification method called Nonlinear Identification through eXtended Outputs (NIXO). The proposed algorithm first expresses the nonlinear part of modal equation of motion (EOM) as a general polynomial of high order, and then removes the terms which are determined to be irrelevant to the mechanical system’s response. This division into dominant and irrelevant nonlinear terms relies on the values of two novel indicators that are particular to NIXO. The heuristic presented here was observed to work well only when the tested structure is excited with various swept-sine input signals of different magnitudes (so that the system oscillates at sufficiently distinctive amplitudes in different experimental tests). The technique is first demonstrated on a noise-free numerical case study employing a reduced model of a curved beam. The results obtained are verified via comparing the true Nonlinear Normal Mode (NNM) to the one computed using the modal EOM pointed out by NIXO. Then the method is demonstrated on experimental measurements collected on a 3D-printed flat beam exhibiting significant natural frequency shifts, and the outcomes are verified by overlaying the identified NNMs on the swept-sine responses.

Advances and Modern Applications of Frequency-Domain Aircraft and Rotorcraft System Identification

This paper provides an overview of advances and applications of aircraft and rotorcraft flight dynamics system identification at the U.S. Army Combat Capabilities Development Command Aviation & Missile Center over the past 20 years. An overarching topic is how frequency-domain system identification has evolved to aid modeling work of modern aircraft and rotorcraft configurations. The paper starts with a brief overview of the frequency-response method for system identification. Subsequently, the paper highlights and demonstrates several new advances using flight-test data from a conventional helicopter, fixed-wing aircraft, advanced coaxial compound rotorcraft, and a small multirotor unmanned aerial vehicle. The first advancement is the use of identification results to improve simulation model fidelity. The next advancement is the Joint Input-Output Method for identification of aircraft with highly correlated inputs. Next, the paper discusses the advancement of flexible constraints, which provide the ability to directly determine physical parameters from flight-test data. The paper then discusses a methodology to identify lower-order linearized dynamic inflow models from higher-order free wake aerodynamic models. Finally, the paper discusses model stitching, which is the technique of combining or stitching together individual linear models and trim data for discrete flight conditions to produce a continuous, full flight-envelope real-time stitched simulation model.

Preserving transfer-behavior in Model Order Reduction for thermoacoustic stability analysis

Thermoacoustic systems are often modeled with a hybrid approach that combines separate models for acoustic propagation and flame dynamics. Model Order Reduction (MOR) may be applied to the acoustic subdomains to reduce the computational cost of parametric studies and robust stability analysis. In the present study, a frequency-weighted pseudo-optimal rational Krylov algorithm is used in combination with frequency-domain System Identification and cumulative reduction framework to perform MOR by preserving the transfer-behavior of the full-order subdomain. The reduced-order subdomain is then coupled with other acoustic subdomains and a flame model to yield a reduced-order thermoacoustic system. Results show that the thermoacoustic modes of the full-order system can be reproduced by the reduced-order model with good accuracy.

Modal Identification for Integrally Bladed Rotors Under Traveling Wave Excitation

Abstract The safety of a fielded integrally bladed rotor (IBR) is often assessed through vibration testing. Responses due to various types of excitation are measured and processed and can be inputs to follow-on analyses, such as mistuning identification. One such excitation technique is the traveling wave excitation (TWE) where all blades are simultaneously excited at phase differences that attempt to replicate naturally occurring mode shapes and certain operating conditions. This test relies on noncontact exciters, e.g., magnets and speakers, that are often not directly measured. As a result, formulating the frequency response function (FRF) is difficult and the extraction of system modal data using FRF fitting techniques in the absence of FRFs is not possible. This paper presents an approach to use measured responses from TWE tests. It is shown that the fast Fourier transform (FFT) of the TWE inputs is mostly independent over the prescribed frequency range. Consequently, the output spectral density matrix can be formulated in an operational modal analysis (OMA) sense, where direct measurement of the inputs is not needed. A full spectral density matrix is then formulated from a single measurement on each blade obtained during a single test, thus reducing the number of measurement locations and testing excitation conditions. This matrix is fit by a polyreference-least squares complex frequency-domain (P-LSCF) system identification technique tailored for OMA-type measurements. The methodology is tested using simulated TWE data for an IBR model using different damping levels. Comparisons between identified modal data and those used to create the model are made and show the methodology accurately predicts underlying system information even for closely spaced modes that are common to IBRs. Finally, the method is used on experimental TWE data of an industrial IBR.

Task-Dependent Adaptations in Closed-Loop Motor Control Based on Electrotactile Feedback

Humans systematically adapt their strategies for closed-loop control based on visual feedback according to the dynamics of the system. Tactile feedback is a key element in many human–machine interfaces, but it is not known if and how well human control adapts to changes in system dynamics when information about the system state is provided using this type of feedback. In this study, 11 participants tracked a pseudorandom trajectory with a virtual, position- or velocity-controlled plant using a joystick. Visual or electrotactile feedback provided the instantaneous error between the target and generated trajectory. Frequency-domain system identification indicated that human control adapted in similar ways to the different control modes (i.e., position/velocity control) for both feedback modalities. For the plant dynamics modeled as gain and integrator, the human controller behaved as a low-pass filter and gain, respectively (under the assumption of quasi-linear behavior). However, while tracking quality was largely similar for both control modes with visual feedback, velocity control enabled substantially worse control with electrotactile feedback compared to position control. Furthermore, for both control modes, the crossover frequency of open-loop transfer functions was lower for electrotactile feedback (0.9 and 1.1 rad/s) than for visual feedback (1.5 and 1.7 rad/s) indicating limited control bandwidth. To summarize, closed-loop control based on electrotactile feedback enables natural adaptations in human control strategy, which is encouraging for tactile feedback-controlled human–machine interfaces, but the lower control bandwidth and lower tracking quality with velocity control may impose functional limitations.

Improved crest factor minimization of multisine excitation signals using nonlinear optimization

In frequency-domain system identification, multisine waveforms are frequently used as an excitation signal. Supplying a low Crest Factor (CF) input signal to the actuator of the system is essential for measuring transfer functions with a high signal-to-noise ratio. In this paper, we present a method for achieving a lower CF compared to state-of-the-art methods. Our two-step method starts with Guillaume’s method, followed by solving a slack reformulation of the ∞-norm minimization problem for additional improvement. The proposed method is compared to the existing ones in terms of the achievable CF. The performance of the CF reduction methods has been analyzed using statistical methods.

System Identification of a Subscale Distributed Electric Propulsion Aircraft

Flight testing of a 21%-scale Cirrus SR22T aircraft with a distributed electric propulsion system was performed with the goal of identifying the influence of distributed propulsion units on the aircraft flight dynamics. Stability and control derivatives for this configuration were identified for a linear aircraft model, including throttle-based control influences of a semispan-distributed array of propulsors. Unknown model parameters were identified from flight test data under unsteady excitation of control effectors using frequency-domain system-identification methods, and the resultant model was validated against independently acquired sets of flight data. The identified throttle-based control derivatives were characteristic of anticipated local thrust contributions from each propulsor and associated proportional yawing moments. Additional throttle-based control influences were also observed, through modulation in the aircraft lift, pitch, and roll characteristics. Furthermore, significant spanwise nonuniformity was observed in the aircraft lift sensitivity to throttle changes, which was linked to three-dimensional influences of the wing aerodynamics. These observations demonstrate the inherent degree of interconnectivity between aerodynamics, propulsion, and control subsystems characteristic of aircraft with distributed electric propulsion systems.

LMS Filter Based Frequency Domain System Identification of Mass – Spring – Damper System with Varying Dynamics

All practical and real-time systems are non-linear and dynamic in nature. In the majority of studies associated with systems, it is assumed that the system is linear and the dynamics of the system is remaining constant. Though these assumptions help in easier mathematical formulations of the systems, it also imposes a lot of restrictions on understanding the system completely and its behavior in depth. In this study, the focus is on capturing the varying dynamics of Mass - Spring – Damper system using a frequency domain-based system identification approach. The system identification technique is based on an adaptive filter which is implemented through MATLAB software.

Experimental identification of process dynamics for real-time control of Directed Energy Deposition

Real-time control of melt pool temperature, deposition width, and height has shown to deliver significant improvements in both material properties and part geometry during the laser based directed energy deposition process. For accurate controller design a mathematical model of the complex DED process is required. In this paper an experimental frequency-domain system identification approach to autonomously obtain a transfer-function model with multi-spectral camera-based melt pool intensity and temperature as input, and laser power as output, are considered in a linear framework. A Maximum-Likelihood frequency domain approach in the stochastic output-error framework is used. It was concluded that both intensity and temperature can be used to model the dynamics of the melt pool, with very little difference between both. Validation of the model on a sine excitation showed general good agreement but also the presence of nonlinear distortions due to the influence of the chosen toolpath.

P-099. Previous preeclampsia and its association with future cardiovascular diseases: A systematic review and meta-analysis

This paper shows how to apply frequency-domain system identification of the parameters of a linear system based on both one-bit stimulation and data acquisition. The proposed technique is based on the usage of maximum-length binary sequences as signal sources. One-bit acquisition, based on a simple comparator is assisted by a sinewave dither signal. Results are compared to those obtained by directly processing the one-bit sequence in absence of dither. Theoretical, simulation and experimental results illustrate the usage of the method and confirm the validity of the presented procedure.

IRCI‐free multiple subband MIMO SAR

An inter-range cell interference (IRCI)-free multiple subband multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) algorithm is proposed to obtain a high-resolution wide swath (HRWS) imaging. The received signals of the proposed configuration are formulated as multiple-input single-output (MISO) system identification problems using the principle of the displaced phase centre in a way that all the subband waveforms are processed simultaneously without the need to separate them at the receiver. This would maximise the bandwidth utilisation efficiency. The channel impulse response in the range dimension is identified using a frequency domain system identification--based estimation algorithm, which is free from IRCI, instead of using conventional matched filters. A pulse repetition frequency lower than the Doppler bandwidth is used to obtain the HRWS imaging, and the resulted azimuth ambiguity is removed using a set of spatial filters applied on the received signals formulated as separate MISO system identification problems. Finally, both simulated and constructed raw data are used to validate the efficiency of the proposed algorithm.

A Computationally Low-Cost Method for Capturing Airframe Flexibility Effects in Landing Dynamic Simulations

Abstract Airframe flexibility effects have typically been captured by modal reduction of the airframe. Although efficient, this model may still be prohibitively expensive for preliminary design studies. This paper employs time- and frequency-domain system identification techniques to form a multi-objective optimization (MOO) problem to identify equivalent transfer functions representing airframe flexibility effects. Pareto-optimal sets are first identified for an equivalent transfer function of a force element between the landing gear (LG) attachment point and the center of gravity (CG) of a 150-passenger regional jet, and a second transfer function from the input LG force to the cockpit acceleration. The reduced models demonstrate the ability to generally capture flexibility effects with reduced computation times. The combination of time-domain and frequency-domain information ensures the positive time-history matches while the model remains physically realizable as it is rooted to frequency response obtained from the finite element model (FEM). It is hypothesized that this physical link allowed the model to be robust to the landing initial conditions.

Bell 412 System Identification and Model Fidelity Assessment for Hover and Forward Flight

Frequency domain system identification of higher order models for the Bell 412 helicopter was performed. First, a frequency response database was derived from flight-test data. For hover, a combination of sweep and 2311-multistep maneuvers had to be used to achieve good results. In addition to the classical six-DoF (degrees of freedom) rigid body states, the identified hover model includes dynamic inflow, rotor coning dynamics, and uses a Padé approximation for the influence of engine dynamics, to improve the response in the vertical axis. The forward flight (60 kn) model includes as extension first-order flapping dynamics, mainly to improve the roll and pitch response. Besides the simple Padé approach used in the hover model, two different engine model structures were investigated but they provided no significant improvement compared to the Padé solution when coupled to the rigid-body model. Finally, a method derived from feedforward principles of model following control is shown, to use the identified hover model to analytically derive an "input filter" correction that improves the fidelity of a linearized FLIGHTLAB simulation model.

Experimental modal analysis and vibro-acoustic testing at leonardo laboratories

This work deals with Experimental Modal Analysis and vibro-acoustic testing performed on several composite panels tested at Leonardo Laboratories, Pomigliano site. The main objective of this paper is to investigate the dynamical behaviour of the structure under test and to evaluate its acoustic properties. Several tests have been performed at the Trasmission Loss Facility of Leonardo.In a modal test, both the applied forces and vibration responses of the excited structure are measured in one or more locations. Exploiting this data, a Modal Model, that essentially contains the same information as the original vibration data, is derived by means of frequency-domain system identification techniques. A home-built Matlab algorithm, named “uMan”, is developed to perform a full Experimental Modal Analysis. Its performances, in terms of capability to build a useful stabilization chart and to curve-fit measured FRFs, are shown. Moreover, a comparison with respect to the state-of-art “Polymax” algorithm in LMS Test.Lab is provided. Finally, the numerical-experimental correlation is performed to verify consistency.The proposed algorithm identifies first mathematical polynomial models, rather than estimating the modal parameters directly from the measurements. Subsequently, these mathematical models are related to the modal parameters. Finally, the obtained Modal Model is compared to the analytical dataset.An acoustic test has been performed to experimentally investigate sound transmission. Two experimental methods have been adopted to evaluate the transmission loss. First, the method that includes measurements of the sound pressure levels using microphones is exploited. Then, the sound intensity method, in which the transmitted sound intensity is measured with a sound intensity probe, is used. By comparing both experimental techniques, the first showed better performance with respect to the other method at low frequencies, while the sound intensity method is more applicable in the medium and high frequency regions in order to predict the noise transmission characteristics.

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.

Characterizing the Complex Modulus of Asphalt Concrete Using a Scanning Laser Doppler Vibrometer.

Asphalt mixtures are the most common types of pavement material used in the world. Characterizing the mechanical behavior of these complex materials is essential in durable, cost-effective, and sustainable pavement design. One of the important properties of asphalt mixtures is the complex modulus of elasticity. This parameter can be determined using different standardized methods, which are often expensive, complex to perform, and sensitive to the experimental setup. Therefore, recently, there has been considerable interest in developing new, easier, and more comprehensive techniques to investigate the mechanical properties of asphalt. The main objective of this research is to develop an alternative method based on an optical measurement technique (laser Doppler vibrometry). To do this, a frequency domain system identification technique based on analytical formulas (Timoshenko’s beam theory) is used to determine the complex modulus of asphalt concrete at its natural frequencies and to form their master curve. The master curve plotted by this method is compared with the master curve obtained from the standard four-point bending test, and it is concluded that the proposed method is able to produce a master curve similar to the master curve of the standard method. Therefore, the proposed method has the potential to replace the standard stiffness tests. Furthermore, the standard stiffness methods usually conduct experiments up to the maximum frequency of 30 Hz. However, the proposed method can provide accurate complex modulus at high frequencies. This makes an accurate comparison between the properties of the asphalt mixtures in high frequencies and the development of more accurate theoretical models for simulation of specimens possible.

Evolution and Analysis of Hapkit: An Open-Source Haptic Device for Educational Applications.

We present the design, evolution and analysis of "Hapkit," a low-cost, open-source kinesthetic haptic device for use in educational applications. Hapkit was developed in 2013 based on the design of the Stanford Haptic Paddle, with the goal of decreasing cost and increasing accessibility for educational applications, including online teaching, K-12 school use, and college dynamic systems and control courses. In order to develop Hapkit for these purposes, we tested a variety of transmission, actuation, and structural materials. Hapkit 3.0, the latest version, uses a capstan drive, inexpensive DC motor, and 3-D printed structural materials. A frequency-domain system identification method was used to characterize Hapkit dynamics across the various designs. This method was validated using a first principles parameter measurement and a transient response analysis. This characterization shows that Hapkit 3.0 has lower damping and Coulomb friction than previous designs. We also performed a user study demonstrating that Hapkit 3.0 improves discrimination of virtual stiffness compared to previous designs. The design evolution of Hapkit resulted in a low-cost, high-performance device appropriate for open-source dissemination and educational applications.

Two-Dimensional Frequency-Domain System Identification

In this paper, we propose two iterative algorithms to identify transfer functions of two-dimensional (2-D) systems. The proposed algorithms are modifications of the 2-D adaptive Fourier decomposition (AFD) and weak pre-orthogonal adaptive Fourier decomposition (W-POAFD). 2-D AFD and W-POAFD are newly established adaptive representation theories for multivariate functions utilizing, respectively, the product-TM system and the product-Szego dictionary. The proposed algorithms give rise to rational approximations with real coefficients to transfer functions. Owing to the modified maximal selection principles, the algorithms achieve a fast convergence rate $\boldsymbol {O(n^{-\frac{1}{2}})}$ . To use 2-D AFD and W-POAFD for system identification not only the theory is revised, but also the practical algorithm codes are provided. Experimental examples show that the proposed algorithms give promising results. The theory and algorithms studied in this paper are valid for any ${n}$ -D case, ${n\geq 2}$ .