Topics in Modal Analysis & Parameter Identification, Volume 8

Experimental modal analysis of complex structures requires a good sensor concept to capture the component’s vibrational behavior ideally. Especially, when the geometry is big or consists of many attached parts and the number of available sensors is limited, the sensor placement in order to maximize the gained output information is relevant. For this purpose, several methods and algorithms are implemented and tested on the stator housing of an axial compressor test rig. These procedures include among others a genetic algorithm, an artificial bee algorithm, a method based on the QR-decomposition, as well as the effective independence method. This work contributes to the provision of more validation data for real structures, which are rarely found in the literature. The resulting measurement data are analyzed in order to evaluate the qualification of the methods presented for modal parameter extraction. The positioning techniques are compared among each other in order to choose the most suitable method for the modal identification of a complex mechanical structure. Additionally, the experimental results are compared to results from a finite element model. In order to improve the fit between experimental data and numerical results, a model updating procedure is carried out.

Robot-driven on-orbit servicing, assembly, and manufacturing (OSAM) promises to enable and enhance a wide range of space technologies in the coming decades, but supporting technologies must still be developed to manage the unique characteristics of this upcoming construction paradigm. One area of need will be in frequent modal characterization of the structure as it is assembled/manufactured in order to ensure stability of robotic and stationkeeping control systems on the platform. This paper discusses recent work in the development of modal testing techniques using robotic systems within the context of OSAM. Rather than utilizing bespoke actuators for modal excitation, this paper investigates the potential for use of the robotic assembly/manufacturing robots themselves as sources of dynamic excitation. Feasibility, processes, and results of this solution are presented using a relevant exemplar OSAM structure. These studies will aid in development of requirements for OSAM robotic and structural systems in the coming decades.

Automated operational modal analysis allows operational modal analysis to be used without the need of a human operator to identify structural modes from a stabilisation diagram. Multiple algorithms for automating this procedure have been proposed, and this paper selects four (Magalhaes 2008, Reynders 2012, Yang 2019, and Kvåle 2020) and benchmarks them using experimental data from the monitored, and previously studied, Hardanger Bridge. It is shown that the Magalhaes 2008 and Kvåle 2020 algorithms have the highest detection rates of all the algorithms but that the Reynders 2012 and Yang 2019 algorithms have higher automation and lowest error rates, respectively.

Regarding structural dynamic behavior, the violin is a very versatile entity to study, since it combines many different effects in one single structure. Investigating this instrument means dealing with the uncertainty in natural materials, geometric nonlinearities, many interfaces, and sound radiation. Hence, this multifaceted structure serves as research subject for present work. The study starts with modal analyses of the raw spruce and maple woods, with the intention to show that an a priori material parameter identification is possible. The identified values serve as input for the orthotropic violin plates in the associated finite element model. Using 2D laser scanning vibrometry, the modal parameters are obtained for each plate. The components are supported on soft foams and on cotton wool in order to show the significant deviations in the measurement results with varying foam compliances.

The aim of this paper is to introduce an identification method for industrial vibro-acoustic systems with multiple inputs using (very) short measurement. The classical time-consuming phase resonance (or normal modes) testing procedures are nowadays almost fully substituted by frequency response functions (FRFs) methods which are used to obtain parametric models (e.g., resonance frequencies, mode shapes in modal analysis, or state-space models in control engineering).

This paper presents a novel nonparametric FRF estimation methodology which allows the user to efficiently estimate broadband transfer functions of multiple-input systems using only one block of measurement (disturbed by transient term and noise). The proposed method is a novel extension of already existing local parametric techniques used for SISO identification. In order to assess the performance of the proposed method, a benchmark study is performed on a tire suspension measurement where the candidate estimator performance is compared to classical H1 and to the windowed-overlapped H1 techniques.

Measuring blade dynamic stress plays a crucial role in forecasting blade high cycle fatigue (HCF) failure during aircraft engine tests. A method to improve the measurement accuracy of blade vibration amplitude is introduced. The gauged blades are calibrated on the shaker to measure dynamic strains and tip amplitudes before being assembled with the rotor. First, a brief strain distribution for each vibration mode is acquired to validate the predicted and measured mode shapes, through which the maximum dynamic strain positions are also identified. Then, the ratios of strain to amplitude for each mode can be established based on Amplitude frequency (AF) techniques to define blade tip amplitude limits during engine tests. Third, the ratios can be substituted into online measured blade tip amplitudes to estimate blade safety, which could make blade vibration monitoring more accurate and thus prevent unnecessary engine shutdowns.

To validate the methods, engine test data of a high bypass ratio aircraft engine fan blades are introduced. Results show that dynamic strain and tip amplitude data of the fan blades are with good correlation. It proves that the blade tip timing (BTT) system works well in predicting the occurrences of fan blade resonances and the measured amplitudes are with reasonable uncertainties. The results reveal that BTT could be a useful tool to quantify blade vibration levels based on AF techniques.

The aim of this work is to suggest the real-time estimation process for the unmeasured response of the vibro-acoustic system. The proposed framework enables the real-time estimation of the unmeasured physical quantities such as applied forces, displacements, and accelerations of entire structure by using very limited number of sensors. A vibro-acoustic FE model is used as a physical model of the target structure, and the FE model updating process is implemented to improve the reliability of the numerical model. Then, an inverse dynamic applied force identification technique for vibro-acoustic system is proposed. The identified forces with certain measured physical information are used to predict the unmeasured physical quantities through the time integration process. To alleviate the computational cost and enable the real-time computation of the FE model, a multi-physics model reduction technique is applied. The proposed real-time estimation framework is implemented on a simple fluid-filled pipe model, and its real-time estimation performance is then evaluated in the various loading conditions.

As systems become more and more complex, representing them with differential equations or transfer functions becomes cumbersome and even more so if the number of inputs and outputs are growing. Using a state space model representation largely alleviates this problem as it provides a convenient and compact way to model and analyze MIMO systems.

In various engineering applications, e.g., structural coupling, virtual sensing, time-domain simulation, and control, state space models have been proven to be a useful and practical system representation. Different “direct” state space model identification algorithms exist in literature, e.g., prediction error methods and time-domain/frequency-domain subspace identification methods. Generally, subspace identification algorithms consist of geometrical projections to estimate the states of the unknown system or to estimate the extended observability matrix from which the state matrices are retrieved. In such methods, the model order is traditionally determined by inspecting and truncating the singular values of the projection (hence the name “subspace” methods). When applied to real, sometimes noisy, measurement data, it is not obvious to decide on the model order. Another issue with the subspace identification techniques and in particular with the frequency-domain variants is that the stability of the poles is not always guaranteed.

In this paper, a modal-based approach to derive a robust and stable state space model starting from a set of measured frequency response functions (FRFs) will be presented. The approach makes use of the Polymax modal parameter estimator to derive a modal model which can be further improved by the iterative MLMM algorithm when needed. The clear stabilization diagram obtained using Polymax can be used as a valid tool to determine the order of the system under test. The obtained modal model is then transformed to an equivalent state space model. The lower and the upper residual terms, which are used to model the out-of-band modes in the modal model, are transformed to the so-called residual compensation modes allowing a straightforward conversion from a modal model to a state space model. Since the modal model contains only stable poles, the stability of the identified state space model is guaranteed. The presented approach will be validated using industrial datasets and compared with the well-known “N4SID” implementations of time- and frequency-domain subspace identification methods.

Considering the extending use of hydrogen as a propellant in terrestrial and aerospace applications with subsequent growing needs for storage, as well as containers for transport, reserve, and distribution, cryogenic tank scrutiny holds an upmost significance. This work thus focuses on characterizing the dynamic behavior of a modeled but representative cryogenic tank to help the certification process of actual containers used in aerospace applications. The core objective of the work is the implementation of an experimental setup and ensuing structural modal analysis of a suspended vibrated tank. However, due to hazardous handling of liquid hydrogen, actual up-to-scale experimental testing is often impossible or prohibited to perform in regular conditions. To counter this hindrance, the innovative approach and main postulate of this work is to consider granular materials as substitutes to cryogenic fluids.

The aim is to obtain a modal behavior similar in terms of mode shapes and natural frequencies to the behavior of a tank filled with liquid hydrogen. Most of the studies regarding this issue are using water as a surrogate material for gas in tank testing. However, since using water as a substitute could not respect isomass and isovolume of liquefied hydrogen simultaneously, an innovative method was attempted via substitution of the gas by a granular meta-material. Apart from the initiated work on this topic, no other study was found to display this approach. The current goal is therefore to explore further possibilities in terms of material substitution as well as filling rate influence, system fixation impact, and change of excitation modes. For that purpose, investigations are carried out on an empty, fully, and partially filled tank subjected to vibration. The natural frequency reflecting the dynamic behavior of the tank for each vibration mode is measured for the different configurations. Notable frequencies of modal deformed shapes are occurring at 555, 1036, 1333, 1500, and 1600 Hz on an empty suspended aluminum tank, with associated shapes of flexion, flexion-torsion, ovalization, trefoil, quadrifoil, lobe modes, and then combined modes. Pre-trials on filled tank display the same deformed shape occurrence but at lower frequencies: 260, 539, 701, 726, and 1020 Hz. First results also show that low-density materials help reach the flexural modes, pointing the surrogate material density as important. Further results will help validate the new methodology.

A novel data-driven structural damage detection approach using an unsupervised convolutional neural network is proposed in this study to assess the health conditions of structures. It is known that many data-driven methods in supervised learning mode have been proposed for structural damage detection in recent decades, but they require large amounts of training data measured from not only undamaged structural scenarios but also various damaged structural scenarios. However, it is impractical to obtain an adequate number of damaged scenarios for the structures being in service to acquire sufficient training data, and labeling huge amounts of training data with specific structural scenarios is time-consuming and costly as well. In this study, the proposed unsupervised deep learning method uses the acceleration responses only measured from the undamaged scenario of an experimental structure as training data, and the acceleration responses measured from various unknown structural scenarios are taken as the testing data. Then, damage-sensitive features are extracted from the reconstruction losses between inputs and outputs of the trained unsupervised convolutional neural network. Finally, the technique of Mahalanobis distance is applied on the extracted features to perform damage detection. Overall, the proposed method provided high performance in damage detection with reduced tuning parameters, and the experimental studies showed an average 93.8% detection accuracy for a laboratory-scale steel building model with damage in the form of bolt loosening at some structural joints and a reduced cross-section column.

Data collected by vehicle sensors can be useful for a multitude of applications. In particular, inertial measurement units (IMU), which collect data during regular driving, can be utilized for vehicle system identification. Information regarding vehicle dynamic properties can be integrated into data-driven city-scale frameworks such as pothole detection and indirect bridge monitoring. The accuracy of the system identification depends on sensing and driving conditions such as vehicle speed, road class, sensor noise, etc. This study aims to quantify the minimum duration of driving data needed to accurately estimate a vehicle’s fundamental modal frequencies. Quarter car models were used in conjunction with ISO 8608 road standards to simulate the vehicle’s in-cabin acceleration for a variety of speeds, vehicle types, and road classes. The automated frequency domain decomposition (AFDD) method was used for estimating the fundamental natural frequencies of the vehicles from the simulated response data. This study found that regardless of speed, approximately 240 seconds of acceleration data is needed to consistently model the vehicle’s first modal frequency. This study considered both compact and SUV vehicle types, traveling at a variety of speeds over Class B and Class D road profiles. The results indicated that there is no direct impact of speed or road type on the accuracy of the model but that the vehicle properties impacted the accuracy of the results. These results are limited by the output-only method of system identification as well as inaccuracy within the AFDD function due to the noise of the data.

Physics-Based Reduced Order Models (ROMs) tend to rely on projection-based reduction. This family of approaches utilizes a series of responses of the full-order model to assemble a suitable basis, subsequently employed to formulate a set of equivalent, low-order equations through projection. However, in a nonlinear setting, physics-based ROMs require an additional approximation to circumvent the bottleneck of projecting and evaluating the nonlinear contributions on the reduced space. This scheme is termed hyper-reduction and enables substantial computational time reduction. The aforementioned hyper-reduction scheme implies a trade-off, relying on a necessary sacrifice on the accuracy of the nonlinear terms’ mapping to achieve rapid or even real-time evaluations of the ROM framework. Since time is essential, especially for digital twins representations in structural health monitoring applications, the hyper-reduction approximation serves as both a blessing and a curse. Our work scrutinizes the possibility of exploiting machine learning (ML) tools in place of hyper-reduction to derive more accurate surrogates of the nonlinear mapping. By retaining the POD-based reduction and introducing the machine learning-boosted surrogate(s) directly on the reduced coordinates, we aim to substitute the projection and update process of the nonlinear terms when integrating forward in time on the low-order dimension. Our approach explores a proof-of-concept case study based on a Nonlinear Auto-regressive neural network with eXogenous Inputs (NARX-NN), trying to potentially derive a superior physics-based ROM in terms of efficiency, suitable for (near) real-time evaluations. The proposed ML-boosted ROM (N3-pROM) is validated in a multi-degree of freedom shear frame under ground motion excitation featuring hysteretic nonlinearities.

In the past few decades, matrix decomposition methods have been explored as suitable Operational Modal Analysis algorithms. For a given vibratory mechanical system, one looks for its coherent spatial–temporal structures through the assumption of separation of variables. In practical situations, this separation of variables is done by decomposing a sampled scalar field that contains the underlying continuous field of the structure in time. In mechanical vibrations, this sampled scalar field is usually a trajectory matrix, \(X \in \mathbb {R}^{n \times m}\), that is composed of n displacement, velocity, or acceleration observations at m distinct spatial points on a structure. Methods such as the Proper Orthogonal Decomposition (POD) and the Smooth Orthogonal Decomposition (SOD) have been used to decompose the trajectory matrix into its modal coordinates and modal matrix. In real-world scenarios, there are practical limitations to these algorithms. First, for the case of POD, the free-response sample covariance matrix must be scaled by the mass matrix to identify the true LNMs of the structure. For complicated structures with nonuniform mass distribution, this is problematic.

Metastructures, a metamaterial-type structure designed with distributed vibration absorbers, are a growing development in the area of passive vibration suppression. Previous research has shown that it is possible for vibration absorbers to be introduced into a structure for broadband vibration suppression without introducing additional mass. The proposed mass-conserved metastructures are modeled using lumped parameter and finite element approaches and are compared to a baseline structure of equal mass to quantify the level of vibration suppression achievable for each metastructure. The objective of this work is to experimentally verify the lumped parameter model of mass-conserved metastructures. This work chooses to focus on the lumped parameter model due to its simplicity and potential application to other metastructure designs. A baseline structure and two metastructure designs are considered in the analysis, and a 3D printer was used to create the metastructures which were then subject to vibration testing. The effectiveness of the vibration suppression will be analyzed using the steady-state and transient responses. The experimental results of the 3D printed metastructures show a similar response to the 1D lumped parameter metastructure model, indicating that a level of vibration suppression can be achieved without adding additional mass to the structure.

Engineers need to effectively communicate the justification and value of their modal testing and model correlation in terminology familiar to decision makers as it relates to the program’s risk tolerance. This communication must relate to the program’s risk tolerance and the metrics used to judge the performance of both the program and individual decision makers. The challenge is the terminologies familiar to engineers and decision makers are quite different and seemingly unrelated. The engineering profession has developed a specific terminology to solve highly technical issues, which are many times themselves unique to very specific engineering problems. It is all too easy for engineers to believe that everyone in their organization, including the decision makers, has an intrinsic understanding of what they do and the value it brings to the program’s success. This is especially true for young engineers who have recently spent the last 4 plus years in an academic engineering learning environment, which has a highly technical research-oriented atmosphere. Effective communication with decision makers is increasingly important as the technical breadth and practical program and project experience level for up and coming decision makers diminish. It is not unusual for the decision makers to have technical knowledge in a domain different from structural dynamics (e.g., electronics or systems). Competition among satellite manufactures has increased the focus on programmatic cost and ability to deliver on schedule. NASA programs are also seeing more restrictive programmatic cost and schedule constraints, which impact both analysis and testing. It should also be noted that a comprehensive suite of tests is required to verify a satellite’s design capability with some margin. These tests include static strength verification tests, shock, acoustic, and vibration tests (sine and random) of systems, subsystems, and components. Each of these verification tests provides opportunities for model correlation and risk reduction. It is important to recognize dynamic loads/modal test models may not include all of the flight hardware (i.e., harness, coax, waveguides, connectors, etc.) and the previously mentioned tests are still required for qualification/verification of the design. This paper provides tips to young engineers on how to bridge this communications gap, have a better understanding of the environment in which decision makers operate, and assist them to better support successful missions. While this paper primarily focuses on modal testing and model correlation as related to spacecraft missions, the concepts and recommendations presented here are equally applicable to other fields such as aeronautics, automotive, power generation, etc.

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pretest analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower-frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling Scheme. AD is derived from a widely used coupling technique called “receptance coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component.” This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.