Intelligent Automatic Operational Modal Analysis: preliminary resultsRosso, Marco Martino; Aloisio, Angelo; Marano, Giuseppe Carlo; Quaranta, Giuseppe
doi: 10.1088/1742-6596/2647/21/212005pmid: N/A
Within the structural health monitoring (SHM) field, consistent research efforts have been invested in developing automatic vibration-based indirect methodologies for inspecting existing heritage conditions. Current trends are mainly focused on output-only automatic operational modal analysis (AOMA), specifically throughout the stochastic subspace identification (SSI) technique among others. In the literature, a widespread workflow is implemented in a four-step solution: choice of the SSI control input parameters, computation of stabilization diagrams, stable poles’ alignments detection, and their final clustering. However, the so far proposed solutions have not provided yet complete answers to some challenging and still open questions. For instance, an arbitrarily poor initial choice of the SSI control parameters may jeopardize the entire procedure. Therefore, in the current study, the authors present a novel intelligent-based AOMA framework in a machine learning perspective. Specifically, random-forest-driven Monte Carlo sampling of control parameters represents a promising intelligent way to automatically choose the proper SSI control parameters. Furthermore, the recurrent stable physical poles in the stabilization diagram among the Monte Carlo simulations deliver some special insights about mode shape confidence intervals. A numerical benchmark is herein analyzed illustrating some preliminary results and potentials of the proposed methodology.
On the improvement of design space subsets formulation for iteratively optimizing structural systemsKhalid, M A; Bansal, S
doi: 10.1088/1742-6596/2647/21/212002pmid: N/A
Structural optimization is the process of identifying the optimal set of design parameters for a structural system. Optimization techniques provide an effective approach for rationally improving structural engineering design, both for the structural system with deterministic and uncertain parameters. It is unanimously agreed that in engineering design applications, knowledge about a planned system is never comprehensive. These uncertainties resulting from incomplete information are often assessed probabilistically. In this probabilistic framework, the system design process is referred to as stochastic system design, and the concomitant design optimization problem is alluded to as stochastic optimization. The stochastic optimization process has been widely used in civil, mechanical, and aeronautical engineering designs. Stochastic system optimization includes two stages where initially the performance measure is approximated either by Taylor series approximation or the metamodels, and in the second stage, the approximated performance function is optimized by implementing the available optimization techniques such as nonlinear programming methods, gradient-based methods, metaheuristic methods, etc. Approaches available in literature can effectively take into account the uncertainties, but still, achieving higher accuracy and lower computational cost remains a challenging task for designing complex and realistic structural systems. To obliviate these aforementioned limitations, a simulation-based approach known as Stochastic Subset Optimization (SSO) is found to be very effective. The basic principle in the original SSO is to reduce the design space size iteratively, which has high plausibility of containing the optimal design solution. However, the success of the approach depends on the shape selection of the design space while implementing the SSO. Therefore, in the present study, the dependency of the original SSO over the selection of the shape of the design subset is overcome by exploring the design space based on the density of simulated design samples with the design space. This improves the applicability of the SSO to the complex, realistic problem. Two benchmark optimization problems: a 2-dimensional bowl-shaped sphere function and a helical compression spring design, are solved with the proposed approach to demonstrate the efficiency of the proposed approach.
Metrological quality of the excitation force in forced vibration test of concrete damsMartins, L L; Gomes, J P; Ribeiro, A S
doi: 10.1088/1742-6596/2647/21/212001pmid: N/A
This paper describes the study of the metrological quality of the excitation force in the context of force vibration test of concrete dams. For this purpose, a measurement uncertainty evaluation was performed, based on available probabilistic information about the input quantities – rotation frequency, mass, radial position, dimension, diameter and density of the generator’s rod – which support the determination of the excitation force in an eccentric masses vibration generator, used by LNEC in concrete dam’s field observation. The uncertainty propagation from the input quantities to the output quantity was performed by a Monte Carlo method, considering the mathematical model used for the determination of the excitation force. Two experimental cases were studied: (A) the use of five weights in the generator in the frequency range of 1 Hz up to 6 Hz; and (B) the use of a single weight in the generator in the frequency interval comprised between 5 Hz and 15 Hz. In the first case, the excitation force estimates and expanded measurement uncertainties (considering a 95 % confidence interval) varied between 3.55 kN ± 0.14 kN and 127.68 kN ± 0.91 kN, being rotation frequency the major contribution for the obtained dispersion of force values. In the second case, the excitation force estimates and expanded measurement uncertainties varied between 16.71 kN ± 0.25 kN and 150.4 kN ± 1.8 kN, being the generator’s rod diameter the main contribution for the output measurement uncertainty. The obtained knowledge is essential to assure confidence and rigorous knowledge about the applied excitation force, namely, in extreme situations near dynamical structural safety limits of the observed concrete dam and of the testing equipment.
Quantification of Polymorphic Uncertainties in Structural Dynamics: Case Study of a Guyed MastMarwitz, Simon; Lahmer, Tom; Zabel, Volkmar
doi: 10.1088/1742-6596/2647/21/212004pmid: N/A
Aging vibration-prone structures may require up-to-date proofs of their load-bearing capacity for retrofitting or life-cycle assessments. The structural vibration response is affected by naturally variable structural properties and loads, known as aleatory uncertainties. With modeling, additional epistemic uncertainties are introduced due to missing knowledge of model parameters. The model responses then include both types of uncertainties in a mixed and nested form. Quantifying these polymorphic uncertainties is particularly important in structural dynamics, where a deterministic model may significantly underestimate responses, such as resonance phenomena.A case study is conducted to characterize the vibration behavior of a guyed mast under polymorphic uncertainties. A simplified linear structural model is built using commercially available FEM software. Polymorphic uncertainties in the input parameters are modeled and propagated using in-house code.Aleatory uncertainties are modeled by probability theory, and a quasi-Monte Carlo simulation based on weighted sampling facilitates an efficient reuse of computed samples. Epistemic uncertainties are modeled by evidence/belief function theory and their propagation is performed using interval optimizations on Radial Basis Function interpolators and quasi-Monte Carlo sequences. Particular emphasis is placed on computational efficiency, as the developed method is designed to be used for more complex numerical models. Statistics and aggregation of belief functions are used to yield explainable results.The case study scenario is a retrofit of a guyed mast based on outdated design documents. Epistemic uncertain parameters include unknown structural damping, cross-section tolerances, material properties, the additional mass from antennas and cables, and the pre-tensioning forces of the guy cables. Aleatory uncertainties arise from temperature effects on the guy cables and the viscosity of the dampers, as well as from icing in winter. The results highlight the intrinsic variations of natural frequencies, the characterization of resonance bands due to epistemic uncertainties, and the effectiveness of a deterministically designed Tuned Mass Damper (TMD) in a structural model influenced by polymorphic uncertainties.The developed methodology is applicable to moderately computationally expensive models of any type. Model runs are efficiently re-used and the uncertainty propagation can be highly parallelized. The method reveals where enhancing knowledge about partly-known model parameters is beneficial and permits robust retrofit designs or increased confidence in life-cycle estimates.
Model updating for the simulation of surface strains on printed circuit boards considering parameter uncertaintySchmidt, H; Käß, M; Lichtinger, R; Hülsebrock, M
doi: 10.1088/1742-6596/2647/21/212006pmid: N/A
The efficient and reliable design of power electronic components plays an important role in the development process of electrically driven vehicles. One key aspect is the reliability of solder joints on printed circuit boards (PCB) that greatly depends on the surface strain at the solder joint locations. It is therefore unavoidable to use precise simulations of surface strains to reliably estimate the solder joint lifetime. This work presents a procedure of model updating of a printed circuit board model that considers the variability of board behavior due to uncertainties in the material composition or the manufacturing process. Hierarchical Bayesian model updating is applied to incorporate this variability. The printed circuit board is seen as a multi-level model that is updated in two steps. Experimental data from system and component level are used to sequentially update the printed circuit board and the board mounting. The experimental data combine modal information and measured frequency response functions. The proposed procedure is applied to a test PCB and the updated model is validated with experimental surface strain data.
Inverse design under uncertainty with surrogate modelsWalton, D B; Featherston, C A; Kennedy, D; Kundu, A
doi: 10.1088/1742-6596/2647/21/212008pmid: N/A
In the drive towards net zero the aerospace industry is motivated to develop more efficient aerostructures that can accommodate the next generation of propulsion systems that fall outside of the well understood types that are currently in use. The lack of established standards for such designs means that engineers are faced with an increased level of uncertainty in their design choices before any prototypes are built. Machine learning models are becoming a popular tool for expediting the development of novel designs due to their ability to explore and predict the optimal parameters of large design spaces. It is also possible to quantify and introduce uncertainty into particular models so that practitioners can be made aware of the potential variation in their realised designs. In this paper Gaussian Process surrogate models of the performance metrics of the early-stage design of an aircraft wing are created to optimize a subset of design parameters based on some prescribed limits of the intended real system response. This defines the inverse design problem that is solved using Markov Chain Monte Carlo sampling. The approach taken requires novel formulation of a Bayesian machine learning framework. In particular, the work investigates the formation of likelihood functions that are flexible given inputs of different scales, can perform marginalisation of stochastic parameters, account for uncertainty in the surrogate model, and optimise the parameters given more than one constraint. A case study is presented in this paper that highlights both a successful implementation of the framework along with a limitation. It is found that the optimization is sensitive to changes in the variances of the likelihoods such that it can be used as a weight to direct the optimization towards a quantity of interest, therefore adjustment of this parameter is used to balance the optimization.
Accurate frequency response function estimation using noise measurements in experimental modal analysisSteffensen, M T; Tcherniak, D; Thomsen, J J
doi: 10.1088/1742-6596/2647/21/212003pmid: N/A
In experimental structural dynamics, reliable estimation of Frequency Response Functions (FRF) is important to correctly characterize a mechanical system. In Experimental Modal Analysis (EMA), the FRFs are used as input to a modal parameter estimation algorithm to obtain the modal characteristics of the system. Errors due to noisy measurements are inevitably present in the FRFs and propagate to the modal parameters. A consistent FRF-estimator with low uncertainty is therefore needed. Different FRF estimators have been proposed with some consistency when certain noise-related assumptions are fulfilled (H1, H2, etc.). To choose the appropriate frequency response function estimator, information about the noise in the experimental setup is desirable. In this work it is shown how to use measurements of noise, to characterize different noise components in the experimental setup and determine the appropriate number of averages needed for the experimental setup. The identified noise components can be used to identify the main source of uncertainty in the experimental setup and which FRF estimator to use.
A two-stage model updating using complex modal dataHenikish, E; Bansal, S
doi: 10.1088/1742-6596/2647/21/212007pmid: N/A
The process of Finite Element (FE) modelling is often associated with uncertainties which necessitates its updating using measured data. Updating dynamical model has a considerable importance in Structural Health Monitoring (SHM), estimating the structural responses, and structural control applications. Among the various presently available approaches for performing model updating, the probabilistic updating approach such as Bayesian model updating has gained a great deal of attention in the last two decades. It can aggregate all the types of uncertainties, e.g., prediction errors, modelling errors, measurement errors, etc., and deal with them as epistemic uncertainties about the system. This paper introduces a two-stage Bayesian model updating procedure of FE dynamical model. The targeted systems encounter a non-classical damping yielding complex modes of vibration. The original FE model is reduced using the method of dynamic condensation, where the reduced FE model is related to the observed Degrees-of-Freedoms (DOFs). Due to the usual availability of a limited number of sensors during real-world applications, modal data used to update the FE model is obtained from multiple setups. Finally, to simulate samples that approximate the posterior Probability Density Function (PDF), a new MWG sampling algorithm is used and compared with Transitional Markov Chain Monte Carlo (TMCMC) algorithm. The proposed approach has been applied to a numerical dynamical system with synthetic modal data acquired from multiple setups. Results revealed that the proposed approach could update the system’s uncertain parameters efficiently with a visible reduction in the uncertainty in both undamaged and damaged system.