On the use of nonlinear normal modes for nonlinear reduced order modelling

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses possible, certain use cases such as uncertainty quantification and real time high-precision simulation remain computationally challenging. This motivates the development of reduced order modelling methods, which can reduce the computational toll of simulations relying on mechanistic principles. The majority of existing reduced order modelling techniques involve projection onto linear bases. Such methods are well established for linear systems but when considering nonlinear systems their application becomes more difficult. Targeted schemes for nonlinear systems are available, which involve the use of multiple linear reduction bases or the enrichment of traditional bases. These methods are however generally limited to weakly nonlinear systems. In this work, nonlinear normal modes (NNMs) are demonstrated as a possible invertible reduction basis for nonlinear systems. The extraction of NNMs from output only data using machine learning methods is demonstrated and a novel NNM-based reduced order modelling scheme introduced. The method is demonstrated on a simulated example of a nonlinear 20 degree-of-freedom (DOF) system

Urinary metabolic profiles in early pregnancy are associated with preterm birth and fetal growth restriction in the Rhea mother-child cohort study

Syftet med studien var att undersöka vilka möjligheter matematikundervisning utomhus kan ge för elevernas utveckling och lärande. Syftet var även att undersöka hur utomhusmatematik kan användas som ett komplement till den traditionella inomhusundervisningen i ämnet matematik. Studien baserades på en kvalitativ forskningsansats där kvalitativa semistrukturerade intervjuer och ostrukturerade observationer användes som metoder för att besvara studiens forskningsfrågor. Sex lärare i F-3 intervjuades och två observationer på två olika skolor genomfördes. Resultatet visar att utomhusmatematiken kompletterar matematikundervisningen inomhus genom ett samspel mellan arbetssätt och miljöer. Resultatet visar även på flera positiva effekter med utomhusmatematik så som verklighetsanknytning, motivation, fysisk aktivitet, hälsa, sinnligt lärande, tillåtande miljö och sociala effekter.  De positiva effekter utomhusmatematiken medföljer för elevernas utveckling och lärande bör uppmärksamma fler lärare om dess möjligheter.

Reduced order modeling of non-linear monopile dynamics via an AE-LSTM scheme

Non-linear analysis is of increasing importance in wind energy engineering as a result of their exposure in extreme conditions and the ever-increasing size and slenderness of wind turbines. Whilst modern computing capabilities facilitate execution of complex analyses, certain applications which require multiple or real-time analyses remain a challenge, motivating adoption of accelerated computing schemes, such as reduced order modelling (ROM) methods. Soil structure interaction (SSI) simulations fall in this class of problems, with the non-linear restoring force significantly affecting the dynamic behaviour of the turbine. In this work, we propose a ROM approach to the SSI problem using a recently developed ROM methodology. We exploit a data-driven non-linear ROM methodology coupling an autoencoder with long short-term memory (LSTM) neural networks. The ROM is trained to emulate a steel monopile foundation constrained by non-linear soil and subject to forces and moments at the top of the foundation, which represent the equivalent loading of an operating turbine under wind and wave forcing. The ROM well approximates the time domain and frequency domain response of the Full Order Model (FOM) over a range of different wind and wave loading regimes, whilst reducing the computational toll by a factor of 300. We further propose an error metric for capturing isolated failure instances of the ROM

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty

Leptin, acylcarnitine metabolites and development of adiposity in the Rhea mother-child cohort in Crete, Greece.

OBJECTIVE: This study aims to investigate relations of serum leptin at age 4 with development of adiposity and linear growth during 3 years of follow-up among 75 Greek children and to identify serum metabolites associated with leptin at age 4 and to characterize their associations with adiposity gain and linear growth. METHODS: Linear regression models that accounted for maternal age, education and gestational weight gain and child's age and sex were used to examine associations of leptin and leptin-associated metabolites measured at age 4 with indicators of adiposity and linear growth at age 7. RESULTS: Each 1-unit increment in natural log-(ln)-transformed leptin corresponded with 0.33 (95% CI: 0.10, 0.55) units greater body mass index-for-age z-score gain during follow-up. Likewise, higher levels of the leptin-associated metabolites methylmalonyl-carnitine and glutaconyl-carnitine corresponded with 0.14 (95% CI: 0.01, 0.27) and 0.07 (95% CI: -0.01, 0.16) units higher body mass index-for-age z-score gain, respectively. These relationships did not differ by sex or baseline weight status and were independent of linear growth. CONCLUSIONS: These findings suggest that leptin, methylmalonyl-carnitine and possibly glutaconyl-carnitine are associated with weight gain during early childhood. Future studies are warranted to confirm these findings in other populations

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This paper assesses numerically the potential of two different spectral estimation approaches supporting non-uniform in time data sampling at sub-Nyquist average rates (i.e., below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks (WSNs) for operational modal analysis (OMA) of civil engineering structures. This consideration relaxes transmission bandwidth constraints in WSNs and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements and structural mode shapes are extracted using the frequency domain decomposition algorithm. The first approach relies on the compressive sensing (CS) theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e., have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling (PSBS) technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion (MAC) is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates (CRs) using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given CR, the performance of the CS-based approach is detrimentally affected by signal sparsity, while the PSBS-based approach achieves MAC>0.96 independently of signal sparsity for CRs as low as 11% the Nyquist rate. It is concluded that the PSBS-based approach reduces effectively data transmission requirements in WSNs for OMA, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity

A neurostructural biomarker of dissociative amnesia: a hippocampal study in dissociative identity disorder

BACKGROUND: Little is known about the neural correlates of dissociative amnesia, a transdiagnostic symptom mostly present in the dissociative disorders and core characteristic of dissociative identity disorder (DID). Given the vital role of the hippocampus in memory, a prime candidate for investigation is whether total and/or subfield hippocampal volume can serve as biological markers of dissociative amnesia. METHODS: A total of 75 women, 32 with DID and 43 matched healthy controls (HC), underwent structural magnetic resonance imaging (MRI). Using Freesurfer (version 6.0), volumes were extracted for bilateral global hippocampus, cornu ammonis (CA) 1-4, the granule cell molecular layer of the dentate gyrus (GC-ML-DG), fimbria, hippocampal-amygdaloid transition area (HATA), parasubiculum, presubiculum and subiculum. Analyses of covariance showed volumetric differences between DID and HC. Partial correlations exhibited relationships between the three factors of the dissociative experience scale scores (dissociative amnesia, absorption, depersonalisation/derealisation) and traumatisation measures with hippocampal global and subfield volumes. RESULTS: Hippocampal volumes were found to be smaller in DID as compared with HC in bilateral global hippocampus and bilateral CA1, right CA4, right GC-ML-DG, and left presubiculum. Dissociative amnesia was the only dissociative symptom that correlated uniquely and significantly with reduced bilateral hippocampal CA1 subfield volumes. Regarding traumatisation, only emotional neglect correlated negatively with bilateral global hippocampus, bilateral CA1, CA4 and GC-ML-DG, and right CA3. CONCLUSION: We propose decreased CA1 volume as a biomarker for dissociative amnesia. We also propose that traumatisation, specifically emotional neglect, is interlinked with dissociative amnesia in having a detrimental effect on hippocampal volume

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments

Measuring sub-mm structural displacements using QDaedalus: a digital clip-on measuring system developed for total stations

The monitoring of rigid structures of modal frequencies greater than 5 Hz and sub-mm displacement is mainly based so far on relative quantities from accelerometers, strain gauges etc. Additionally geodetic techniques such as GPS and Robotic Total Stations (RTS) are constrained by their low accuracy (few mm) and their low sampling rates. In this study the application of QDaedalus is presented, which constitutes a measuring system developed at the Geodesy and Geodynamics Lab, ETH Zurich and consists of a small CCD camera and Total Station, for the monitoring of the oscillations of a rigid structure. In collaboration with the Institute of Structural Engineering of ETH Zurich and EMPA, the QDaedalus system was used for monitoring of the sub-mm displacement of a rigid prototype beam and the estimation of its modal frequencies up to 30 Hz. The results of the QDaedalus data analysis were compared to those of accelerometers and proved to hold sufficient accuracy and suitably supplementing the existing monitoring techniques