Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Extracting dynamical equations from experimental data is NP-hard

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP-hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70 years).Comment: For mathematical details, see arXiv:0908.2128[math-ph]. v2: final version, accepted in Phys. Rev. Let

Prediction and Simulator Verification of Roll/Lateral Adverse Aeroservoelastic Rotorcraft–Pilot Couplings

The involuntary interaction of a pilot with an aircraft can be described as pilot-assisted oscillations. Such phenomena are usually only addressed late in the design process when they manifest themselves during ground/flight testing. Methods to be able to predict such phenomena as early as possible are therefore useful. This work describes a technique to predict the adverse aeroservoelastic rotorcraft–pilot couplings, specifically between a rotorcraft’s roll motion and the resultant involuntary pilot lateral cyclic motion. By coupling linear vehicle aeroservoelastic models and experimentally identified pilot biodynamic models, pilot-assisted oscillations and no-pilot-assisted oscillation conditions have been numerically predicted for a soft-in-plane hingeless helicopter with a lightly damped regressive lead–lag mode that strongly interacts with the roll modeat a frequency within the biodynamic band of the pilots. These predictions have then been verified using real-time flight-simulation experiments. The absence of any similar adverse couplings experienced while using only rigid-body models in the flight simulator verified that the observed phenomena were indeed aeroelastic in nature. The excellent agreement between the numerical predictions and the observed experimental results indicates that the techniques developed in this paper can be used to highlight the proneness of new or existing designs to pilot-assisted oscillation

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion that may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of non-linear aeroelastic systems. The LASSO minimises the residual sum of squares with the addition of an l(Sub 1) penalty term on the parameter vector of the traditional l(sub 2) minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudo-linear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) Active Aeroelastic Wing project using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data

Seasonal Dynamic Factor Analysis and Bootstrap Inference: Application to Electricity Market Forecasting

In this work, we propose the Seasonal Dynamic Factor Analysis (SeaDFA), an extension of Nonstationary Dynamic Factor Analysis, through which one can deal with dimensionality reduction in vectors of time series in such a way that both common and specific components are extracted. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal ones, by means of the common factors following a multiplicative seasonal VARIMA(p, d, q) × (P, D, Q)s model. Additionally, a bootstrap procedure that does not need a backward representation of the model is proposed to be able to make inference for all the parameters in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing enhanced coverage of forecasting intervals. A challenging application is provided. The new proposed model and a bootstrap scheme are applied to an innovative subject in electricity markets: the computation of long-term point forecasts and prediction intervals of electricity prices. Several appendices with technical details, an illustrative example, and an additional table are available online as Supplementary Materials

Structural identifiability of surface binding reactions involving heterogeneous analyte : application to surface plasmon resonance experiments

Binding affinities are useful measures of target interaction and have an important role in understanding biochemical reactions that involve binding mechanisms. Surface plasmon resonance (SPR) provides convenient real-time measurement of the reaction that enables subsequent estimation of the reaction constants necessary to determine binding affinity. Three models are considered for application to SPR experiments—the well mixed Langmuir model and two models that represent the binding reaction in the presence of transport effects. One of these models, the effective rate constant approximation, can be derived from the other by applying a quasi-steady state assumption. Uniqueness of the reaction constants with respect to SPR measurements is considered via a structural identifiability analysis. It is shown that the models are structurally unidentifiable unless the sample concentration is known. The models are also considered for analytes with heterogeneity in the binding kinetics. This heterogeneity further confounds the identifiability of key parameters necessary for reliable estimation of the binding affinit

Variability in concentrations of potentially toxic elements in urban parks from six European cities

Use of a harmonised sampling regime has allowed comparison of concentrations of copper, chromium, nickel, lead and zinc in six urban parks located in different European cities differing markedly in their climate and industrial history. Wide concentrations ranges were found for copper, lead and zinc at most sites, but for chromium and nickel a wide range was only seen in the Italian park, where levels were also considerably greater than in other soils. As might be expected, the soils from older cities with a legacy of heavy manufacturing industry (Glasgow, Torino) were richest in potentially toxic elements (PTEs); soils from Ljubljana, Sevilla and Uppsala had intermediate metal contents, and soils from the most recently established park, in the least industrialised city (Aveiro), displayed lowest concentrations. When principal component analysis was applied to the data, associations were revealed between pH and organic carbon content; and between all five PTEs. When pH and organic carbon content were excluded from the PCA, a distinction became clear between copper, lead and zinc (the "urban" metals) on the one hand, and chromium and nickel on the other. Similar results were obtained for the surface (0-10 cm depth) and sub-surface (10-20 cm depth) samples. Comparisons with target or limit concentrations were limited by the existence of different legislation in different countries and the fact that few guidelines deal specifically with public-access urban soils intended for recreational use

Studies of moss reproductive development indicate that auxin biosynthesis in apical stem cells may constitute an ancestral function for focal growth control

The plant hormone auxin is a key factor for regulation of plant development, and this function was probably reinforced during the evolution of early land plants. We have extended the available toolbox to allow detailed studies of how auxin biosynthesis and responses are regulated in moss reproductive organs, their stem cells and gametes to better elucidate the function of auxin in the morphogenesis of early land plants. We measured auxin metabolites and identified IPyA (indole-3-pyruvic acid) as the main biosynthesis pathway inPhyscomitrium(Physcomitrella)patensand established knock-out, overexpressor and reporter lines for biosynthesis genes which were analyzed alongside previously reported auxin-sensing and transport reporters. Vegetative and reproductive apical stem cells synthesize auxin. Sustained stem cell activity depends on an inability to sense the auxin produced while progeny of the stem cells respond to the auxin, aiding in the control of cell division, expansion and differentiation. Gamete precursors are dependent on a certain degree of auxin sensing, while the final differentiation is a low auxin-sensing process. Tha data presented indicate that low auxin activity may represent a conserved hallmark of land plant gametes, and that local auxin biosynthesis in apical stem cells may be part of an ancestral mechanism to control focal growth

Investigations of the pi N total cross sections at high energies using new FESR: log nu or (log nu)^2

We propose to use rich informations on pi p total cross sections below N= 10 GeV in addition to high-energy data in order to discriminate whether these cross sections increase like log nu or (log nu)^2 at high energies, since it is difficult to discriminate between asymptotic log nu and (log nu)^2 fits from high-energy data alone. A finite-energy sum rule (FESR) which is derived in the spirit of the P' sum rule as well as the n=1 moment FESR have been required to constrain the high-energy parameters. We then searched for the best fit of pi p total cross sections above 70 GeV in terms of high-energy parameters constrained by these two FESR. We can show from this analysis that the (log nu)^2 behaviours is preferred to the log nu behaviours.Comment: to be published in Phys. Rev. D 5 pages, 2 eps figure