Time-invariant Representation Research Articles

Implementation and Linearization of a Coupled Panel and Vortex Particle Method in State-Space Form

This paper describes the implementation and linearization of a coupled panel and vortex particle method in a state-variable form. More specifically, the coupled panel and vortex particle dynamics are formulated as a nonlinear system of ordinary differential equations in first-order form to be self-contained and inherently linearizable. Linearization of this coupled panel and vortex particle method is demonstrated via finite differencing and a novel analytical linearization technique to yield a linear time-invariant representation. The code is implemented in MATLAB® and validated against an open-source aerodynamic solver for a fixed wing in both stationary and unsteady conditions. The linearized models are verified against the nonlinear dynamics both in the time and frequency domains. Linearized models accurately represent the wake dynamics about the equilibrium condition for moderate amplitude inputs and for input frequencies covering the typical frequency range of flight dynamics and flight controls, i.e., 0.3–30 rad/s. Analytical linearization is shown to abate the cost of linearization over perturbation methods by O(n2), where n is the total number of states of the system. Linearized models of the coupled panel and vortex particle dynamics have applications in the flight dynamics of both fixed- and rotary-wing vehicles, where these dynamics can be used to augment the rigid-body dynamics. The coupled rigid-body and wake dynamics can be leveraged to assess the stability, response characteristics, and handling qualities of vehicles experiencing aerodynamic interactions between rotors, wings, and/or obstacles.

Measurement Based Linear and Nonlinear Time Invariant Representations for High Voltage Inductive Transformer Frequency Response up to 10 kHz

Measurement Based Linear and Nonlinear Time Invariant Representations for High Voltage Inductive Transformer Frequency Response up to 10 kHz

Surgical phase classification and operative skill assessment through spatial context aware CNNs and time-invariant feature extracting autoencoders

Automated surgical video analysis promises improved healthcare. We propose novel spatial context aware combined loss function for end-to-end Encoder-Decoder training for Surgical Phase Classification (SPC) on laparoscopic cholecystectomy (LC) videos. Proposed loss function leverages on fine-grained class activation maps obtained from fused multi-layer Layer-CAM for supervised learning of SPC, obtaining improved Layer-CAM explanations. Post classification, we introduce graph theory to incorporate known hierarchies of surgical phases. We report peak SPC accuracy of 96.16%, precision of 94.08% and recall of 90.02% on public dataset Cholec80, with 7 phases. Our proposed method utilizes just 73.5% of parameters as against existing state-of-the-art methodology, achieving improvement of 0.5% in accuracy, 1.76% in precision with comparable recall, with an order less standard deviation. We also propose DNN based surgical skill assessment methodology. This approach utilizes surgical phase prediction scores from the final fully-connected layer of spatial-context aware classifier to form multi-channel temporal signal of surgical phases. Time-invariant representation is obtained from this temporal signal through time- and frequency-domain analyses. Autoencoder based time-invariant features are utilized for reconstruction and identification of prominent peaks in dissimilarity curves. We devise a surgical skill measure (SSM) based on spatial-context aware temporal-prominence-of-peaks curve. SSM values are expected to be high when executed skillfully, aligning with expert assessed GOALS metric. We illustrate this trend on Cholec80 and m2cai16-tool datasets, in comparison with GOALS metric. Concurrence in the trend of SSM with respect to GOALS metric is obtained on these test videos, making it a promising step towards automated surgical skill assessment.

Estimate End-Winding Temperature for Water-Cooled Interior Permanent Magnet Motors Under Variable-Speed Driving Cycles: A Solution to the Exact Challenge

Since the temperature response of an electric machine under a constant duty can be obtained by a single experiment, it is the variable driving cycles that constitute the exact challenge in real-time thermal modeling. This article proposes an excitation-based methodology for real-time temperature estimation. Great detail is presented for the implementation procedure specific to estimating the end-winding temperature of a water-cooled interior permanent-magnet synchronous motor (IPMSM). In this methodology, a linear time-invariant (LTI) representation is devised for the speed-dependent parameter-varying heat-transfer problem of electric machines, followed by a generic solution via Duhamel’s theorem. Each of the response functions in the Duhamel’s integral thermal model is represented by a well-defined auxiliary problem. Computational fluid dynamics (CFD) simulations with calibrated parameters can be conducted to solve these auxiliary problems for the response functions. Because the CFD model features the least equivalent parameters that need experimental calibration, the present methodology can make the most of the geometry and material information and greatly reduce the experimental efforts compared to a data-driven method. Moreover, the present methodology can avoid the need for solving ill-posed inverse heat-transfer problems, and thus the resulted real-time thermal model is pretty reliable and robust.

A Novel Loss for Change Point Detection Models With Time-Invariant Representations

A Novel Loss for Change Point Detection Models With Time-Invariant Representations

Change Point Detection in Multi-Channel Time Series Via a Time-Invariant Representation

Change Point Detection in Multi-Channel Time Series Via a Time-Invariant Representation

Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm’s hidden variables

In this paper, we outline the research conducted by the first named author and his associates on the axiom-preserving, thus isotopic completion of quantum mechanics into hadronic mechanics according to the historical legacy by A. Einstein, B. Podolsky and N. Rosen that quantum mechanics is not a complete theory and review the ensuing exact representation of the magnetic moment and spin of the Deuteron in its ground state thanks to the isotopic completion of Pauli’s matrices with an explicit and concrete content of D. Bohm’s hidden variablelambda. We then outline the independent studies conducted by the second named author on the representation of the conventional Pauli’s matrices via geometric Clifford algebras. We finally show that the combination of the two studies allows a mathematically rigorous, numerically exact and time invariant geometric representation of the magnetic moment, spin and hidden variable of the Deuteron in its ground state.

Black-Box Impedance-Based Stability Assessment of Dynamic Interactions Between Converters and Grid

This paper proposes an impedance/admittance-based methodology for stability assessment of converter-based device connections to power systems. The proposed methodology is designed to model the dynamics of detailed black-box converter models, derived from impedance frequency response measurements. From the converter’s impedance frequency response measurements, a linear time-invariant (LTI) representation of its dynamics is obtained in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> domain using a vector fitting technique. This representation is incorporated in the state-space representation of the whole power system in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> domain, which is used to perform stability assessment considering traditional eigenvalue analysis and participation factors computation. The proposed methodology is tested in the 39 Bus New England system, including detailed models of a VSC windfarm and a modular multilevel converter (MMC) technology-based STATCOM. It has been found that the proposed impedance-based methodology is able to accurately predict the dynamic performance of black-box converter models, unstable operating conditions and converter control interactions between devices.

Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Studies have shown that Parkinson’s, epilepsy and other brain deficits are closely related to the ability of neurons to synchronize with their neighbors. Therefore, the neurobiological mechanism and synchronization behavior of neurons has attracted much attention in recent years. In this contribution, it is numerically investigated the complex nonlinear behaviour of the Hindmarsh–Rose neuron system through the time responses, system bifurcation diagram and Lyapunov exponent under different system parameters. The system presents different and complex dynamic behaviors with the variation of parameter. Then, the identification of the nonlinear dynamics and topologies of the Hindmarsh–Rose neural networks under unknown dynamical environment is discussed. By using the deterministic learning algorithm, the unknown dynamics and topologies of the Hindmarsh–Rose system are locally accurately identified. Additionally, the identified system dynamics can be stored and represented in the form of constant neural networks due to the convergence of system parameters. Finally, based on the time-invariant representation of system dynamics, a fast dynamical pattern recognition method via system synchronization is constructed. The achievements of this work will provide more incentives and possibilities for biological experiments and medical treatment as well as other related clinical researches, such as the quantifying and explaining of neurobiological mechanism, early diagnosis, classification and control (treatment) of neurologic diseases, such as Parkinson’s and epilepsy. Simulations are included to verify the effectiveness of the proposed method.

Change Point Detection in Time Series Data Using Autoencoders With a Time-Invariant Representation

Change point detection (CPD) aims to locate abrupt property changes in time series data. Recent CPD methods demonstrated the potential of using deep learning techniques, but often lack the ability to identify more subtle changes in the autocorrelation statistics of the signal and suffer from a high false alarm rate. To address these issues, we employ an autoencoder-based methodology with a novel loss function, through which the used autoencoders learn a partially time-invariant representation that is tailored for CPD. The result is a flexible method that allows the user to indicate whether change points should be sought in the time domain, frequency domain or both. Detectable change points include abrupt changes in the slope, mean, variance, autocorrelation function and frequency spectrum. We demonstrate that our proposed method is consistently highly competitive or superior to baseline methods on diverse simulated and real-life benchmark data sets. Finally, we mitigate the issue of false detection alarms through the use of a postprocessing procedure that combines a matched filter and a newly proposed change point score. We show that this combination drastically improves the performance of our method as well as all baseline methods.

Investigation of Linear Higher Harmonic Control Algorithm for Rotorcraft Vibration Reduction

Abstract A linear quadratic Gaussian (LQG) controller for active vibratory loads reduction in helicopters is proposed based on a revisited higher harmonic control (HHC) input by active trailing-edge flaps (ATEFs). Conventional individual blade control (IBC) input is redefined using N − 1/rev interblade phase lead, N/rev collective, and N + 1/rev interblade phase lag signals where 1/rev frequency modulation originates from the multiblade coordinate (MBC) transform. A Mach-scaled flap blade is designed and analyzed by the multibody dynamics analysis DYMORE. A linear time-invariant representation is identified from N/rev envelopes of the input and output responses obtained by DYMORE analysis. A matlab/simulink closed-loop control simulation is designed using the identified state-space realization. The N/rev vibratory loads are reduced up to 52% with flap deflections and the linear control results match well with the nonlinear responses obtained from DYMORE. Furthermore, the multivariable closed-loop stability estimated by the loop transfer functions using disk margin analysis reveals sufficient gain and phase margins.

Stable and dynamic representations of value in the prefrontal cortex.

Optimal decision-making requires that stimulus-value associations are kept up to date by constantly comparing the expected value of a stimulus with its experienced outcome. To do this, value information must be held in mind when a stimulus and outcome are separated in time. However, little is known about the neural mechanisms of working memory (WM) for value. Contradicting theories have suggested WM requires either persistent or transient neuronal activity, with stable or dynamic representations, respectively. To test these hypotheses, we recorded neuronal activity in the orbitofrontal and anterior cingulate cortex of two monkeys performing a valuation task. We found that features of all hypotheses were simultaneously present in prefrontal activity, and no single hypothesis was exclusively supported. Instead, mixed dynamics supported robust, time invariant value representations while also encoding the information in a temporally specific manner. We suggest that this hybrid coding is a critical mechanism supporting flexible cognitive abilities.

Energy-Based State-Space Representation of Modular Multilevel Converters with a Constant Equilibrium Point in Steady-State Operation

The internal currents and voltages of modular multilevel converters (MMCs) contain multiple frequency components in steady-state operation and remain time-periodic even when transformed into a synchronously rotating reference frame. This prevents a straightforward state-space representation, where a constant equilibrium point is reached and all state variables converge to constant values under steady-state conditions. Such steady-state time-invariant (SSTI) representations are needed for linearization and eigenvalue-based analysis of small-signal stability. This paper presents an energy-based model of an MMC with a modulation strategy where the insertion indices are compensated for the oscillations in the sum arm voltage. The formulation of the model allows for deriving, by the application of Park transformations at three different frequencies, an SSTI representation that accurately captures the internal dynamics of the MMC. This model can be simplified to a reduced-order model that maintains accurate reproduction of the external behavior at the ac- and dc-sides while neglecting some of the internal dynamics. The validity and accuracy of these two SSTI MMC models are verified by time-domain simulations and their utilization for eigenvalue-based analysis of MMC dynamics is demonstrated by examples.

Surface-atmosphere exchange in a box: Making the control volume a suitable representation for in-situ observations

Using the eddy-covariance (EC) method to determine net surface-atmosphere exchange relies on extensive simplifications of the mass balance concept. Among others, it is assumed that the 3-D flux field within a control volume is divergence-free, which is shown to be violated e.g. from large-eddy simulations. To practically evaluate the severity of these assumptions, case studies have monitored the surrounding of an EC tower, so the control volume can be represented more explicitly. Alternatively, diagnostic tests during data processing can be used to subset the EC data for periods that more likely fulfill the underlying assumptions. However, these existing methods are constrained either by their degree of realism, resource demand, temporal coverage, varying spatial representativeness, or combinations thereof.It is hypothesized that these deficiencies can be overcome by using the environmental response function (ERF) technique: Relating flux observations at very high spatio-temporal resolution to meteorological forcings and surface properties, and utilizing the extracted relationships to map a single, regular and stationary control volume explicitly in 3-D space and time. Here, the novel ERF virtual control volume (VCV) concept and its implications are derived, and Xu et al. (this issue) are presenting its first practical application.Initial results show that even from a single EC tower, ERF-VCV reduces advective errors by at least one order of magnitude, and incorporates net low-frequency flux contributions. In the same process tower location bias is treated through attaining a fixed-frame, thus equitable and time-invariant representation of the net surface-atmosphere exchange across a target domain. With regard to the frequently observed non-closure of the surface energy balance, this offers the potential for reconciling “spatial heterogeneity” and “storage term” theories. In extension, ERF promises a rectifying observational operator for unbiased model-data comparison, assimilation, and process representation at model grid scale.

Two Body IsoElectronium Model of the Heliumic Systems

In preceding works, one of us (R. M. Santilli) has shown that, according to quantum chemistry, identical electrons cannot create the strong bond occurring in molecular structures due to their strongly repulsive Coulomb interaction; has constructed hadronic chemistry as a non-unitary covering of quantum chemistry solely valid at mutual distances of 10-13cm; has introduced contact non-Hamiltonian interactions in the deep penetration of the wavepackets of valence electrons that overcomes said Coulomb repulsion, resulting in a strongly attractive bond of valence electron pairs in singlet called ’isoelectronium’ and shown that the new valence bond allows an exact and time invariant representation of the binding energy of the hydrogen and water molecules. By using these advances and our inference that (from the fact that an atomic lone pair of electrons form a coordinate covalent bond identified by G. N. Lewis) the lone pairs of electrons are indeed isoelectronium, in this paper we present, apparently for the first time, a new structure model of the Helium atom under the name of Iso-Helium, in which the two electrons of a given orbital are strongly coupled into the isoelectronium that provided a quantitative description of Pauli exclusion principle. In particular, as a result of the strongly bound state of Santilli isoelectronium, the iso-Helium reduces to be a two-body system, thus admitting exact analytic solution. The presented analytic solution is applicable to all Helium-like systems. Using it we have calculated effective charge on the nuclei of Helium-like systems that are in excellent agreement with the literature values.

An approach to design MIMO FO controllers for unstable nonlinear plants

This paper develops an approach to control unstable nonlinear multi-inputs multi-output (MIMO) square plants using MIMO fractional order (FO) controllers. The controller design uses the linear time invariant (LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix (TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function (TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D (Derivative) TF is related to a FO TF of the form D±, ± = [0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.

Santilli Synthesis of the Neutron According to Hadronic Mechanics

In 1920 H. Rutherford conjectured that neutron is a compressed hydrogen atom in the core of the stars. W. Pauli noted that such synthesis of neutron violates the conservation of the angular momentum. Therefore, E. Fermi proposed emission of massless particle, called "neutrino". However, R.M. Santilli more recently noted that, even though the angular angular momentum would be conserved, the neutrino hypothesis does not allow non-relativistic quantum mechanics to be valid because the rest energy of the neutron is bigger than the sum of the rest energies of the proton and electron, under these conditions Schrodinger equation becomes inconsistent. Similarly, Santilli showed that relativistic quantum mechanics is also inapplicable (rather than violated) because, even though exactly valid for the electron at large distance from the proton in the hydrogen atom, the celebrated Dirac's equation is clearly inapplicable for the representation of electron when immersed inside the proton. In this paper, we study Santilli's decades of mathematical, theoretical and experimental research, first for the construction of the covering hadronic mechanics, and then the resulting numerically exact and time invariant representation at the non-relativistic and relativistic levels of "all" chararcteristics of the neutron in its synthesis from a proton and an electron. In particular, we show that, within said covering context, the representation of proton as an extended particle implies the existence of an orbital angular momentum of the electron within the hyperdense proton which is totally non-existence for quantum mechanics, under which the total angular momentum is conserved without any need for the conjectural neutrino. We finally study Santilli's suggestive hypothesis of the "etherino" as a longitudinal impulse (rather than particle) from the ether as a universal substratum that delivers missing energy for the synthesis of the neutron.

Exact and Invariant Representation of Nuclear Magnetic Moments and Spins According to Hadronic Mechanics

In order to render this paper minimally self-sufficient, we review and specialize the main structure of the isomathematics to nuclear constituents as extended and deformable charge distributions under linear and non-linear, local and non-local and Hamiltonian as well non-Hamiltonian interactions; we then review and specialize for the nuclear structure the main laws of the isotopic branch of hadronic mechanics known as isomechanics; we review and specialize the method for turning quantum mechanical nuclear models for point-like nucleons into covering isomechanical models for extended and deformable constituents under the most general known realization of strong interactions; we then review and specialize to nuclear structures the consequential notion of isoparticles; we then review the ensuing, first known, numerically exact and time invariant representation of the magnetic moments of stable nuclides; we then review the structure of the neutron as a bound state according to isomechanics of an isoproton and an isoelectron; and we finally review the ensuing three-body structure of the Deuteron. Via the use of the preceding advances. We then present, apparently for the first time, a numerically exact and time invariant representation of the spin of stable nuclides, firstly, via their approximation as isotopic bound states of isodeuterons, isoneutron and isoprotons, and secondly, via their reduction to isobound states of isoprotons and isoelectrons. Some observations on the nuclear configurations so obtained have also been presented in the case of the first model and in view of the second option we have identified in isoelectrons the nuclear glue which tightly holds isonucleons of stable nuclide in the atomic nucleus in the preferred orientation of their intrinsic spins. In Appendix A, we provide a technical review specialized for the first time to nuclear physics of the Lie-Santilli theory and its main application to the notion of isoparticles as isoirreducible isounitary isorepresentations of the Lorentz-Poincare-Santilli isosymmetry.

Studies on Santilli Three-Body Model of the Deuteron According to Hadronic Mechanics

In this paper, we outline the inapplicability (rather than the violation) of quantum mechanics for the representation of the synthesis of the neutron from the Hydrogen atom in the core of a star, and we outline the corresponding inability of quantum mechanics for a consistent representation of all characteristics of the deuteron as a two-body state of one proton and one neutron in its ground state. We then outline the first representation of all characteristics of the neutron achieved by R. M. Santilli via a a generalized two-body bound state of one proton and one electron in conditions of total mutual penetration according to the laws of hadronic mechanics, thus implying the mutation of particles into isoparticles under the Lorentz-Santilli isosymmetry. We then outline the first representation of all characteristics of the deuteron also achieved by R. M. Santilli via a generalized three-body bound state of two isoprotons and one isoelectron, including the first known exact and time invariant representation of the deuteron spin, magnetic moment, binding energy, stability, charge radius, dipole moment, etc. We finally study further advances of Santilli three-body model of the deuteron in preparation of its extension to all nuclei, such as: the admission of exact analytic solution for the structure of the deuteron as a restricted three-body system; the validity in first approximation of the structure of the deuteron as a two-body system of one isoproton and one iso neutron; the importance for the representation of experimental data of the deformability of the charge distribution of the proton and the neutron which is prohibited by quantum mechanics but readily permitted by hadronic mechanics in the notion of isoparticle; and other aspects.

Identification of Parameterized Gray-Box State-Space Systems: From a Black-Box Linear Time-Invariant Representation to a Structured One

While determining the order as well as the matrices of a black-box linear state-space model is now an easy problem to solve, it is well-known that the estimated (fully parameterized) state-space matrices are unique modulo a non-singular similarity transformation matrix. This could have serious consequences if the system being identified is a real physical system. Indeed, if the true model contains physical parameters, then the identified system could no longer have the physical parameters in a form that can be extracted easily. By assuming that the system has been identified consistently in a fully parameterized form, the question addressed in this paper then is how to recover the physical parameters from this initially estimated black-box form. Two solutions to solve such a parameterization problem are more precisely introduced. First, a solution based on a null-space-based reformulation of a set of equations arising from the aforementioned similarity transformation problem is considered. Second, an algorithm dedicated to nonsmooth optimization is presented to transform the initial fully parameterized model into the structured state-space parameterization of the system to be identified. A specific constraint on the similarity transformation between both system representations is added to avoid singularity. By assuming that the physical state-space form is identifiable and the initial fully parameterized model is consistent, it is proved that the global solutions of these two optimization problems are unique. The proposed algorithms are presented, along with an example of a physical system.