Inverse Theory Research Articles

Assessment of State-Space Building Energy System Models in Terms of Stability and Controllability

Building energy management system involves the development of control strategies for the heating, ventilation, and air-conditioning (HVAC), as well as lighting, systems. Building energy modeling is a significant part of designing such strategies. In order to analyze the feasibility of a building energy system model for any desired control strategy, a mathematical assessment tool is developed in this paper. A multi-input multi-output (MIMO) building energy system model, consisting of an outdoor wall, an external wall, two partition walls, one roof, and a ceiling, has been considered as the virtual test setup. A methodology for conducting stability and controllability assessment tests on the building energy model is proposed using inverse dynamics input theory (IDIT). IDIT enables the decoupling of control variables so as to enable the conversion of an MIMO system to a number of independent single-input single-output systems. The controllability is assessed based on the design properties for continuous systems: asymptotes and transmission zeros. The results show that the relative humidity and air temperature of the building space were controllable for all operating points; however, in unconditioned situations, where the humidity levels of the building space were greater than that of the outdoor levels, the models were unstable.

Q-compensated full waveform inversion for velocity and density

Full waveform inversion (FWI) makes full use of the seismic waveforms to find high-resolution velocity and density models by minimising residuals between the calculated and recorded data. Q attenuation widely exists in the subsurface media, leading to weak amplitude and misplacement of reflectors. However, the commonly used Q-compensated FWI (QFWI) based on the second-order wave equation has difficulties in simultaneously inverting velocity and density fields. A QFWI method based on new first-order viscoacoustic quasi-differential equations is proposed to simultaneously produce velocity and density fields. Based on the adjoint state inversion theory, Q-compensated forward-propagated operators, adjoint operators, and gradient equations are derived using the newly derived first-order viscoacoustic quasi-differential wave equations. The time-domain multi-scale decomposition method is introduced to update the velocity and density models from a low to a high wavenumber. Numerical examples on an actual work area model and a modified attenuating Marmousi model show that the proposed QFWI method produces higher-accuracy velocity and density models with iterations by correcting the Q attenuation than the conventional acoustic FWI. Even when the Q model is extremely inaccurate, the proposed QFWI obtains acceptable inversion results. Compared to the conventional QFWI, our QFWI better inverts velocity field in the case of an inaccurate density model. Finally, we verify the adaptability of our QFWI to field data.

A cross-country analysis of the relationship between human capital and foreign direct investment

PurposeThe Zhang–Markusen (Z-M) inverse U-shape theory uses education as a human capital variable to investigate the impact of educational attainment on foreign direct investment (FDI) inflows to a country. The objective of this research is to empirically test this theory in a cross-country framework.Design/methodology/approachFixed effect panel regression has been used to test the Z-M hypothesis for 172 countries for the period 1990–2015. For the purpose of this study, countries were divided into four groups as per the World Bank classification: Low-income economies, lower middle-income countries, upper middle-income economies and high-income economies.FindingsThe findings of this study reinforce the proposition that macroeconomic factors are the major determinants of FDI inflows into various countries. The authors find that the size of the market measured by gross domestic product (GDP), the growth potential of the market measured by real GDP growth rate and the availability of infrastructure are the major factors that enhance the attractiveness of a country as an FDI destination.Originality/valueThough the Z-M theory has been empirically tested in cross-country frameworks, no consensus has been reached. Thus, it is interesting to look again at the validity of the Z-M hypothesis using data covering longer and more recent periods. The study includes both macroeconomic and human capital determinants of FDI, so as to arrive at a comprehensive model explaining the FDI flows into various countries.

Robust Static Structural System Identification Using Rotations

Deflections are commonly measured in the static structural system identification of structures. Comparatively less attention has been paid to the possibility of measuring rotations for structural system identification purposes, despite the many advantages of using inclinometers, such as a high resolution and being reference free. Although some work using rotations can be found in the literature, this paper, for the very first time, proposes a statistical analysis that justifies the theoretical advantage of measuring rotations. The analytical expressions for the target parameters are obtained via static structural system identification using the constrained observability method first. Combined with the inverse distribution theory, the probability density function of the estimations of the target parameters can be obtained. Comparative studies on a simply supported bridge and a frame structure demonstrate the advantage of measuring rotations regarding the unbiasedness and the extent of variation in the estimations. To achieve robust parameter estimations, four strategies to use redundant rotations are proposed and compared. Numerical verifications on a bridge structure and a high-rise building have shown promising results.

Anti-cavitation optimal design and experimental research on tidal turbines based on improved inverse BEM

To capture tidal current energy to the greatest extent possible, the turbines must to be large in-scale. When the turbine is close to the free surface, with high energy-flow density, unsteady cavitation on the blade surface has a large negative impact on the efficiency and life of the turbine. This paper presents a revised theoretical analysis of hydrodynamics optimization of horizontal-axis tidal turbines, including cavitation effects, based on improved inverse blade element momentum (BEM) theory. The cavitation performance is reflected by the minimum pressure coefficient peak value on the blade surface, based on which the cavitation prediction model is established. The cavitation prediction model and improved inverse BEM theory are combined; additionally, the mathematical model of multi-objective optimization is established. To verify the effectiveness of the proposed methodology, a 10-kW current turbine was designed, and computational fluid dynamics (CFD) was used to validate the hydrodynamics characteristics of the resulting turbine blades. The experimental model was designed according to the similarity theory, and a cavitation mechanism visualization experiment and a performance parameter test experiment were carried out in a cavitation water tunnel. The simulation and experimental results revealed that the proposed design method achieves the optimization goal.

Non-polynomial zigzag theories with C° finite element formulation for buckling analysis of laminated composite and sandwich plates

In this present work, non-polynomial zigzag theories (algebraic zigzag theory (AZT), exponential zigzag theory (EZT), hyperbolic zigzag theory (HZT), inverse hyperbolic zigzag theory (IZT), logarithmic zigzag theory (LZT) and trigonometric zigzag theory (TZT)) are performed for buckling response of laminated composite and sandwich plates. The present models assume parabolic variation of out – plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag models able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. An efficient eight noded C° continuous isoparametric serendipity element is established and employed to examine the buckling analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical examples are carried out to study the effects of span to thickness ratio, ply orientation, lay-up number, modular ratio, loading condition and boundary condition on the buckling response. To ensure the capability of the proposed models, higher modes of buckling are obtained for laminated plates and sandwich plates. Further, the efficiency and superiority of the proposed models is ascertained by comparing it with 3 D elasticity solution and also with various existing shear deformation theories in the literature. Most remarkably, the present models are accurately estimates the buckling load parameter and they are insensitive of shear-locking.

SeReMpy: Seismic reservoir modeling Python library

Seismic reservoir characterization is a subfield of geophysics that combines seismic and rock-physics modeling with mathematical inverse theory to predict reservoir variables from the measured seismic data. An open-source comprehensive modeling library that includes the main concepts and tools is still missing. We have developed a Python library called SeReMpy with state-of-the-art of seismic reservoir modeling for reservoir properties characterization using seismic and rock-physics models and Bayesian inverse theory. The most innovative component of the library is the Bayesian seismic and rock-physics inversion to predict the spatial distribution of petrophysical and elastic properties from seismic data. The inversion algorithms include Bayesian analytical solutions of the linear-Gaussian inverse problem and Markov chain Monte Carlo (MCMC) numerical methods for nonlinear problems. The library includes four modules: geostatistics, rock physics, facies, and inversion, as well as several scripts with illustrative examples and applications. We illustrate the use of the functions of the module and develop codes for practical inversion problems using synthetic and real data. The applications include a rock-physics model for the prediction of elastic properties and facies using well-log data, a geostatistical simulation of continuous and discrete properties using well logs, a geostatistical interpolation and simulation of 2D maps of temperature, an elastic inversion of partial stacked seismograms with Bayesian linearized amplitude-variation-with-offset inversion, a rock-physics inversion of partial stacked seismograms with MCMC methods, and a 2D seismic inversion.

Finite-difference approximation of the inverse Sturm–Liouville problem with frozen argument

This paper deals with the discrete system being the finite-difference approximation of the Sturm–Liouville problem with frozen argument. The inverse problem theory is developed for this discrete system. We describe the two principal cases: degenerate and non-degenerate. For these two cases, appropriate inverse problems statements are provided, uniqueness theorems are proved, and reconstruction algorithms are obtained. Moreover, the relationship between the eigenvalues of the continuous problem and its finite-difference approximation is investigated. We obtain the “correction terms” for approximation of the discrete problem eigenvalues by using the eigenvalues of the continuous problem. Relying on these results, we develop a numerical algorithm for recovering the potential of the Sturm–Liouville operator with frozen argument from a finite set of eigenvalues. The effectiveness of this algorithm is illustrated by numerical examples.

Numerical Analysis of Thick Isotropic and Transversely Isotropic Plates in Bending using FE Based New Inverse Shear Deformation Theory

In this work, using new inverse trigonometric kinematic displacement function, the bending solution of simply supported isotropic and transversely isotopic thin, moderately thin and thick square plates with aspect ratio variations is given. The paper introduces a new inverse trigonometric shear deformation theory (nITSDT) for the bi-directional bending study, which is variationally compatible. The transverse shear stress can be obtained directly from the constitutive relationships on the top and bottom surfaces of the plate that satisfy the shear stress free surface conditions, so the theory does not need a factor for shear correction. The dynamic version of the virtual work principle is used to obtain the governing equations and boundary conditions of the theory. The Finite Element (FE) solution has been developed using MATLAB code based on the present theory for simply supported laminated composite plates. In order to illustrate the efficiency of the proposed theory, the results of displacements and stresses are compared with those of other refined theories and exact solution. The findings obtained from the use of the theory are found to agree well with the precise results of elasticity.

Remarks on Modeling the Oil Film Generation of Rod Seals

The oil film generation of a U-cup rod seal and the oil film thickness on the rod after outstroke were analyzed analytically, numerically, and experimentally. The analyzed sealing system consists of an unmodified, commercially available U-cup, a polished rod, and mineral oil. The inverse theory of hydrodynamic lubrication (IHL) and an elastohydrodynamic lubrication (EHL) model—both based on the Reynolds equation for thin lubricating films—were utilized to simulate the oil film generation. In the EHL analysis, physical parameters and numerical EHL parameters were varied. Both the analytical and numerical results for the varied parameters show that the film thickness follows a square-root function (i.e., with a function exponent of 0.5) with respect to the product of dynamic viscosity and rod speed, also referred to as the duty parameter. In comparison to the analytical and numerical results, the film thickness obtained via ellipsometry measurements is a function of the duty parameter with an exponent of approximately 0.85. Possible causes for the discrepancy between theory and experiments are discussed. A potential remedy for the modeling gap is proposed.

Estimation of electron fluxes in the Earth's geostationary orbit with Tikhonov regularization during a magnetically quiet period

Electron energy fluxes in the Earth's outer radiation belt are estimated using an inverse theory of the Tikhonov regularization based upon observations in geostationary orbits. Particle Detector (PD) experiment aboard a geostationary satellite GEO-KOMPSAT-2A (GK2A) at a geographic longitude of 128.2°E provided observations of electrons within a 150–2,400 keV energy range with an unprecedented energy resolution of ΔE/E in the range of 5–25%. Instrument response functions, calculated with Monte-Carlo simulations, are deconvoluted with electron observations. Using regularization parameters determined from Generalized Cross Validation (GCV), the Tikhonov method was applied to observations made during a geomagnetically quiet period. This Tikhonov regularization method, now possible for observations in the Earth's radiation belt for the first time, allows direct inference of electron fluxes without resorting to predetermined functional forms. Comparisons of our results with those from conventional methods indicate differences among the results as large as ∼200%.

Influence of porosity distribution on static and buckling responses of porous functionally graded plates

This article studies the effect of porosity distribution on static and buckling response of a functionally graded (FG) porous plate with all its four edges simply supported and subjected to a transverse load. The plate’s displacement field is approximated based on an inverse hyperbolic shear deformation theory (IHSDT) involving five variables. In this theory, inplane displacements vary as an inverse hyperbolic function through the plate thickness, so account for non-linear variation of transverse shear stresses and satisfies traction free boundary conditions on the surfaces of plate without the need of any shear correction factors. The governing equations of motion are derived using the principle of virtual work, and thus, the expressions of its strain energy and work done are obtained. Effective material properties of porous plate are assumed with an additional term of porosity in the direction of thickness. Power-law is used for continuous variation of material properties along the thickness direction. In this study, five types of porosity distribution functions are considered. The effect of the porosity parameter, the power-law exponent, side-thickness ratio, and aspect ratio on the static and buckling responses of the porous FG plate is evaluated. In problem-solving, the Navier solution technique is used to obtain the exact solutions. The non-dimensional deflections and critical buckling loads of FG porous plate are thus obtained. The results are compared with available results in the literature, and good agreement is found. Moreover, the results are presented to study the effects of various parameters on the dimensionless deflections, stresses, and critical uni-axial and bi-axial buckling loads.

The Non-Unicity of the Film Thickness in the Hydrodynamic Lubrication: Novel Approach Generating Equivalent Micro-Grooves and Roughness

Since the 1960s, all studies have assumed that a film thickness “<i>h</i>” provides a unique pressure field “<i>p</i>” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that with different ratios of the averaged film thickness to the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known from Patir and Cheng theory.

Scholte Wave Dispersion Modeling and Subsequent Application in Seabed Shear-Wave Velocity Profile Inversion

Recent studies have illustrated that the Multichannel Analysis of Surface Waves (MASW) method is an effective geoacoustic parameter inversion tool. This particular tool employs the dispersion property of broadband Scholte-type surface wave signals, which propagate along the interface between the sea water and seafloor. It is of critical importance to establish the theoretical Scholte wave dispersion curve computation model. In this typical study, the stiffness matrix method is introduced to compute the phase speed of the Scholte wave in a layered ocean environment with an elastic bottom. By computing the phase velocity in environments with a typical complexly varying seabed, it is observed that the coupling phenomenon occurs among Scholte waves corresponding to the fundamental mode and the first higher-order mode for the model with a low shear-velocity layer. Afterwards, few differences are highlighted, which should be taken into consideration while applying the MASW method in the seabed. Finally, based on the ingeniously developed nonlinear Bayesian inversion theory, the seafloor shear wave velocity profile in the southern Yellow Sea of China is inverted by employing multi-order Scholte wave dispersion curves. These inversion results illustrate that the shear wave speed is below 700 m/s in the upper layers of bottom sediments. Due to the alternation of argillaceous layers and sandy layers in the experimental area, there are several low-shear-wave-velocity layers in the inversion profile.

Nonlinear free vibration analysis of laminated composite plates and shell panels using non-polynomial higher-order shear deformation theory

In the present work, nonlinear free vibration analysis of composite laminated plates and shallow cylindrical/spherical/hyperboloid shell panels considering geometric nonlinearity is carried out using non-polynomial inverse trigonometric higher-order shear deformation theory with seven degrees of freedo (DOFs). The present theory assumes parabolic variation of out-of-plane stresses and satisfies traction-free boundary conditions on the top and bottom surfaces of the composite as a priori. A nonlinear finite element model is developed and applied to obtain discretized nonlinear equations. The geometric nonlinearity in sense of Green-Lagrange considering von-Kármán assumptions is incorporated in formulation. An eight noded efficient C 0 continuous isoparametric rectangular finite element is implemented in the present nonlinear analysis. The efficacy and accuracy of the present theory and finite element model is validated with the available literature results. For the analysis, various types of plates and shell panels with different material properties, lamination schemes, thickness ratios, aspect ratios, modular ratios, curvature ratios, and boundary conditions are considered. The effects of these different geometric and material properties on nonlinear frequency ratios at various amplitude ratios are examined in detail.

Comparison of Single-Well Microseismic Focal Mechanism Inversions with Different Source Models

ABSTRACT Through downhole monitoring, the focal mechanisms of microearthquakes can be quantitatively determined, thus providing valuable information for characterizing the fracturing process and the in situ stress status. The double-couple (DC) and moment tensor (MT) source models are commonly used to study microearthquakes. However, the DC model fails to include non-DC mechanisms, and MT inversion from single-well data is still challenging. One possible way to address this is using the shear–tensile general dislocation (GD) source model. We provide a detailed comparison of the DC, GD, and MT models, and introduce the differences in their modeling and inversion theories. These three models are described by four, five, and six parameters, and correspond to a single point, a straight line, and the entire space in the Hudson source-type plots, respectively. Both the DC and GD models yield nonlinear inversions, whereas the MT inversion is linear. Synthetic tests set up from a field single-well monitoring case are performed to study the resolvability of the DC, GD, and MT models in single-well focal mechanism inversions. The results indicate that the inversion error increases from DC→GD→MT for a single-well acquisition system, and the GD and DC inversions are both stable, whereas the MT inversion deviates from the inputs in cases with a perfectly vertical receiver array, 5% model velocity perturbations, 10 m horizontal source location errors, or 40% noise levels. We also find that the focal mechanism inversion mainly depends on the horizontal source–receiver azimuth coverage, and that the nonvertical well direction is helpful for constraining single-well inversions. According to our study, focal mechanism inversions based on the GD model can obtain reliable solutions from near-vertical single-well data, which will help improve non-DC earthquake studies.

Modified Variable Structure Estimation and Control for Constrained Landing on Mars

Landing on Mars is one the most important space missions undergoing various system and environmental uncertainties. Subsequently, an exact model to represent the dynamic system cannot be provided in advance. In this regard, the present paper has focused on designing an integrated estimation and control algorithm bringing accurate navigation in the presence of uncertainties for the landing problem. The proposed algorithm has been shaped based on the variable structure control framework. This algorithm alleviates the requirement of Jacobian via substituting statistical linearization for the analytical one and utilizing generalized matrix inverse theory. Performance of the proposed algorithm has been investigated via Monte Carlo simulations in the presence of different uncertainties including stochastic initial conditions of the coupled Mars lander dynamics, atmosphere instability and modeling errors of the exerted forces and moments, time delay of actuators, geometric constraint of the landing site as well as the saturation limitations of actuators. In addition, the obtained results have been compared to the results obtained from combination of well-known extended Kalman filter and PID controller. This study clearly shows the precise and robust performance of the proposed integrated estimation and control algorithm and proves its superiority against existing widespread algorithms.

Periodic Jacobi operators with complex coefficients

We present certain results on the direct and inverse spectral theory of the Jacobi operator with complex periodic coefficients. For instance, we show that any N -th degree polynomial whose leading coefficient is (-1)^N is the Hill discriminant of finitely many discrete N -periodic Schrödinger operators (Theorem 1). Also, in the case where the spectrum is a closed interval we prove a result (Theorem 2) which is the analog of Borg's Theorem for the non-self-adjoint Jacobi case.

An inverse spectral problem for second-order functional-differential pencils with two delays

Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such problems were obtained only in one very particular situation. Here we address this gap by obtaining necessary and sufficient conditions in the case of functional-differential pencils possessing a more general form along with a nonlinear dependence on the spectral parameter. For this purpose, we develop the so-called transformation operator approach, which allows reducing the inverse problem to a nonlinear vectorial integral equation. In Appendix A, we obtain as a corollary the analogous result for Sturm–Liouville operators with delay. Remarkably, the present paper is the first work dealing with an inverse problem for functional-differential pencils in any form. Besides generality of the pencils under consideration, an important advantage of studying the inverse problem for them is the possibility of recovering both delayed terms, which is impossible for the Sturm–Liouville operators with two delays. The latter, in turn, is illustrated even for different values of these two delays by a counterexample in Appendix B. We also provide a brief survey on the contemporary state of the inverse spectral theory for operators with delay observing recently answered long-term open questions.

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

In the present work, the doubly curved spherical and cylindrical laminated composite shells are modelled and analysed in the framework of non-polynomial axiomatic approach. The inverse hyperbolic shear deformation theory originally developed for the laminated composite plates is extended to model the deformation characteristics of laminated composite shells. The mathematical formulation is developed under the assumption of linear structural kinematics and linear-elastic-orthotropic material behaviour. The governing equations of the model are obtained using the principle of virtual work and solved in exact manner for simply supported boundary conditions following the Navier solution methodology. The bending response of thick and thin spherical and cylindrical shells subjected to different types of transverse loads such as point load, uniform load and sinusoidal load is analysed in the framework of developed methodology. The obtained results due to inverse hyperbolic shear deformation theory are compared with other shell theories and on the basis of this comparison, the validity and applicability of the inverse hyperbolic shear deformation theory for doubly curved spherical and cylindrical shells is ensured.