Inverse Theory Research Articles

Design and analysis of inverse fuzzysoft set for triangular and trapezoidal membership function in decision making

Decision making plays a vital role within uncertain, imprecise situations in recent years. A numerical actualize called soft set by Molodtsov was started to bargain uncertain condition. Herein article, inverse triangular and trapezoidal fuzzy soft set theory is analyzed in decision making. Inverse fuzzysoft set theory is an extension of fuzzy soft set theory which gives deeper insights in decision making and gives a technique to portray the character of each object in the universe. An application of inverse triangular and trapezoidal fuzzy soft set is established in the course of case study in multi-criteria decision making.

Nonextensive statistical mechanics for robust physical parameter estimation: the role of entropic index

The problem of inferencing parameters of complex systems from measured data has been extensively studied based on the inverse problem theory. Classically, an inverse problem is formulated as an optimisation task in which the objective function is based on the maximisation of Boltzmann–Gibbs entropy under appropriate constraints. In this classical framework, errors are assumed to follow a Gaussian-behaviour. However, in many situations, the errors are non-Gaussian and therefore the classical approach is predestined to failure. To mitigate the inverse-problem sensitivity to non-Gaussian errors, we have considered in this study a q-generalised objective function within the context of nonextensive statistical mechanics. In this regard, the errors are assumed to follow the q-Gaussian distribution, which arises from the maximisation of the nonadditive Tsallis entropy. We study the robustness properties of the q-objective function, which is a generalisation of the classical objective function, through the so-called influence function. In this work, we analyse and discuss from an analytical and numerical perspective, the role of the entropic index (q) of Tsallis entropy on the effectiveness and robustness in the inference of physical parameters from with strongly noisy-data. In this perspective, we show that exists an optimum value for the entropic index at the limit $$q \rightarrow 3$$ , which implies in $$\delta _q = 3 - q \approx 0$$ in the q-objective function. To validate our proposal, we consider a classic geophysical inverse problem by employing a realistic geological model and a data set contaminated by spikes.

Optimization inversion analysis of a geo-stress field in a deep mine area: a case study

The characteristics and evolution of the geo-stress field are the research bases of overburden migration, roadway surrounding rock stability, and dynamic disaster prevention in deep coal mines. However, the present understanding of mine geological stress mainly depends on measurements obtained at a few discrete points, leading to obviously insufficient knowledge of the geo-stress field in the whole mining area. In this study, a novel optimal inversion analysis model of the geo-stress field was established based on multiobjective constraint technology, solid mechanics, optimization analysis, and stress inversion theory. Then, a 3D numerical simulation analysis model with large-scale general finite element software as the solver was constructed for the optimization of the boundary conditions of the geo-stress field. This simulation model identified the key links between the stress field boundary loads and the actual measurement data by directly solving the multiobjective optimization problem. Six on-site measurement points were selected at the Xinji No. 1 mine, and the magnitude and orientation of the geo-stress at these points were measured with the hollow inclusion strain gauge method. The distribution of the geo-stress and the main influential factors were then analyzed numerically. The results of the study are of great significance for investigating the geo-stress distribution.

Hybrid Systems, Iterative Learning Control, and Non-minimum Phase

Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples of systems benefiting from hybrid modeling. They are also prime examples of repetitive processes; gait cycles in walking, product assembly tasks in robotic manipulation, and material deposition in additive manufacturing. Thus, they would also benefit substantially from Iterative Learning Control (ILC), a class of feedforward controllers for repetitive systems that achieve high performance in output reference tracking by learning from the errors of past process cycles. However, the literature is bereft of ILC syntheses from hybrid models. The main thrust of this dissertation is to provide a boradly applicable theory of ILC for deterministic, discrete-time hybrid systems, i.e. piecewise defined (PWD) systems. In summary, the three main gaps addressed by this dissertation are (1) the lack of compatibility between existing hybrid modeling frameworks and ILC synthesis techniques, (2) the failure of ILC based on Newton's method (NILC) for systems with unstable inverses, and (3) the lack of inversion and stable inversion theory for piecewise affine (PWA) systems (a subset of PWD systems). These issues are addressed by (1) developing a closed-form representation for PWD systems, (2) developing a new ILC framework informed by NILC but with the new ability to incorporate stabilizing model inversion techniques, and (3) deriving conventional and stable model inversion theories for PWA systems.

Robust adaptive input-output control for a class of modular robotic systems via inverse optimality theory

This paper introduces a model-based robust adaptive input-output control framework for a family of robotic systems that include under-actuation, nonholonomic, and constrained properties. The proposed control framework can provide fast and effective controller generation for modular robotic systems (MRS) with interchangeable subsystems. The controller was first derived based on the general properties of nonholonomic robotic dynamic models while considering under-actuation and constraints. Then the adaptive control technique is introduced to overcome the effects such as inertia and force uncertainties. Robust augmentation is implemented via inverse optimality theory, which is verified with respect to a meaningful cost function. A simulation study on an aerial manipulator system with model uncertainty and disturbance was provided to demonstrate the characteristics and effectiveness of the proposed controller.

Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation

Abstract. Hourly precipitation over a region is often simultaneously simulated by numerical models and observed by multiple data sources. An accurate precipitation representation based on all available information is a valuable result for numerous applications and a critical aspect of climate monitoring. The inverse problem theory offers an ideal framework for the combination of observations with a numerical model background. In particular, we have considered a modified ensemble optimal interpolation scheme. The deviations between background and observations are used to adjust for deficiencies in the ensemble. A data transformation based on Gaussian anamorphosis has been used to optimally exploit the potential of the spatial analysis, given that precipitation is approximated with a gamma distribution and the spatial analysis requires normally distributed variables. For each point, the spatial analysis returns the shape and rate parameters of its gamma distribution. The ensemble-based statistical interpolation scheme with Gaussian anamorphosis for precipitation (EnSI-GAP) is implemented in a way that the covariance matrices are locally stationary, and the background error covariance matrix undergoes a localization process. Concepts and methods that are usually found in data assimilation are here applied to spatial analysis, where they have been adapted in an original way to represent precipitation at finer spatial scales than those resolved by the background, at least where the observational network is dense enough. The EnSI-GAP setup requires the specification of a restricted number of parameters, and specifically, the explicit values of the error variances are not needed, since they are inferred from the available data. The examples of applications presented over Norway provide a better understanding of EnSI-GAP. The data sources considered are those typically used at national meteorological services, such as local area models, weather radars, and in situ observations. For this last data source, measurements from both traditional and opportunistic sensors have been considered.

Fracture detection from Azimuth-dependent seismic inversion in joint time\u2013frequency domain

Detection of fracture properties can be implemented using azimuth-dependent seismic inversion for optimal model parameters in time or frequency domain. Considering the respective potentials for sensitivities of inversion resolution and anti-noise performance in time and frequency domain, we propose a more robust azimuth-dependent seismic inversion method to achieve fracture detection by combining the Bayesian inference and joint time–frequency-domain inversion theory. Both Cauchy Sparse and low-frequency constraint regularizations are introduced to reduce multi-solvability of model space and improve inversion reliability of model parameters. Synthetic data examples demonstrate that the frequency bandwidth of inversion result is almost the same for time, frequency and joint time–frequency domain inversion in seismic dominant frequency band using the noise-free data, but the frequency bandwidth in joint time–frequency domain is larger than that in time and frequency domains using low- signal-to-noise-ratio (SNR) data. The results of cross-correlation coefficients validate that the joint time–frequency-domain inversion retains both the excellent characteristics of high resolution in frequency-domain inversion and the advantage of strong anti-noise ability in time-domain inversion. A field data example further demonstrates that our proposed inversion approach in joint time–frequency domain may provide a more stable technique for fracture detection in fractured reservoirs.

A shape-finding approach of tree-like structure based on grouping strategy and generalized inverse matrix theory

Unstable link models in equilibrium transfer their loads only through axial forces and the generalized inverse matrix theory can be used in the shape-finding analysis of unstable link structures. According to this principle and the generalized inverse matrix theory, a shape-finding approach for tree-like structure is proposed, which forms a progressive process to update the shape of branching model until the potential energy of the model reaches minimum. In the proposed approach, members of the branching model are grouped and the total length of the members in the same group are constrained. The total length can be redistributed among the members in the same group in the shape-finding process. The redistribution of length is particularly useful for the shape-finding of tree-like structure as it can avoid the generation of inefficient members in the shape-found structure. Changing the grouping mode of members is a way to generate multiple schemes of structural shapes. Numerical examples illustrate the features of the approach and validate its effectiveness.

Multistatic Specular Meteor Radar Network in Peru: System Description and Initial Results

AbstractThe mesosphere and lower thermosphere (MLT) region is dominated globally by dynamics at various scales: planetary waves, tides, gravity waves, and stratified turbulence. The latter two can coexist and be significant at horizontal scales less than 500 km, scales that are difficult to measure. This study presents a recently deployed multistatic specular meteor radar system, SIMONe Peru, which can be used to observe these scales. The radars are positioned at and around the Jicamarca Radio Observatory, which is located at the magnetic equator. Besides presenting preliminary results of typically reported large‐scale features, like the dominant diurnal tide at low latitudes, we show results on selected days of spatially and temporally resolved winds obtained with two methods based on: (a) estimation of mean wind and their gradients (gradient method), and (b) an inverse theory with Tikhonov regularization (regularized wind field inversion method). The gradient method allows improved MLT vertical velocities and, for the first time, low‐latitude wind field parameters such as horizontal divergence and relative vorticity. The regularized wind field inversion method allows the estimation of spatial structure within the observed area and has the potential to outperform the gradient method, in particular when more detections are available or when fine adaptive tuning of the regularization factor is done. SIMONe Peru adds important information at low latitudes to currently scarce MLT continuous observing capabilities. Results contribute to studies of the MLT dynamics at different scales inherently connected to lower atmospheric forcing and E‐region dynamo related ionospheric variability.

Modelling interactions of cationic dimers in He droplets: microsolvation trends in HenK2+ clusters.

We report the results of a detailed theoretical investigation of small K2+-doped He clusters. The structural characteristics and stabilities of such cations are determined from ab initio electronic structure calculations at the MRCI+Q level of theory. The underlying interactions show a multireference character and such effects are analyzed. The interaction potentials are constructed employing an interpolation technique within the inverse problem theory method, while the nuclear quantum effects are computed for the trimers, their spatial arrangements are discussed, and information was extracted on the orientational anisotropy of the forces. We found that energetically the most stable conformer corresponds to linear arrangements that are taking place under large amplitude vibrations, with high zero-point energy. We have further looked into the behavior of higher-order species with various He atoms surrounding the cationic dopant. By using a sum of potentials approach and an evolutionary programming method, we analyzed the structural stability of clusters with up to six He atoms in comparison with interactions energies obtained from MRCI+Q quantum chemistry computations. Structures containing Hen motifs that characterize pure rare gas clusters, appear for the larger K2+-doped He clusters, showing selective growth during the microsolvation process of the alkali-dimer cation surrounded by He atoms. Such results indicate the existence of local solvation microstructures in these aggregates, where the cationic impurity could get trapped for a short time, contributing to the slow ionic mobility observed experimentally in ultra-cold He-droplets.

Measurement of reflection coefficient for a double-layered scaled model using the inverse filter

A method of measuring the reflection coefficient for a double-layered scaled model using the inverse filter is presented. First, the response of the circuit and underwater acoustical channel is measured, and the retransmitted inverse signal isestimated with the least square method for solving the cost function, which is constructed by the inverse filtering theory. Then, by retransmitting the inverse signal, the incident signal at the position of the double-layered scaled model is focused with high-main-lobe resolution, low side-lobelevel and a narrow pulse signal in temporal domain. The focus improves the measurement accuracy of the reflection coefficient for the double-layered scaled model in low frequencies. The feasibility of replacing the whole cylindrical with the double-layered scaled model is verified by simulation. The validity of the proposed method is verified by experiments carried out in a cylindrical tank for a double-layered scaled model at the frequency 0.5 kHz~10 kHz. The experimental results show that the proposed method is effective to the measurement of the reflection coefficient for the double-layered scaled model.The experimental results for the double-layered scaled model with acoustical coating on different shells have strongly directive significance for the process design and improvement of the acoustical coating.

Hygro-thermo-mechanical bending of laminated composite plates using an innovative computational four variable refined quasi-3D HSDT model

The current investigation presents hygro-thermo-mechanical analysis of simply supported anti-symmetric composite plates by using an original computational four unknown's quasi-3D inverse tangent hyperbolic theory. The developed formulations take into account the thickness stretching effect and contain indeterminate integral variables to reduce the number of unknowns. The present model ensures the transverse shear stresses nullity at the top and the bottom surfaces without using any shear correction factor. The governing equations are determined with the help of virtual work principle. The analytical solution of the hygro-thermo-mechanical analysis is derived via Navier's procedure. The accuracy and efficiency of current model is checked by comparing the results with others models found in the literature. Several numerical results are presented in graphs form to show the effects of the aspect, geometry and modulus ratio on the stress and transverse displacement of the simply supported anti-symmetric composite plates.

Oscillations of 2D ESTER models

Context.Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotatingδScuti stars that seem to match theoretical expectations.Aims.In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings.Methods.In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra.Results.Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

Control effect analysis for arch auxiliary system on long term deflection of long span prestressed concrete continuous beam bridge

In order to explore the control effect of arch assisted system on long-term deflection of long-span PC continuous girder bridge, an evaluation framework of long-term deflection control effect is proposed. Firstly, the functional relationship between long-term deflection and structural parameters is fitted based on the measured data, and the deflection prediction model is established; Secondly, based on the calculation method of bending stiffness of inversion theory, the evaluation framework of long-term deflection control effect based on the analogy stiffness method is proposed; Finally, based on the engineering example, under the premise of equal load sharing ratio, the above frame is applied to carry out parameter analysis. The results show that the deflection prediction model based on the measured data has good correlation, and the established evaluation framework can quantitatively evaluate the control effect of arch auxiliary system on long-term deflection.

Radon Transforms in Hyperbolic Spaces and Their Discrete Counterparts

In the hyperbolic disc (or more generally in real hyperbolic spaces) we consider the horospherical Radon transform R and the geodesic Radon transform X. Composition with their respective dual operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree T, separately studied as acting on functions on the vertices or on the edges. This leads to a new theory of spherical functions and Radon inversion on the edges of a tree.

Estimation of tensile strengths of metals using spherical indentation test and database

The indentation technique provides a non-destructive characterization method for in-service equipment. Recent years have seen an increased interest in determination of tensile properties from spherical indentation test (SIT) through inverse optimization theory, while this approach is computational costing and time consuming. This paper aims to propose a novel method for estimation of strength properties based on the application of a database. Firstly, systematically varied Ludwik constitutive parameter vectors were used to establish a database that contains indentation force-depth curves (extracted from the simulated results of indentation test) and corresponding strength values (calculated with the parameter vectors). The indentation force-depth curve of a concerned material was then processed by the database, as a result of which the yield and ultimate strengths can be obtained. A series of virtual materials were used to validate the accuracy of this method. The results show that the database method provides an impressive accuracy and stability in estimating strengths. The database method was subsequently applied to eight real materials. It is found that the predicted strengths agree well with the values from uniaxial tests for most materials, while the database method may be not suitable for materials that show obvious tension-compression asymmetry.

Inverse design method of microscatterer array for realizing scattering field intensity shaping

It is a novel and interesting idea to inversely design the scattering structure with the desired scattering field intensity distribution in a given target area as the known information. The inverse design method proposed in this paper does not need to be optimized, and the spatial distribution and dielectric constant distribution of the micro-scatterer array can be quickly analytically calculated according to the desired scattering field intensity in the target area. First, based on the spatial Fourier transform and angular spectrum transformation, the plane wave sources required in all directions are inversely obtained from the electric field intensity distribution required in the target area. Then, based on the theory of induced source, a method of irradiating the array of all-dielectric micro-scatterers with incident electromagnetic field to generate the required plane wave source is proposed. The scattering fields generated by these micro-scatterers will be superimposed on the target area to achieve the desired scattering field strength intensity. Finally, according to the proposed inverse design theory model, a specific three-dimensional (3D) design is carried out. In the 3D example, we study the scattering field intensity distribution of the point-focused shape of the square surface target area, and show an all-dielectric micro-sphere distribution design. Its spatial distribution and permittivity distribution are both obtained through the rapid analytical calculation of the desired scattered field intensity shape in the target area. Finally, based on the principle of linear superposition, we quickly and easily generate the complex shapes of “I”, “T”, and “X” in the target area. The satisfactory results of full-wave simulation show that the proposed inverse design method is effective and feasible.

Comparison and analysis of different schools of Chinese auricular acupuncture

Based on the literature regarding auricular acupuncture in recent 60 years, the theoretical basis, acupuncturemethods and dominant diseases are analyzed and compared, and three major auricular acupuncture schools are proposed. The first school is the sinicized auricular acupuncture school derived from French Nogier auricular acupuncture school, which can be further divided into three branches: Huang's auricular acupuncture school, Guan's auricular acupuncture school and Chen-Xu's auricular acupuncture school. The second school is Xuanyuan auricular acupuncture school inherited and developed from classical Chinese auricular acupuncture. The third school is Yuchi 's auricular acupuncture school which is based on Chinese and western medical theories but different from the embryo inversion theory of Nogier auricular acupuncture school. Furthermore, the similarities and differences of the theoretical sources, the distribution characteristics of auricular points and the clinical application characteristics of different auricular acupuncture schools are analyzed, so as to provide useful reference for the clinical application, basic research and national standards of auricular acupuncture in the future.

Does running speed affect the response of joint level mechanics in non-rearfoot strike runners to footwear of varying longitudinal bending stiffness?

BackgroundModifying the longitudinal bending stiffness (LBS) of footwear has become a popular method to improve sport performance. It has been demonstrated to influence running economy by altering lower extremity joint level mechanics. Previous studies have only examined within-participant effects at one running speed. Research questionDo joint level mechanics differ in response to varying footwear LBS at a range of running speeds? MethodsThis study utilized a cross-sectional repeated measure study design using a convenience sample. Ten well trained non-rearfoot strike male distance runners ran at 3.89, 4.70, and 5.56 m/s (14, 17, 20 km/hr) in footwear of three different LBS levels. Mechanics and energetics of the metatarsophalangeal joint (MTPJ), ankle, knee, and hip joints during stance phase were assessed using an 8-camera optical motion capture system (fs = 200 Hz), a force instrumented treadmill (fs = 1000 Hz) and standard inverse dynamics theory. ResultsRange of motion and negative work decreased and angular stiffness increased for the MTPJ with increasing LBS at all speeds (p < .001). Peak MTPJ moment did not change at any speed in response to increased LBS. Negative work at the ankle decreased in the stiff shoe at 17 km/hr (p = .036). Peak ankle plantar flexion velocity decreased with increasing LBS at all speeds (p < .05). SignificanceWhile changes in MTPJ mechanics were consistent across speeds, decreased negative ankle work was only observed at 17 km/hr in the stiff shoe, suggesting that perhaps tuned footwear LBS may need to focus primarily on metabolically beneficial changes in ankle plantar flexor mechanical behavior to improve performance in distance runners. Tuning footwear stiffness may also be beneficial to clinical populations, as clinicians seek to optimize their patients’ locomotion economy.

Structure of English Locative Inversion

A sentence structure involves the packaging of meaning. Words and their order decide the meaning of a sentence conveyed. This study discussed two points of problems. The first one is locative inversion structure in sentences taken from Corpus of Contemporary American English. The other problem is the constraints of locative inversion in the English grammar. The problems are discussed based on the theory of inversion by Hewings (2005). Method used to collect the data was documentation method. The analysis was conducted using descriptive qualitative method. The result of the analysis is shown using informal method. As results, this study shows that locative inversion structure is different from canonical structures. It has a distinct feature contrasting it with canonical structure. It also has several constraints regarding subject, predicate, and salient information affecting its formation. &#x0D;