Analytical Expansion Research Articles

Improved Analytic Expansions in Hybrid A-Star Path Planning for Non-Holonomic Robots

In this study, we concisely investigate two phases in the hybrid A-star algorithm for non-holonomic robots: the forward search phase and analytic expansion phase. The forward search phase considers the kinematics of the robot model in order to plan continuous motion of the robot in discrete grid maps. Reeds-Shepp (RS) curve in the analytic expansion phase augments the accuracy and the speed of the algorithm. However, RS curves are often produced close to obstacles, especially at corners. Consequently, the robot may collide with obstacles through the process of movement at these corners because of the measurement errors or errors of motor controllers. Therefore, we propose an improved RS method to eventually improve the hybrid A-star algorithm’s performance in terms of safety for robots to move in indoor environments. The advantage of the proposed method is that the non-holonomic robot has multiple options of curvature or turning radius to move safer on pathways. To select a safer route among multiple routes to a goal configuration, we introduce a cost function to evaluate the cost of risk of robot collision, and the cost of movement of the robot along the route. In addition, generated paths by the forward search phase always consist of unnecessary turning points. To overcome this issue, we present a fine-tuning of motion primitive in the forward search phase to make the route smoother without using complex path smoothing techniques. In the end, the effectiveness of the improved method is verified via its performance in simulations using benchmark maps where cost of risk of collision and number of turning points are reduced by up to around 20%.

Global path planning based on BIM and physics engine for UGVs in indoor environments

This paper proposes a global path planning (GPP) system based on building information modeling (BIM) and physics engine for unmanned ground vehicles (UGVs) operations in indoor environments. Firstly, UGV configuration is integrated into BIM as a knowledge base of GPP system by customized IFC structure, with which a multi-layer map generation method is proposed with improved logic and efficiency. Secondly, a UGV-centric A* path planning algorithm is designed by considering UGV's properties, including mobility-based primitive expansion, geometry-based collision checking, mobility-based cost setting, and mobility-based analytical expansion. Finally, a reliable trajectory generation method is developed based on physics engine, followed with a novel spatiotemporal coordination method for efficient collision avoidance. The whole GPP system is validated in a representative university building floor and a common inspection UGV. It is demonstrated that UGV-integrated BIM improves the resources interoperability for the whole system, and the map components are clarified clearly for efficient generation and maintenance. Besides, the UGV-centric A* performs a 100% success rate in congested environments where traditional A* always fail. It can even reduce almost 50% of the trajectory time and steering jerk in open scenarios than traditional A*, but still with an acceptable computation speed (less than 0.6 s). Finally, trajectory coordination saves 50% of path traveling time compared with the general queue method.

Understanding and formation-A process of becoming a nurse.

Nursing is a complicated and multifaceted profession that sets high demands in preparing nursing students for the profession. In today's education, the emphasis is often on knowledge and skills, that is, epistemology. In caring science another approach is sought, an approach based on human sciences in which knowledge will serve a more profound understanding, that is, the ontology. Consequently, the question of what this 'understanding' in clinical education is and how it is promoted in clinical nursing education becomes important to clarify. Therefore, the aim here is to explicate the phenomenon of understanding in clinical education as experienced by third-year undergraduate nursing students ready for graduation. This study, with a hermeneutic approach, is based on a secondary analysis of focus group interviews with undergraduate nursing students. The analytical expansion of the original material suggests three interrelated themes that illuminate the phenomenon of understanding in clinical education. These findings are deepened and enriched through philosophical abstraction. In the process of understanding, episteme, techne and phronesis can be viewed as inherent parts of the structure of thought in nursing. The perspective advanced in this study adds new aspects to the phenomenon of understanding and its meaning and significance in the dynamic process of formation and becoming in clinical education. The focus in clinical nursing education should be on learning reflective, critical thinking and the ways of being a nurse, rather than drilling students on particular skills. In the rapidly changing world of the 21st century, an understanding-based education is needed as a more meaningful and authentic approach. Therefore, an ontological turn in nursing education, through which the main focus shifts from a traditional epistemology to an epistemology in the service of ontology, is suggested. Further studies are needed in the development and implementation of an understanding-based, interpretative education in nursing.

Chiral discrimination by polarization singularities of a metal sphere

The practical applications of chiral discrimination are usually limited by the weak chiral response of enantiomers and the high complexity of detection methods. Here, we propose to use the C lines (i.e., lines of polarization singularities) emerged in light scattering by a metal sphere to detect small chiral particles. Using full-wave numerical simulations and analytical multipole expansions, we determined the absorption dissymmetry of deep-subwavelength helices (i.e., chiral particles) at different positions on the C lines. We find that the absorption dissymmetry can be much larger than that induced by circularly polarized plane wave excitation, and it can be attributed to the asymmetric absorption of the induced electric and magnetic dipoles. We also show that the absorption dissymmetry strongly depends on the anisotropy of the helices. The results may find applications in optical manipulations, optical sensing, and chiral quantum optics.

Rotational g factors and Lorentz forces of molecules and solids from density functional perturbation theory

Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic $g$ factors. We develop an efficient first-principles methodology based on density-functional perturbation theory to calculate this effect in both molecules and solids to linear order in the applied field. Our methodology is based on two linear-response quantities: the macroscopic polarization response to an atomic displacement (i.e., Born effective charge tensor), and the antisymmetric part of its first real-space moment (the symmetric part corresponding to the dynamical quadrupole tensor). The latter quantity is calculated via an analytical expansion of the current induced by a long-wavelength phonon perturbation, and compared to numerical derivatives of finite-wavevector calculations. We validate our methodology in finite systems by computing the gyromagnetic $g$ factor of several simple molecules, demonstrating excellent agreement with experiment and previous density-functional theory and quantum chemistry calculations. In addition, we demonstrate the utility of our method in extended systems by computing the energy splitting of the low-frequency transverse-optical phonon mode of cubic SrTiO$_3$ in the presence of a magnetic field.

Secondary Qualitative Analysis of Moral Injury in Obstetric and Neonatal Nurses

ObjectiveTo investigate the presence of symptoms of moral injury in obstetric and neonatal nurses. DesignA secondary qualitative analysis using an analytic expansion of three primary studies. SettingPostal mail and electronic surveys. ParticipantsI used three primary studies: participants in the first consisted of 78 labor and delivery nurses, participants in the second consisted of 75 nurse-midwives, and participants in the third consisted of 22 NICU nurses. MethodsI used Krippendorff’s content analysis method for qualitative data to reanalyze the three primary data sets. The categories I used in this analysis were the 10 symptoms of moral injury that are assessed by the Moral Injury Symptoms Scale–Health Professionals Version. ResultsWhen combining the three types of obstetric and neonatal participants, the top three most frequently cited symptoms of moral injury were moral concern, guilt, and self-condemnation. For participants in labor and delivery units and NICUs, moral concern was the most often described symptom, whereas for participants in midwifery it was guilt. None of the participants reported loss of meaning in their lives, loss of faith, or religious struggle. Participants who worked in NICUs did not describe any symptoms of shame or difficulty forgiving. ConclusionIn addition to the primary symptoms of moral injury, reported secondary consequences of moral injury can include depression, anxiety, anger, self-harm, and social problems. Interventions such as acceptance and commitment therapy are needed to help nurses address the potential for moral injury and repair its effects. Since the COVID-19 pandemic, now more than ever, moral injury needs to be recognized in obstetric and neonatal nurses and not just in the military population.

On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.

Dynamics of Frozen Orbit and Its Critical Case in the Zonal Problem

This paper investigates the dynamical behaviors of Earth frozen orbits including the critical inclination orbit in the zonal problem with terms of perturbations up to J15. From the mean element theory, an analytical expansion of the dynamics model is derived to obtain the frozen conditions. The global existence of Earth frozen orbits is numerically illustrated by exploration of equilibria in the equations of motion based on Lagrangian formulations. Frozen orbits are widely located at the inclination between 0° and 90°, which may be grouped into families: one for the elliptic orbit case, another for the quasicircular orbit case and the other for the critical inclination orbit case. For the elliptic and quasicircular orbit cases, orbits evolve periodically around the frozen ones, and elliptic orbits tend to be more sensitive than quasicircular ones with respect to variation of initial orbital elements. Frozen orbit bifurcations near the critical inclination are shown to illustrate the origins, evolutions, and stability of frozen orbits. For the last critical inclination case, it is observed that eccentricities keep evolving periodically instead of being frozen at the specified ones compared with that in the J2 problem, and then a relationship between the evolution period and terms of zonal perturbations is illustrated.

Two-loop bispectrum of large-scale structure

The bispectrum is the leading non-Gaussian statistic in large-scale structure, carrying valuable information on cosmology that is complementary to the power spectrum. To access this information, we need to model the bispectrum in the weakly non-linear regime. In this work we present the first two-loop, i.e., next-to-next-to-leading order perturbative description of the bispectrum within an effective field theory (EFT) framework. Using an analytic expansion of the perturbative kernels up to $F_6$ we derive a renormalized bispectrum that is demonstrated to be independent of the UV cutoff. We show that the EFT parameters associated with the four independent second-order EFT operators known from the one-loop bispectrum are sufficient to absorb the UV sensitivity of the two-loop contributions in the double-hard region. In addition, we employ a simplified treatment of the single-hard region, introducing one extra EFT parameter at two-loop order. We compare our results to N-body simulations using the realization-based grid-PT method and find good agreement within the expected range, as well as consistent values for the EFT parameters. The two-loop terms start to become relevant at $k\approx 0.07h~\mathrm{Mpc}^{-1}$. The range of wavenumbers with percent-level agreement, independently of the shape, extends from $0.08h~\mathrm{Mpc}^{-1}$ to $0.15h~\mathrm{Mpc}^{-1}$ when going from one to two loops at $z=0$. In addition, we quantify the impact of using exact instead of Einstein-de-Sitter kernels for the one-loop bispectrum, and discuss in how far their impact can be absorbed into a shift of the EFT parameters.

Directional scrambling of quantum information in helical multiferroics

Local excitations as carriers of quantum information spread out in the system in ways governed by the underlying interaction and symmetry. Understanding this phenomenon, also called quantum scrambling, is a prerequisite for employing interacting systems for quantum information processing. The character and direction dependence of quantum scrambling can be inferred from the out-of-time-ordered commutators (OTOCs) containing information on correlation buildup and entanglement spreading. Employing OTOC, we study and quantify the directionality of quantum information propagation in oxide-based helical spin systems hosting a spin-driven ferroelectric order. In these systems, magnetoelectricity permits the spin dynamics and associated information content to be controlled by an electric field coupled to the emergent ferroelectric order. We show that topologically nontrivial quantum phases, such as chiral or helical spin ordering, allow for electric-field controlled anisotropic scrambling and a direction-dependent buildup of quantum correlations. Based on general symmetry considerations, we find that starting from a pure state (e.g., the ground state) or a finite temperature state is essential for observing directional asymmetry in scrambling. In the systematic numerical studies of OTOC on finite-size helical multiferroic chains, we quantify the directional asymmetry of the scrambling and verify the conjectured form of the OTOC around the ballistic wavefront. The obtained direction-dependent butterfly velocity ${v}_{\mathrm{B}}(\mathbf{n})$ provides information on the speed of the ballistic wavefront. In general, our calculations show an early time power-law behavior of OTOC, as expected from an analytic expansion for small times. The long-time behavior of OTOC reveals the importance of (non)integrability of the underlying Hamiltonian as well as the implications of conserved quantities such as the $z$ projection of the total spin. The results point to the potential of spin-driven ferroelectric materials for the use in solid-state-based quantum information processing.

A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets

In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination, and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter’s inner and co-orbital resonances and Neptune’s exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

Interchangeability in Military Interprofessional Health Care Teams: Lessons Into Collective Self-healing and the Benefits Thereof

Interchangeability-i.e., the capacity to change places with another-is necessary for military interprofessional health care teams (MIHTs) to provide around-the-clock patient care. However, while interchangeability is clearly a necessity for modern health care delivery, it raises uncomfortable questions for civilian health care teams where it is usually labeled as unsafe. This perception surfaces because interchangeability runs counter to some of health care's cultural beliefs including those around patient ownership and professional scopes of practice. It is, therefore, not surprising that little is known about whether and how some level of interchangeability can be harnessed to improve the productivity of health care teams overall. In this article, we explore the notion of interchangeability in the particular context of MIHTs given that these health care teams are familiar with it. This exploration will offer insights into how interchangeability could maximize civilian health care teams' capacity to adapt. We conducted a secondary analysis of interview data as an analytic expansion: "the kind of study in which the researcher makes further use of a primary data set in order to ask new or emerging questions that derive from having conducted the original analysis but were not envisioned within the original scope of the primary study aims". Within our secondary analysis approach, we used thematic analysis as our analytical tool to describe (1) what interchangeability looks like in MIHT teams, (2) how it is fostered in MIHTs, and (3) how it is enacted in MIHTs. Interchangeability was realized in MIHTs when individual team members adapted to take on roles and/or tasks that were not clearly niched in their specific areas of expertise but instead drew on the broad foundation of their clinical skill set. Cross-training and distributed leadership were ways in which MIHT members described how interchangeability was fostered. Furthermore, five features of working within MIHT teams were identified as key conditions to enact interchangeability: knowing your team members; being able to work with what/who you have; actively seeking others' expertise; situating your role within the broader picture of the mission; and maintaining a learning/teaching mindset. Interchangeability can be understood through the theoretical lens of Swarm Intelligence and more specifically, the principle of collective self-healing-which is the ability of collectives to continue to successfully perform despite disruption, challenges, or the loss of a team member. Our findings highlight how MIHTs have adopted interchangeability in a wide array of contexts to realize collective self-healing. Despite the discomfort it provokes, we suggest that interchangeability could be a powerful asset to civilian health care teams.

Memory efficient finite volume schemes with twisted boundary conditions

In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size l^2 times (Nl)^2, a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the Lambda parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value Lambda _{overline{mathrm{MS}}}sqrt{8 t_0} =0.603(17) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

On the Symmetry and Recovery of Steady Continuously Stratified Periodic Water Waves

This paper considers two-dimensional steady continuously stratified periodic water waves. We first use the moving plane method to establish that the stratified water waves must be symmetric provided streamlines in a neighborhood of the trough line are monotone. Further, we prove that all streamlines are real analytic (including the free surface) by applying the Schauder estimates on the uniform oblique derivative problem. Finally we provide an analytic expansion method to recover the water waves from relative horizontal velocity on the axis of symmetry and wave height. All results in this paper hold for stratified waves of large (or small) amplitude.

Coherent forward scattering peak and multifractality

It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions $D_1$ and $D_2$, and by the spectral form factor. We check our results using a 1D Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems.

Expansion formula for the magnetic field of a periodically deformed circular current loop

A method is derived to obtain an expansion formula for the magnetic field generated by a closed planar wire carrying a steady electric current. The parametric equation of the loop is , with R the radius of the circle, H ∈ [0, R) the radial deformation amplitude, and f(ϕ)∈[−1, 1] a periodic function. The method is based on the replacement of the factor by an infinite series in terms of Gegenbauer polynomials, as well as the use of the Taylor series. This approach makes it feasible to write as the circular loop magnetic field contribution plus a sum of powers of H/R. Analytic formulas for the magnetic field are obtained from truncated finite expansions outside the neighborhood of the wire. These showed to be computationally less expensive than numerical integration in regions where the dipole approximation is not enough to describe the field properly. Illustrative examples of the magnetic field due to circular wires deformed harmonically are developed in the article, obtaining exact expansion coefficients and accurate descriptions. The method can be also applied when the deformation function f(ϕ) is a linear combination of harmonic functions. In that case, we provide the exact formulas for the expansion coefficients of . Error estimates are calculated to identify the regions in where the analytical expansions perform well. Finally, first-order deformation formulas for the magnetic field are studied for generic even deformation functions f(ϕ).

The integration of non-conventional therapeutic modalities in Nursing as a motivating factor for Nursing care

Evidence of the utilization of non-conventional therapeutic modalities by nurses and the outcomes for clients was scarce in Portugal in 2011, when one of the author’s primary study took place (Santos, 2011). Data analysis did not address the deep reasons why nurses used complementary/alternative therapies. Objectives: Thus, a new research question: What are nurse’s motivations to integrate non-conventional therapeutic modalities in their practice? Method: Interview transcripts and observation records of fifteen nurses, working in Portuguese hospitals, from all types of units of care; and ten nurses and seventeen patients at the pain unit of the Cancer Oncology Institute, was analyzed. Secondary qualitative analysis, using analytic expansion (Thorn, 2013), was conducted. Simplified theoretical model (Burtson and Stichler, 2010) was used as Theoretical Framework. Results: Three themes were identified: Nursing care values; Knowledge base; Acting according to values and knowledge base. There is also evidence of the impact of promoters (compassion satisfaction and nurse job satisfaction) of nurse caring. Discussion: The meanings of action and the need for a trusting relationship are key elements of nursing care. Nurses are motivated to care by the satisfaction they derive from caregiving, as Burston & Strichler (2010) state. Interaction opportunities, praise and recognition, and compassion satisfaction, all of them are promoter’s factors of nursing job satisfaction. Further research is needed to confirm the impact of care promoters in different cultures and measure the factors of nursing care, to support changes in nursing practice.

Metal-insulator transition and antiferromagnetism in the generalized Hubbard model: Treatment of correlation effects

The ground state for the half-filled $t-t'$ Hubbard model is treated within the Hartree-Fock approximation and the slave boson approach including correlations. The criterium for the metal-insulator transition in the Slater scenario is formulated using an analytical free-energy expansion in the next-nearest-neighbor transfer integral $t'$ and in direct antiferromagnetic gap $\Delta$. The correlation effects are generally demonstrated to favor the first-order transition. For a square lattice with a strong van Hove singularity, accidental close degeneracy of antiferromagnetic and paramagnetic phases is analytically found in a wide parameter region. As a result, there exists an interval of $t'$ values for which the metal-insulator transition is of the first order due to the existence of the van Hove singularity. This interval is very sensitive to model parameters (direct exchange integral) or external parameters. For the simple and body-centered cubic lattices, the transition from the insulator antiferromagnetic state with increasing $t'$ occurs to the phase of an antiferromagnetic metal and is a second-order transition which is followed by a transition to a paramagnetic metal. These results are quantitatively modified when taking into account the intersite Heisenberg interaction, which can induce first-order transitions. A comparison with the Monte Carlo results is performed.

Bending of light and inhomogeneous Picard–Fuchs equation

The bending of light rays by gravitational sources is one of the first evidence of general relativity. When the gravitational source is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions up to a finite order in terms of the parameters of orbit and the background spacetime has been derived. However, it has not been clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard–Fuchs equation, which has been applied to compute effective superpotentials on D-branes in the Calabi–Yau manifolds. From the analytic expression of the bending angle, the full order expansions in both weak and strong deflection limits are obtained. We show that the result can be obtained by the direct integration approach as well. We also discuss how the charge of the gravitational source affects the bending angle and show that a similar analytic expression can be obtained for the extremal Reissner–Nordström spacetime.

Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated.