Adaptive Criterion Research Articles

A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation

Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.

Perirenal fat thickness is a powerful predictor for surgical outcomes of transperitoneal laparoscopic adrenalectomy.

Laparoscopic adrenalectomy has been the gold standard surgical procedure. However, the adaptation criteria for malignant tumors and predictors of perioperative outcomes are not well defined. Therefore, this study tried to identify valid predictors for perioperative outcomes of laparoscopic adrenalectomy and consider the adaptation criteria. We retrospectively reviewed the preoperative and perioperative data of 216 patients who underwent transperitoneal laparoscopic adrenalectomy in our hospital. Preoperative factors associated with perioperative outcomes were analyzed using multiple regression analysis. Among 216 patients, 165 (76.4%), 26 (12.0%), and 25 (11.6%) were suspected of having benign tumors, pheochromocytoma, and malignant tumors, respectively. Median tumor size was 25.0 mm (interquartile range 18.0-35.0); median perirenal fat thickness was 9.2 mm (interquartile range 4.9-15.6) on preoperative computed tomography scans. The median operative time was 145.5 min (interquartile range 117.5-184.0) and the median estimated blood loss was 0.0 mL (interquartile range 0.0-27.3). Perirenal fat thickness (p < 0.001), tumor size (p < 0.001), and malignant tumors (p = 0.020) were associated with operative time, and perirenal fat thickness (p = 0.038) and malignant tumors (p = 0.002) were associated with estimated blood loss. Perirenal fat thickness, tumor size, and malignant tumors are valid predictors of the surgical outcomes of transperitoneal laparoscopic adrenalectomy. As only perirenal fat thickness is associated with both surgical outcomes except for malignant tumors, it is a powerful predictor. Transperitoneal laparoscopic adrenalectomy for large malignant adrenal tumors with thick perirenal fat should be performed with caution.

Clinical performance of non-carious cervical lesions restored with using self-etch mode of adhesives according to the FDI criteria.

The purpose of this study was to evaluate the 18-month retrospective study of self-etch adhesive (Prime&Bond One Select) and self-etch mode of universal adhesives (Single Bond Universal, Gluma Bond Universal) applied to non-carious cervical lesions according to the World Dental Federation criteria. Thirty patients without any systemic disease, good oral hygiene, having at least 20 teeth and six non-carious cervical lesions treated using a self-etch mode of adhesives operated between January and March 2017. Accordingly, 335 restorations were evaluated according to the World Dental Federation criteria at 3, 6, 12 and 18 months. Pillai's Trace test was used to determine the interaction of criteria with time and adhesive systems. IBM SPSS Statistics 21.0 program was used in the analysis. Value of P < 0.05 was accepted as a criterion for statistical significance. At the end of 18 months, participation was 100%. There was a statistically significant difference P < 0.05 between Prime&Bond One Select and Single Bond Universal, Prime&Bond One Select and Gluma Bond Universal in the 18-month period. In terms of marginal staining, fracture of material and retention, recurrence of caries, erosion and abfraction, tooth integrity criteria at the end of the 18 months, Prime&Bond One Select performed clinically very good, Single Bond Universal and Gluma Bond Universal performed clinically good according to World Dental Federation criteria. Marginal adaptation criteria, Prime&Bond One Select, Single Bond Universal and Gluma Bond Universal performed clinically good. Retention loss rate was found to be the lowest in Prime&Bond One Select and the highest in Gluma Bond Universal. Accordingly, 18-month evaluation of all adhesives used in the study showed clinically acceptable results in all of the World Dental Federation criteria.

The dark side of niche construction

Niche construction denotes the alteration, destruction, or creation of environmental features through the activities of an organism, modifying the relation between organism and environment. The concept of niche construction found application in various fields of research: evolutionary biology, enculturation, ontogenetic development, and local organism-environment coordination. This is because it provides a useful tool emphasizing different aspects of the dynamic interplay between organisms and their actively constructed environment. Traditionally, niche construction is considered a positive mechanism in the complementarity of organism and environment. In contrast, this paper sheds light on the dark side of niche construction, that is, the different manners in which organisms may modify environmental features that are in some way or another harmful to them. First, the paper introduces a paradigmatic distinction of four kinds of niche construction as commonly addressed in recent literature, using more or less extended spatio-temporal scales as the distinguishing feature. Second, the paper elaborates on the concept of negative niche construction, providing normative criteria of (mal)adaptation that are suitable for the evaluation of environmental alterations, given the chosen spatio-temporal scale. Of particular interest are inter-scale conflicts: those cases of environmental constructions which appear adaptive concerning one spatio-temporal scale but maladaptive concerning another. Third, the paper distinguishes the concept of niche construction as a valuable instrument to better understand central aspects of modern medicine and the entangled contribution of evolutionary, socio-cultural, personal, and situational aspects to different health issues, using chronic pain as an illustrative case study.

Evaluation of morphological changes based on cone beam CT for adaptive radiotherapy

BackgroundDuring radiotherapy treatment, morphological changes can occur in patients (as weight loss). This can lead to significant dosimetric consequences on target volumes and/or organs at risk. The process of adaptive radiotherapy can compensate for these variations. Its deployment in the clinic is slowed by the considerable additional workload for the medical teams. The need for a tool facilitating the detection of patients whose treatment plans need adaptation has been clearly expressed in clinical practice, hence the usefulness of studying the impact of these morphological changes before the decision of adaptive radiotherapy. MethodsWe considered the cases of 26 patients treated for pelvic cancer where CBCT (Cone Beam Computed Tomography) repositioning images were used. These images have undergone pre-processing to improve their quality and obtain a more precise registration using seven algorithms. We compared the results obtained in order to choose the most adequate algorithm allowing the calculation of external morphological differences using similarity metrics, such as DSC, NCC, MI and TC. ResultsIn this study, we showed that the “rigid body” algorithm, based on the rigid registration, gives the best results. The conservation of external contours allowed quantification of the variation in the external volumes of the patients. The obtained variations were on average (6.12±1.69)% and (4.36±1.22)% for rectum and prostate cancers, respectively. ConclusionMorphological changes evaluated in this study may influence the quality of patient treatment; hence the need for adaptive radiotherapy to take these variations into consideration. However, a rigorous evaluation of the dosimetric impact of these morphological variations is necessary to determine decision criteria for treatment plan adaptation.

Adaptive time multiscale algorithms for fluid–structure interaction with impacts - Application to a row of PWR fuel assemblies under seismic loading

The present article is dedicated to numerical methods for the simulation of the response of PWR fuel assemblies under external mechanical loading such as earthquakes. It proposes new algorithms to manage impact sequences within the time multiscale resolution of a strongly coupled fluid–structure partitioned problem. Preserving the computational efficiency imposes an adaptive strategy to adjust the time scale to force the solution of the costly pressure problem for the fluid only when it is necessary to account for the brutal variations in the structure acceleration resulting from significant impacts. The adaptation criteria must be built upon a thorough monitoring and characterization of all impacts, including the duration of the flight sequence before it occurs and the relative velocity between impact entities. Finally, solutions to mitigate the consequences of missed and unresolved impacts in time are provided to avoid spurious amplification of the variation of the acceleration under impact in the fluid velocity field through the time integration scheme. This leads to two classes of adaptive time multiscale algorithms, extensively tested and qualified through two chosen cases of growing complexity. The paper is completed by a full experimental validation of the proposed fluid–structure framework with contact and impacts, using the results available for a row of six fuel scale assembly immersed in water and submitted to a seismic excitation on a shaking table.

Adaptive Gamification in Science Education: An Analysis of the Impact of Implementation and Adapted Game Elements on Students’ Motivation

In recent years, gamification has captured the attention of researchers and educators, particularly in science education, where students often express negative emotions. Gamification methods aim to motivate learners to participate in learning by incorporating intrinsic and extrinsic motivational factors. However, the effectiveness of gamification has yielded varying outcomes, prompting researchers to explore adaptive gamification as an alternative approach. Nevertheless, there needs to be more research on adaptive gamification approaches, particularly concerning motivation, which is the primary objective of gamification. In this study, we developed and tested an adaptive gamification environment based on specific motivational and psychological frameworks. This environment incorporated adaptive criteria, learning strategies, gaming elements, and all crucial aspects of science education for six classes of third-grade students in primary school. We employed a quantitative approach to gain insights into the motivational impact on students and their perception of the adaptive gamification application. We aimed to understand how each game element experienced by students influenced their motivation. Based on our findings, students were more motivated to learn science when using an adaptive gamification environment. Additionally, the adaptation process was largely successful, as students generally liked the game elements integrated into their lessons, indicating the effectiveness of the multidimensional framework employed in enhancing students’ experiences and engagement.

Low Switching Power Neuromorphic Perovskite Devices with Quick Relearning Functionality

AbstractIn the quest to reduce energy consumption, there is a growing demand for technology beyond silicon as electronic materials for neuromorphic artificial intelligence devices. Equipped with the criteria of energy efficiency and excellent adaptability, organohalide perovskites can emulate the characteristics of synaptic functions in the human brain. In this aspect, this study designs and develops CsFAPbI3‐based memristive neuromorphic devices that can switch at low power and show larger endurance by adopting the powder engineering methodology. The neuromorphic characteristics of the CsFAPbI3‐based devices exhibit an ultra‐high paired‐pulse facilitation index for an applied electric stimuli pulse. Moreover, the transition from short‐term to long‐term memory requires ultra‐low energy with long relaxation times. The learning and training cycles illustrate that the CsFAPbI3‐based devices exhibit faster learning and memorization process owing to their larger carrier lifetime compared to other perovskites. The results provide a pathway to attain low‐power neuromorphic devices that are synchronic to the human brain's performance.

The impact of emotional intelligence (EQ) in the B2B exchange processes: Increasing salespeople’s adaptive selling behaviour (ASB)

In today’s globalised markets, the business-to-business (B2B) exchange processes have become much more complex, as a result adaptive selling behaviour (ASB) has become essential to sales success within B2B organisations. This study has explored the phenomenon by examining whether emotional intelligence (EQ) has an impact on salespeople’s adaptive selling behaviour. Scholars have suggested that individuals possessing high EQ traits are more likely to be successful in adaptive selling, however there are limited studies available to address the gap in research. The research question is as follows, RQ1: To what extent does EQ have an impact on salespeople’s ASB? An exploratory qualitative approach, which consisted of a semi-structured interview, complemented with the Schutte Self-Report Emotional Intelligence Test (SSEIT) and a case study performance assessment, was conducted on 8 salespeople, employed in a B2B telemarketing company. The results of the thematic analysis have identified consistent themes within the interview, indicating that higher EQ scores could potentially enhance sales behaviour adaptability. 6 themes were identified as being reflective of the ‘Analytical’ adaptation criteria, 6 themes were identified for ‘Driver’ adaptation, 6 themes were identified for ‘Amiable’ adaptation and 8 themes were identified for ‘Expressive’ adaptation. These results highlight practical implications of incorporating EQ into employee selection, performance management and leadership training policies, within the current workforce.

The method of ensuring the road-holding ability of the motor grader during the performance of technological operations

Problem. The article proposes a method of ensuring course stability of a motor grader during technological operations. As a system for adapting the motor grader to changing operating conditions, it is proposed to simultaneously use the mechanism for turning the front wheels in the horizontal plane and the mechanism for tilting the front wheels in the vertical plane. Goal. Development of a method of adapting a motor grader to changing external load conditions during technological operations. Methodology. As a criterion for adaptation, the index of permissible deviation of the motor grader from the planned trajectory of movement at the distance of the given length was used. Originality. The proposed criterion depends on the type of technological operation performed and the type of parameters of the developed environment. Results. The method of ensuring road-holding ability of the motor grader involves the analysis of the movement of the machine on the work site and the development of recommendations for the effective use of the adaptation system. Practical value. On the basis of the obtained results of experimental studies, a graphical and analytical analysis was performed, which made it possible to provide recommendations on the choice of turning angles and inclination of the wheels as a function of the angle of the transverse inclination of the support surface and the coefficient of adhesion.

Diverse contributions of nature to climate change adaptation in an upland landscape

ABSTRACT Nature provides numerous functions and services that can contribute to societal climate change adaptation. These ‘adaptation services’ can be sustained, latent, or novel, depend on persistence or transformation of ecosystems, and require varying co-production by people. Adaptation services also include climate mitigation. We present an approach to explore an extensive set of land use and climate scenarios that outline possible futures for a landscape, and quantify the contributions of adaptation services. We quantified adaptation success across six criteria relevant to the region, characterised the contributions of different types of adaptation services, and mapped spatial variation in contributions across the landscape. We built an integrated model of the Mackenzie District (an upland landscape of Aotearoa New Zealand), and analysed 1200 hypothetical scenarios for the period 2060–2070. We found many adaptation options, with 46% of scenarios meeting the criteria for successful adaptation. Four sustained, two latent and five novel services co-produced through financial input made diverse contributions to economic profit, profit resilience, climate change mitigation, climate risk adaptation, landscape cultural heritage and biodiversity. Successful adaptation scenarios were multifunctional, relying on alternative combinations of services allowed by spatial heterogeneity. By accounting for the numerous relationships between people and natural components within complex landscape systems, our advanced simulation approach can inform participatory pathway development by quantifying the potential for nature to contribute to future climate change adaptation.

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

Morphology of the heart during the period of progressive growth in conditions of prolonged exposure to low temperatures

Annotation. The aim of the research is to study the cardiac morphology during the period of growth under prolonged exposure to low temperatures. The main group consisted of outbred white rats (260 males and 190 females) undergoing active development, aged 4 weeks at the beginning of the experiment, and was kept in a room with an air temperature of +4±1 °C. The control group of animals was kept in a room with an air temperature of +20±10 °C. The experiment lasted for sixteen weeks. Research methods: macromorphometric study of the heart, histological study of paraffin sections, and ultrastructural study. Micromorphometric study was performed on semi-thin sections stained with 0.1% solution of toluidine blue at an ocular magnification of 10 and objective of 90, using a multi-purpose test system of short segments (Weibel grid) and an automatic analyzer of microscopic images “Integral-2MT”. PAS stain by A.L.Shabadash was used to detect glycogen, and the number of glycogen granules per unit area was counted on electronograms at a magnification of 20000 using a 1 cm2 area square. The stereological study of the electronograms was carried out at a magnification of 8000 using a Weibel grid. The statistical processing of the obtained results was carried out using the SPSS statistical program package, STATISTICA v. 10.0. It was found that the adaptation of the myocardium to the cold occurs according to the universal mechanism of adaptation to various extreme conditions associated with a deficit of energy metabolism. Therefore, the effect of cold can be regarded as non-specific. Based on the conducted research, the following stages of the adaptation process are defined: 1) short-term stress reaction (first 5 days); 2) myocardial hypertrophy (from 2nd to 6th weeks); 3) long-term, stable adaptation (more than 6 weeks). Morphological criteria for myocardial adaptation to long-term cold exposure have been identified: 1) physiological hypertrophy of the myocardium, mainly of the right ventricle; 2) the energy reserve of cardiomyocytes in the form of mitochondrial hyperplasia and glycogen accumulation. We plan to study the microcirculatory bed of the myocardium during the adaptation of the body to prolonged action of low temperature in the future.

Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes.

State of health of medical students

This article discusses the state of health of young students studying Pharmacy, Industrial Pharmacy at the Volyn Medical University. The purpose of the article is to determine the state of health of students of higher education in the medical profession. The results of the analysis of students' medical records allow us to state the presence of problems in their state of health. Each student of higher education during the academic year, on average, was ill 2–3 times and missed 10–15 days of study at the institute (depending on age and gender).&#x0D; Most often, students are sick with viral respiratory diseases (43-51 cases per 100 examined), diseases of the digestive organs (10-18 cases), vision (3-15 cases) and excretory system (5-12 cases), injuries (10-20 cases ) and infectious diseases (7– 14 cases).&#x0D; One of the integral criteria of adaptation is the assessment of the state of health on the basis of morbidity indicators, the level of which allows to most objectively reflect the degree of health loss, as well as to determine the priorities of prevention. Given the fact that the environmental factor has priority in the development of diseases in young people (up to 30%), the dominance of the specified pathologies may indicate the formation of an environmental maladaptation syndrome. Along with that, today the range of factors of the internal student environment has significantly expanded, which determine up to 12.5% of cases of illness in junior courses.&#x0D; According to the results of our research, the largest group in the structure of students' diseases is acute respiratory viral diseases. Influenza among students of higher education, of various ages, is registered in one-third to one-half of cases.&#x0D; In connection with the deterioration of students' health, it is necessary to introduce special, health-improving classes into the educational process, which would allow providing individual assistance to students in the prevention of diseases and health preservation.

Universal structures for adaptation in biochemical reaction networks

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.

An efficient adaptive length scale insensitive phase-field model for three-dimensional fracture of solids using trilinear multi-node elements

As a diffused fracture theory, phase-field models can seamlessly simulate complex crack patterns such as extending, branching, and merging. Despite the success of phase-field models, there are two issues in previous methods of three-dimensional (3-D) fracture. Firstly, the nonlinear governing equations lead to the huge computational costs, which hinder the application of phase-field models in 3-D problems. Secondly, these models, which are mostly developed based on a simple quadratic degradation function, provide numerical solutions that are sensitive to a length scale. Hence, this work addresses an efficient adaptive phase-field model with the aid of trilinear multi-node elements. The order of the elements remains constant with the increase of the number of nodes. As the mesh size and length scale significantly influence the numerical precision, a robust adaptive criterion is established in which the element refinement is controlled by both internal length scale and phase-field. According to the criterion, an expected mesh density in the failure domain can be obtained even for nonuniform initial mesh. Besides, being able to extend the phase-field regularized cohesive zone model, the adaptive model provides length scale insensitive responses for both crack path and peak load. The failure of brittle and quasi-brittle materials in three-dimensional conditions, including simple and mixed-mode fracture, can be simulated by the proposed model. Several benchmark examples are analyzed to show the efficiency and accuracy of the trilinear element-based adaptive phase-field model (TAPFM), and the results are compared with the standard phase-field model as well as experimental data.

Realization of an Adaptation Criterion in Grid Generation Technology for Constructions Bounded by Surfaces of Revolution with Parallel Axes of Revolution1

Realization of an Adaptation Criterion in Grid Generation Technology for Constructions Bounded by Surfaces of Revolution with Parallel Axes of Revolution1

Cooperative Strategy of Trajectory Tracking and Stability Control for 4WID Autonomous Vehicles Under Extreme Conditions

Trajectory tracking and stability control are two essential functions of autonomous vehicles, and there is inevitable mutual interference between them, especially under extreme conditions. Towards addressing this challenge, this paper proposes a novel cooperative strategy of trajectory tracking and stability control for four-wheel independent drive (4WID) autonomous vehicles. An adaptive trajectory tracking controller is designed based on the model predictive control (MPC) theory, in which the tire cornering stiffness is modified in real-time leverages the lateral force estimated by the square-root cubature Kalman filter (SCKF). Then, the vehicle stability controller is designed based on the sliding mode control (SMC), in which the tire force saturation constraint and the relative weight of yaw rate and sideslip angle are considered. Furthermore, a weight adaptive criterion with normalized stability index is defined to develop the cooperative strategy of trajectory tracking and stability control. The feasibility and adaptability of the proposed method to different extreme conditions are verified by hardware-in-the-loop (HIL) test and CarSim-Simulink co-simulation. Finally, an experimental case is presented to demonstrate the realizability of the proposed method.

Wideband Synchronous Measurement-Based Detection and Location of High Impedance Fault for Resonant Distribution Systems With Integration of DERs

The increasing integration of distributed energy resources (DERs) into the distribution system has caused interference with the signals stimulated by high impedance faults (HIFs). Many existing HIF detection or location methods that are only based on the superficial nonlinearity features of signals rather than the deep laws, will become invalid. This paper proposes a detection and location scheme for HIFs by theoretically analyzing the relationships between signals and systems. By establishing the equivalent circuit of a resonant distribution system, an online method to calculate the kernel system parameters is proposed, based on which an adaptive criterion for HIF detection is provided. In this way, the ability to detect HIF is adequately exploited and independent of DER influences. The method is able to detect HIF over 8.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{k}{\Omega }$ </tex-math></inline-formula> under common operating conditions. Furthermore, the nonlinearity of HIF is analyzed by deriving laws about how wideband signals distribute in the system. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\mathrm{ rd}}$ </tex-math></inline-formula> harmonic component of zero-sequence signals is proved to be superior in HIF location in terms of signal content and discrimination, which is also demonstrated to be valid under the influence of DER harmonic injection. On this basis, a HIF location method utilizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\mathrm{ rd}}$ </tex-math></inline-formula> harmonic zero-sequence signals is proposed. The effectiveness of the method and its robustness to the DER interference are validated by simulated and field HIFs in 10kV systems.