Golden Ratio Research Articles

Phase-based video vibration measurement and fault feature extraction method for compound faults of rolling bearings

Vibration characterization of rotating machinery is crucial for determining rotational and failure frequencies. Traditional contact measurement methods have limitations, while high-speed cameras offer a non-contact alternative for measuring target vibrations, spatial phase-based techniques have recently been widely used in detecting subtle vibrations and show good robustness to imaging noise. In this paper, a vision-based vibration extraction method for rotating machinery is proposed, aiming at extracting minor vibrations of bearings from them and further analyzing their fault frequencies. To address the challenge of separating a single fault frequency from the extracted compound faulty vibration signals, kurtosis is employed to analyze the inverse convolution period of multiple periodic components, and the MOMEDA filter length is optimized using the golden section algorithm. MOMEDA is then used to enhance each periodic pulse separately, and fault frequency is obtained through envelope spectrum demodulation. In the experimental part, a phase-based method is used to extract minor vibration displacements from rotor vibration video, which is subsequently compared with eddy current sensors in both time and frequency domains to verify the accuracy of the proposed method in extracting vibration displacements based on vision. Finally, vibration signals are extracted from the bearing compound fault video, and the single fault frequency characteristics of the bearing are successfully separated using the adaptive MOMEDA method, which provides an efficient and reliable method in the field of rotating machinery fault diagnosis.

Computing Quadratic Eigenvalues and Solvent by a New Minimization Method and a Split-Linearization Technique

To solve quadratic eigenvalue problems (QEPs), especially the gyroscopic systems, two methods are proposed: an iterative direct detection method (DDM) of the complex eigenvalues of the original QEP, and a split-linearization method (SLM) for finding the solvent matrix, which results to a standard linear eigenvalue problem (LEP) being solved to compute all eigenvalues by the symmetry extension. Reducing the dimension to one-half, the LEP is recast in a simpler QEP involving the square of the solvent. We set up two new merit functions which are minimized to detect the complex eigenvalues from the original QEP and a simpler QEP. For each eigen-parameter the merit function consists of the Euclidean norm of each derived eigen-equation, whose vector variable is solved from a derived inhomogeneous linear system. Then, the golden section search algorithm is employed to minimize the merit functions and locate the complex eigenvalue as a local minimal point. The results are compared with that computed by the cyclic-reduction-based solvent (CRS) method.

'Golden Ratio Yoshimura' for meta-stable and massively reconfigurable deployment.

Yoshimura origami is a classical folding pattern that has inspired many deployable structure designs. Its applications span from space exploration, kinetic architectures and soft robots to even everyday household items. However, despite its wide usage, Yoshimura has been fixated on a set of design constraints to ensure its flat foldability. Through extensive kinematic analysis and prototype tests, this study presents a new Yoshimura that intentionally defies these constraints. Remarkably, one can impart a unique meta-stability by using the Golden Ratio angle ([Formula: see text]) to define the triangular facets of a generalized Yoshimura (with [Formula: see text], where [Formula: see text] is the number of rhombi shapes along its cylindrical circumference). As a result, when its facets are strategically popped out, a 'Golden Ratio Yoshimura' boom with [Formula: see text] modules can be theoretically reconfigured into [Formula: see text] geometrically unique and load-bearing shapes. This result not only challenges the existing design norms but also opens up a new avenue to create deployable and versatile structural systems.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Profiling patent compounds in lipid nanoparticle formulations of siRNA

Lipid nanoparticles (LNPs) have emerged as a prominent delivery system for nucleic acid drugs, attracting significant attention especially through the successful development of several commercial products. As a key component in LNPs, cationic lipids along serve as key technical barrier to block competitors by building up complex patent thicket. However, there have been few studies as yet that have comprehensively analyzed the patented compounds in LNP formulations, despite a large number of technical reviews and original articles. In the context, this study focuses on analyzing the macroscopic landscapes and microscopic molecular characteristics of LNP patents, aiming to provide a valuable reference for researchers and developers in making informed technological and commercial decisions. By mining 2,994 patents, 265 formulas, 7,674 compounds and 28,789 fragments, this work sketched the empirical golden ratio of lipid materials in LNP formulation, disclosed the advanced technology in the formulation, characterized high-frequency fragments of heads, linkers and tails in both novel cationic lipids as well as targeting lipids, and established a virtual focus library of LNP materials.

A new perspective: Quantitative description of the Cupid’s peak aesthetics essence

ObjectivesThe Cupid's peak triangle theory was established to reveal the aesthetics essence of the Cupid's peak through Gold-ratio deviation, to provide quantitative theoretical basis for lip plastic and cosmetic surgery. Materials and MethodsModel the Cupid's peak line on the lip bow ridge and construct expressions for Cupid's peak parameters and their associated triangle theory using the Angle Circle (AC) and Radius Circle (RC) of the Cupid's peak line. Calculate and establish functional relationships for Cupid's peak parameters and the concept of the Cupid's peak index Golden Ratio Deviation. ResultsIn the Cupid's Peak Triangle Theory, important parameters describing Cupid's peak morphology include Cupid's peak angle (ACp), arc (RCp), the smooth connection point (SI) of the Cupid's peak arc and line, and the Cupid's peak index (CPI). The parameters are interrelated in their functional relationships. ACp determines RCp, the SI point determines the proportion of the Cupid's peak arc to the line, and CPI determines GRD. Cupid's peak parameter ranges in the normal population are as follows: ACp is 109o-160o, RCp is 1.24-0.35 radians, CPI is 0.614-0.508, and GRD is 0.62-17.85%. ConclusionsThe Cupid's peak triangle theory reveals the functional relationship between the Cupid's peak parameters and quantifies the aesthetics essence of lip shape. Clinical RelevanceThe morphology of the Cupid's peak serves as a tangible manifestation of lip shape aesthetics. This study aims to elucidate the aesthetic essence and general principles of Cupid's peak morphology, offering a quantitative theoretical foundation for lip plastic and cosmetic surgery.

Investigation of the relationship between hallux valgus, quadriceps angle, and body image perception in young adults

Purpose: Our study aimed to identify the presence and severity of hallux valgus deformity in young adults, using both by the Manchester classification and goniometry, to evaluate the Quadriceps angle (Q angle), and to examine the relationship between some anatomical parameters and body image perception. Materials and Methods: A total of 158 individuals aged 18-30 (111 females, 47 males) who voluntarily agreed to participate in the study were included. Demographic characteristics, Quadriceps angle, and hallux valgus angle were measured. Hallux valgus and Quadriceps angles were determined using a goniometer, while the Manchester scale was employed to evaluate the level of Hallux valgus deformity. The Golden Ratio for the lower extremity was calculated by taking the ratio of lower extremity length to leg length, and the body image perception score was determined. Results: Body weight, height and body mass index showed statistically significant differences in terms of gender, while age parameter did not show statistically significant difference between genders. Also, no significant difference in Quadriceps angle was observed between genders for both right and left sides, while a significant difference in Hallux valgus angle was noted. A high, positive, and significant relationship was found between Manchester classification and hallux valgus, while Golden ratio values did not significantly differ by gender. Additionally, body image perception scores were higher in males (162.60±25.45 points) than in females (153.51±25.89 points). Conclusion: Deviations from their normal values of the hallux valgus and quadriceps angle which affect the musculoskeletal system, may lead to some health problems, as well as difficulties in performing daily life activities, and concerns about aesthetics. Failure to fulfil one’s normal functions or not to find oneself aesthetically insufficient will also make it likely that the body image perception will deteriorate.

Performance evaluation of sustainable energy alternatives to obtain efficient hybrid energy investments

This study evaluates the synergy of coalition for hybrid renewable energy (RWB) system alternatives. In this context, the alternative sources of hybrid RWB system are examined to illustrate the impact-relation directions among them with multi SWARA based on q-ROFs and golden cut. Next, the performances of renewable alternatives are measured in terms of the synergy of coalition with game theory and Shapley value. It is concluded that solar energy is the most suitable RWB alternative for synergy to increase efficiency in investments. However, biomass does not have a significant influence on providing synergy in energy investments. Therefore, solar energy should be prioritized for hybrid energy investments. Especially with the effect of technological developments, the efficiency of solar energy investments increases significantly. Thus, solar energy investments have become quite suitable for increasing the synergy in hybrid energy projects. Furthermore, necessary research should be conducted to make biomass energy more efficient.

Floating-point photonic iterative solver demonstrated for Newton–Raphson method

Though photonic computing systems offer advantages in speed, scalability, and power consumption, they often have a limited dynamic encoding range due to low signal-to-noise ratios. Compared to digital floating-point encoding, photonic fixed-point encoding limits the precision of photonic computing when applied to scientific problems. In the case of iterative algorithms such as those commonly applied in machine learning or differential equation solvers, techniques like precision decomposition and residue iteration can be applied to increase accuracy at a greater computing cost. However, the analog nature of photonic symbols allows for modulation of both amplitude and frequency, opening the possibility of encoding both the significand and exponent of floating-point values on photonic computing systems to expand the dynamic range without expending additional energy. With appropriate schema, element-wise floating-point multiplication can be performed intrinsically through the interference of light. Herein, we present a method for configurable, signed, floating-point encoding and multiplication on a limited precision photonic primitive consisting of a directly modulated Mach–Zehnder interferometer. We demonstrate this method using Newton's method to find the Golden Ratio within ±0.11%, with six-level exponent encoding for a signed trinary digit-equivalent significand, corresponding to an effective increase of 243× in the photonic primitive's dynamic range.

Comparative evaluation of facial divine proportions in males and females with average growth pattern

Facial beauty of an individual depends on proportion and its relationship to various facial parts which varies in each individual. The values of measured proportion in beautiful faces are likely to approximate divine proportion and may show variation with ethinicity, sex, growth pattern. Hence, aim of the study was to evaluate and compare vertical and horizontal parameters of facial divine proportions in male and female subjects with average growth pattern. 30 subjects (18-30 yrs age) with average growth pattern (based on cephalometric measurements FMA, Yaxis, GoGn-SN and facial axis angle) were divided into two groups as Group I (Male subjects, n=15) ; Group II (female subjects, n=15). Standardized frontal facial photographs of all the subjects were obtained. Nine vertical and four horizontal parameters were measured on all the facial photographs using IC Measure software and were used to evaluate horizontal and vertical facial proportions and then compared to divine proportions considering 1.618 as 100%. Horizontal and Vertical facial proportion in males were higher than females. Group I showed that three of seven vertical facial proportions were close to divine proportion (1.618) whereas only one vertical facial proportion in Group II were close to divine proportions. Horizontal facial proportions in both the groups deviated more from divine proportion (1.618).There was difference between males and females for the vertical and horizontal facial proportions with values being larger in males. This should be considered as an accessory guideline in planning orthodontic or orthognathic treatment.

Enhanced LaRC05 failure criteria for investigating low-velocity impact on fiber-reinforced composites: An experimental and computational study

A finite element model was developed using both continuum and discrete damage modeling techniques to provide detailed predictions for ply-by-ply damage progression in composite laminates during low-velocity impact (LVI) events. A new fiber failure model was incorporated into the LaRC05 failure criteria to predict fiber pull-out and fiber crushing during the fiber damage evolution. In addition, the selective range golden section search (SRGSS) algorithm was implemented to efficiently predict fiber breakage, pull-out, splitting, kinking and crushing, and matrix cracking. The delamination was captured by cohesive element layers embedded between every adjacent composite ply. The interactions of intralaminar matrix cracking and delamination were modeled by deploying cohesive elements within each composite ply. The prediction results were validated by 30 J and 75 J drop-weight tests with different-sized impactors, as well as X-Ray CT inspections on 254 mm by 304.8 mm [0/45/90/-45]4s IM7/977–3 laminates. The model predicted the maximum deflection and contact duration with <2 % error, and the peak load, damaged areas, and absorbed energy with <8 % error. The matrix fracture plane and the fiber kink band angle were found with 1° precision 48 % faster via the SRGSS algorithm. The detailed sequences of damage occurrence were predicted by analyzing the energy dissipation histories through various damage modes. Although this modeling methodology was developed for LVI scenarios, it has broad applications for predicting failures in composites.

Is the golden ratio present in the coxal bone? An anatomical pilot study.

The coxal bone is crucial for movement, stability, and childbirth. Although most morphometric studies estimate gender and age, ratio, correlation and index calculations, there are no studies on the golden ratios in the coxal bone. Inspired by this idea, we investigated the presence of the golden ratio in the coxal bones. In this study, 95 adult dry coxal bones were measured using a digital caliper. Morphometric measurements were conducted based on 18 identified parameters. 12 of these parameters were related to the distances between two points in various parts of the bone. New ratios were determined with those measurements. In our study, we detected a constant coefficient between the following lengths: anterior superior iliac spine (ASIS)- posterior superior iliac spine (PSIS) and anterior inferior iliac spine (AIIS)- posterior inferior iliac spine (PIIS), vertical and transverse diameters of the acetabulum (AC), ASIS-AC and AIIS-AC, PSIS-AC and PIIS-AC, ASIS-auricular surface and AIIS-auricular surface, ASIS-symphyseal surface and AIIS-symphyseal surface (respectively, 1.29, 1.05, 1.18, 2.32, 1.26, 1.32). In order to check the accuracy of this hypothesis, length of between AIIS-PIIS, transverse diameter of the acetabulum, length of between PIIS-AC, length of between AIIS-AC, shortest distance between AIIS-auricular surface, length of between AIIS-symphyseal surface were estimated with the help of new equations. We detected constant ratios between some lengths in the coxal bone. Estimated distances should be taken into account during surgical procedures to prevent complications. In this context, the constant ratios identified in our study will serve as a guide for surgeons.

Rational approximation of golden angles: Accelerated reconstructions for radial MRI.

To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio-based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Label adversarial domain adaptation network for predicting remaining useful life based on cross-domain condition

Most data-driven methods for predicting remaining useful life assume that the data under different operating conditions follow the same distribution. However, this assumption rarely holds in real-world situation. Additionally, traditional methods do not fully utilize the hidden label information from the target domain or account for the transfer quality of source domain data. To address these issues, Label Adversarial Domain Adaptation (LADA) network is introduced in this paper. Specifically, LADA aims to filter the source domain data and maximize the use of hidden label information from the target domain. Firstly, a similarity measurement indicator based on the pearson correlation coefficient (PCC) and dynamic time warping (DTW) is employed to filter source domain data similar to the target domain data distribution. Then, in order to fully utilize the hidden label information from the target domain, the cloud model and golden section are utilized to create pseudo class labels. Furthermore, a feature difference module is established that minimizes the disparity between domain features. This is realized by using the maximum mean difference (MMD) and Kolmogorov–Smirnov (K–S) statistical test. The experimental results indicate that LADA has advantages in cross-domain RUL prediction.

Relationship between the Ideal Female Buttock and the Golden Ratio.

Relationship between the Ideal Female Buttock and the Golden Ratio.

Comparison of craniofacial anthropometric measurements with the golden ratio in young adults

Comparison of craniofacial anthropometric measurements with the golden ratio in young adults

An integrated expert recommender system approach to environmental service priorities in renewable energy

The purpose of this study is to analyze the investment success of renewable energy generation projects design. A novel model has been constructed for this purpose. At the first stage, collaborative filtering methodology is taken into consideration to complete missing evaluations. After that, M-SWARA based on QUSFSs with golden cut is used to compute the weights of these factors. Finally, the components of the service design are ranked by TOPSIS approach. The main contribution of the paper is that a new methodology (M-SWARA) has been created in this study by making improvements to SWARA. With the help of this new model, causal directions between the indicators can also be examined. Similarly, collaborative filtering methodology is taken into consideration to complete missing evaluations. In this process, the decision makers are allowed to leave the questions they wanted blank. This situation is considered as the superiority of the proposed model compared to many previous models in the literature. The findings indicate that cost is the most significant factor for the success of renewable energy investments because it gets the highest weight (.261). The ranking results also demonstrate that product is the most essential component of the service design of renewable energy investments. Therefore, solving the high-cost problem is of vital importance to increase these investments. First, renewable energy companies can reduce costs with more effective financial management. To carry out this process effectively, a finance department consisting of qualified personnel is needed. Thanks to this team, current situations in the financial markets will be better followed and this will play an important role in reducing costs.

Golden Ratio Realistically and Theoretically

Golden Ratio Realistically and Theoretically

A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ-Fibonacci statistical convergence, strong Δ-Fibonacci summability, and Δ-Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers.

On Quark–Lepton Mixing and the Leptonic CP Violation

In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark-and-lepton sector is a difficult task, unless one introduces ad hoc relations among the matrices that diagonalize such different kinds of fermions. In this paper, we discuss in detail the possibility that the PMNS matrix is given by the product UPMNS=VCKM★T★, where T comes from the diagonalization of a see-saw like mass matrix that can be of a Bimaximal (BM), Tri-Bimaximal (TBM) and Golden Ratio (GR) form, and identify the leading corrections to such patterns that allow for a good fit to the leptonic mixing matrix as well as to the CP phase. We also show that the modified versions of BM, TBM and GR can easily accommodate the solar and atmospheric mass differences.

Method for determining phase shift using two-phase interpolation transformation

This study focuses on a method for accurately determining the phase shift between two harmonic signals. The proposed technique compares the waveform of the combined signal, which is obtained by applying a two-phase interpolation transformation, with a set of predefined reference functions. This study aims to develop a method for accurately measuring the phase shift between two harmonic signals to reduce the measurement errors caused by phase asymmetry in signal transmission channels and minimize the costs associated with parameter control. The sources of error in the proposed measurement method are identified and addressed. The task involves setting up the measurement objective to determine the phase shift between two harmonic signals. This section presents the analyses of known methods for measuring phase shifts using of analog-to-digital conversion. The next step involves selecting indicators and criteria to determine how closely the investigated signal matches the reference function. Then, we propose the synthesis of an algorithm to find the extremum of the sum of squares deviations for the set of reference functions and the investigated signal, relying on the golden ratio method. Finally, the paper will analyze possible sources of error that could affect the measurement outcome. The methods used are the following: methodology for conducting digital signal processing and measuring error estimation, numerical methods for extremum search, and methodology for single-factor experiments. The following results were obtained. A proposed compensation method for measuring phase shift is based on comparing the shape of the normalized signal, which is obtained as a result of the summation of harmonic signals after their semiperiodical transformation, with a set of normalized reference functions synthesized by computational means. A list of measurement and auxiliary operations, which should be ideally conducted to implement this measurement method, has been determined. An analysis of the components of measurement errors was conducted. Conclusions. The scientific novelty of the obtained results lies in the following: a method for measuring the phase shift of a signal has been developed, which, in our opinion, should be classified as a compensatory measurement method. This will significantly reduce the error component caused by the phase asymmetry of signal transmission channels and reduce the costs of controlling parameters (up to 10%) without decreasing the quality of control; a list of the measuring and auxiliary operations necessary for the implementation of the proposed measurement method has been identified; sources of errors have been determined.