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The growing demand for solar energy conversion underscores the need for precise parameter extraction methods in photovoltaic (PV) plants. This study focuses on enhancing accuracy in PV system parameter extraction, essential for optimizing PV models under diverse environmental conditions. Utilizing primary PV models (single diode, double diode, and three diode) and PV module models, the research emphasizes the importance of accurate parameter identification. In response to the limitations of existing metaheuristic algorithms, the study introduces the enhanced prairie dog optimizer (En-PDO). This novel algorithm integrates the strengths of the prairie dog optimizer (PDO) with random learning and logarithmic spiral search mechanisms. Evaluation against the PDO, and a comprehensive comparison with eighteen recent algorithms, spanning diverse optimization techniques, highlight En-PDO’s exceptional performance across different solar cell models and CEC2020 functions. Application of En-PDO to single diode, double diode, three diode, and PV module models, using experimental datasets (R.T.C. France silicon and Photowatt-PWP201 solar cells) and CEC2020 test functions, demonstrates its consistent superiority. En-PDO achieves competitive or superior root mean square error values, showcasing its efficacy in accurately modeling the behavior of diverse solar cells and performing optimally on CEC2020 test functions. These findings position En-PDO as a robust and reliable approach for precise parameter estimation in solar cell models, emphasizing its potential and advancements compared to existing algorithms.

In this article it constructs tooth surface equation of a new type of bevel gear which is logarithmic spiral bevel gear by the tooth trace and the tooth profile curve with space geometric knowledge. By means of the CAD software which can intuitively understand the complex curves and surfaces and the MATLAB software platform, it makes the complex mathematical theory be easier to understand and apply correctly, and verifies the correctness of the tooth surface equations.

Software defect prediction has caused widespread concern among software engineering researchers, which aims to erect a software defect prediction model according to historical data. Among all the techniques used in this field, extreme learning machine is widely used by researchers because of its simple structure and excellent learning speed. At the same time, the prediction performance of extreme learning machine is greatly affected by the random selection of parameters and the weak generalization ability. In this sense, in order to improve the prediction performance of the model, researchers uses swarm intelligence optimization algorithm to provide the optimal parameters for the model. Sparrow search algorithm is a new meta-heuristic algorithm that simulates the foraging and anti-predation behavior of the sparrow group. However, the original sparrow search algorithm is easily trapped to local optimal solutions in the later stage of the iterations. To improve the global optimization ability of the original sparrow search algorithm, this paper proposed an adaptive variable sparrow search algorithm (AVSSA) based on adaptive hyper-parameters and variable logarithmic spiral. This work run experiments of AVSSA in eight benchmark functions, and obtained the satisfactory results. In the traditional software defect prediction algorithm, the imbalance of data distribution is also one of the main reasons that affect the performance of the model. Therefore, this paper uses the adaptive variable sparrow search algorithm to optimize the extreme learning machine as the base predictor for Bagging ensemble learning (AVSEB). A new software defect prediction ensemble learning model is proposed in this paper. Firstly, the model used the unstable cut-points algorithm to preprocess Bagging sample set in this model. Then, the adaptive variable sparrow search algorithm is used to optimize the extreme learning machine as the base predictor of ensemble learning. Finally, the voting method is used to output the prediction results of software defects. Based on the experimental results, the evaluation index of our proposed algorithm is significantly superior to the other four advanced comparison algorithms in 15 open software defect datasets. According to the test results of Friedman ranking and Holm’s post hoc test, this paper proposed algorithm has obvious statistical significance compared with other advanced prediction algorithms.

Background A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes. Results Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants. Conclusions The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.

Based on the accurate 3D model of logarithmic spiral bevel gear, the operation of spiral cone gear engagement is analyzed and simulated by ANSYS. Through the nonlinear static contact analysis of different positions, the stress change rule and the maximum contact stress is obtained. Compared with the theoretical contact stress strength rule, this paper also analyzes the dynamic operation situation of the gear pairs, obtains the dynamic contact situation rule at different engagement times and different rotating speeds, the influence of the rotating speed on the gear contact characteristics is compared too. The static, dynamic performance and change rules of the gear engagement is obtained, which lay a solid foundation for the further research, design and manufacture of spiral bevel gears.

We present a neutron guide which is curved in the shape of a logarithmic spiral. Simulations and calculations for such a spiral guide are presented and the potential use of the guide for a reflectometer is investigated and compared to the conventional circularly curved guide geometry. We concentrate on the specific case of a beamport at the SINQ source. For this application, the spiral guide shows a 30% increased flux on the region of interest while at the same time reducing background scattering due to beam converging.

A volute represents the most recognisable characteristic of the capital of the Ionic order. The geometric construction of its spiral form has occupied scholars since Renaissance times since Vitruvius’ description provided a variety of shapes that fit given constraints. Based on 16 analysed methods, the present research shows the continuity of the idea of drawing a Ionic volute as the involute of a polygonal chain within the eye. Namely, if a volute spiral is formed by several consecutive circular arcs, it can be defined as the involute of the polyline that connects the centres of corresponding arcs, whereby the polyline is the evolute of the chosen volute. In addition, by adopting suitable rectilinear discretisation of arithmetic and logarithmic spirals for an evolute form, two novel mathematically derived volute shapes are created. With a complete fit into Vitruvian constraints, such volutes indicate the great possibilities of the mathematical treatment of Ionic volutes.

This paper explores the esthetics of a kind of logarithmic spiral tilings that has not been investigated. It possesses the form similar to the structure of spiral galaxies, which globally displays the cyclic symmetry. The paper first studies the symmetry group associated with the spiral tiling. Then, using the generators of the group, the construction method of such tilings is analyzed in detail. To create colorful patterns on spiral tilings, a special dynamical system which is compatible with its symmetry group is designed. To promote the esthetic appeal of spiral patterns, a simple but practical strategy for generating patterns of color symmetry is presented. Based on the resulting patterns, several interesting methods are proposed to construct more types of derived spiral patterns.

The starfish optimization algorithm (SFOA) is a metaheuristic evolutionary intelligence algorithm with a great global search capability and strong adaptability. Although the SFOA has a good global search capability, it is not accurate enough in local search and converges slowly. To further enhance this convergence ability and global optimization ability, an enhanced starfish optimization algorithm (SFOAL) is proposed that combines sine chaotic mapping, t-distribution mutation, and logarithmic spiral reverse learning. The SFOAL can remarkably enhance both the global and local convergence capabilities of the algorithm, leading to a more rapid convergence speed and greater stability. In total, 23 benchmark functions and CEC2021 were used to test the development, search, and convergence capabilities of the SFOAL. The SFOAL was compared in detail with other algorithms. The experimental results demonstrated that the overall performance of the SFOAL was better than that of other algorithms, and the joint strategy could effectively balance the development and search capabilities to obtain stronger global and local optimization capabilities. For solving practical problems, the SFOAL was used to optimize the back propagation (BP) neural network to solve the ultra-wideband line-of-sight positioning problem. The results showed that the SFOAL-BP neural network had a smaller average position error compared to the random BP neural network and the SFOA-BP neural network, so it can be used to solve practical application problems.

To improve the performance of the sparrow search algorithm in solving complex optimization problems, this study proposes a novel variant called the Improved Beetle Antennae Search-Based Sparrow Search Algorithm (IBSSA). A new elite dynamic opposite learning strategy is proposed in the population initialization stage to enhance population diversity. In the update stage of the discoverer, a staged inertia weight guidance mechanism is used to improve the update formula of the discoverer, promote the information exchange between individuals, and improve the algorithm’s ability to optimize on a global level. After the follower’s position is updated, the logarithmic spiral opposition-based learning strategy is introduced to disturb the initial position of the individual in the beetle antennae search algorithm to obtain a more purposeful solution. To address the issue of decreased diversity and susceptibility to local optima in the sparrow population during later stages, the improved beetle antennae search algorithm and sparrow search algorithm are combined using a greedy strategy. This integration aims to improve convergence accuracy. On 20 benchmark test functions and the CEC2017 Test suite, IBSSA performed better than other advanced algorithms. Moreover, six engineering optimization problems were used to demonstrate the improved algorithm’s effectiveness and feasibility.