Vector Size Research Articles

Depth Sensors-Based Action Recognition Using a Modified K-Ary Entropy Classifier

Surveillance system is acquiring an ample interest in the field of computer vision. Existing surveillance system usually relies on optical or wearable sensors for indoor and outdoor activities. These sensors give reasonable performance in a simulation environment. However, when used under realistic settings, they could cause a large number of false alarms. Moreover, in a real-world scenario, positioning a depth camera at too great a distance from the subject could compromise image quality and result in the loss of depth information. Furthermore, depth information in RGB images may be lost when converting a 3D image to a 2D image. Therefore, extensive surveillance system research is moving on fused sensors, which has greatly improved action recognition performance. By taking into account the concept of fused sensors, this paper proposed a novel idea of a modified K-Ary entropy classifier algorithm to map the arbitrary size of vectors to a fixed-size subtree pattern for graph classification and to solve complex feature selection and classification problems using RGB-D data. The main aim of this paper is to increase the space between the intra-substructure nodes of a tree through entropy accumulation. Hence, the likelihood of classifying the minority class as belonging to the majority class has been reduced. The working of the proposed model has been described as follows: First, the depth and RGB images from three benchmark datasets have been taken as the input for the model. Then, using 2.5D cloud point modeling and ridge extraction, full-body features, and point-based features have been retrieved. Finally, for the efficacy of the surveillance system, a modified K-Ary entropy accumulation classifier is optimized by the probability-based incremental learning (PBIL) algorithm has been used. In both qualitative and quantitative experimental results, the testing results have shown 95.05%, 95.56%, and 95.08% performance over SYSU-ACTION, PRECIS HAR, and Northwestern-UCLA (N-UCLA) datasets. The proposed system could apply to various real-world emerging applications like human target tracking, security-critical human event detection, perimeter security, internet security, public safety etc.

Iris Liveness Detection Using Fragmental Energy of Haar Transformed Iris Images Using Ensemble of Machine Learning Classifiers

Contactless verification is possible with iris biometric identification, which helps prevent infections like COVID-19 from spreading. Biometric systems have grown unsteady and dangerous as a result of spoofing assaults employing contact lenses, replayed the video, and print attacks. The work demonstrates an iris liveness detection approach by utilizing fragmental coefficients of Haar transformed Iris images as signatures to prevent spoofing attacks for the very first time in the identification of iris liveness. Seven assorted feature creation ways are studied in the presented solutions, and these created features are explored for the training of eight distinct machine learning classifiers and ensembles. The predicted iris liveness identification variants are evaluated using recall, F-measure, precision, accuracy, APCER, BPCER, and ACER. Three standard datasets were used in the investigation. The main contribution of our study is achieving a good accuracy of 99.18% with a smaller feature vector. The fragmental coefficients of Haar transformed iris image of size 8 * 8 utilizing random forest algorithm showed superior iris liveness detection with reduced featured vector size (64 features). Random forest gave 99.18% accuracy. Additionally, conduct an extensive experiment on cross datasets for detailed analysis. The results of our experiments show that the iris biometric template is decreased in size to make the proposed framework suitable for algorithmic verification in real-time environments and settings.

УТОЧНЕННЯ ШВИДКОСТІ МЕТЕОРА ЯК ВИПАДКОВОЇ ВЕЛИЧИНИ ЗА ДОПОМОГОЮ ТЕОРЕТИЧНОГО РОЗРАХУНКУ ЇЇ ФУНКЦІЇ ЩІЛЬНОСТІ РОЗПОДІЛУ

When processing the results of simultaneous double-station video observations of meteors and subsequent cataloging of their kinematic parameters, the accuracy of the obtained results, that is, the error of each parameter, is important. The most important characteristic of a meteor is its velocity, because it affects the accuracy of determining the semi-major axis and the eccentricity of the heliocentric orbit of the meteoroid – on the one hand, and on the physics of the meteor motion in the atmosphere – on the other. Since after calculating the velocity vector direction, the velocity vector sizes can be searched “independently” (the results will be partially correlated) for each of the points, it is suggested to use these two values ​​to precize the velocity of the meteor, for example, finding its weighted average value. Earlier, we proposed to search all meteor kinematic parameters as random variables by Monte Carlo method, obtaining probability density distributions for each parameter. Since when calculating the meteor velocity in this way, we get two distributions for each of the observation points, it is suggested to find their section as a product of two input distributions with further normalization of its area by one. At first, a scheme for multiplying histograms was implemented, which was not very convenient because it gave a large scatter of the points of the resulting distribution. In this work, it is proposed to use the fact that both input velocity distributions are of normal type with high probability (probability 0.998 within three standard deviations) and to use the multiplication of analytical functions of the normal distribution, the result of which will also be a Gaussian function. Appropriate theoretical calculations were made, and this approach was tested on an individual meteor. It is shown that the scheme is mathematically and physically justified and gives effective results.

UTILIZING INTERACTIVE VECTOR GRAPHICS TO ENHANCE USER EXPERIENCE IN ENGAGING WITH COMPLEX USER INTERFACE DESIGN

In the shift towards the Fourth Industrial Revolution (IR4.0), there are a multitude of user interventions that are heavily dependent on screen-based content which are highly correlated with the Internet of Things (IOT). This has raised certain usability issues, primarily when utilizing pixel graphics in dealing with complex User Interface (UI) design on devices with smaller screen size. This paper addresses the delay in timing, as the main part of the usability issue, which is caused by the increased of user interaction in completing task given. This paper studies the conversion rate outcomes from pixel graphics to interactive Scalable Vector Graphics (SVG) as a solution in reducing user interaction thus enhancing overall user experience (UX). The research design focuses on 2 analysis stages, which starts with a comparison stage that is exploratory in nature, followed by a regression analytics as part of the usability testing. The comparative analysis utilizes A/B testing that is composed of a control group and a treatment group, which measures the time spent based on actions per-page, in determining the effect size of both pixel and vector graphics through specified observations. The regression analytics that follows through is explanatory in nature and measures the indirect effects of the time delay, in defining that there is a significant relationship between time spent against actions per-page. The findings contribute towards establishing a more impactful use of graphic format in the adaptation to UI design that maximizes UX outcomes, which defines effective usability towards conversion optimizations.

How environmental factors affecting COVID-19 transmission? case study: Riyadh region in Saudi Arabia

In this study, I have conducted non-medical, non-clinical-care research that will enable immediate exploring of how environmental factors affect spread of COVID-19 in Kingdom of Saudi Arabia (KSA). It focusses on climatic environmental factors that affect the distribution and population size of disease vectors and the relationship(s) between each of these environmental variables that provided from National Center for Metrology and COVID-19 infected cases from Ministry of Health in KSA. I used daily environmental data, including minimum, maximum, and averages temperatures (°C), rainfall amounts (mm), wind speed (KTS/Deg) and relative humidity (%) over the Riyadh region in Saudi Arabia. Spearman's rank correlation coefficient used to analyze the data. The results showed that average temperatures, minimum temperatures, and maximum temperatures were significantly correlated with a COVID-19 epidemic, (r = 0.527; 0.509; 0.530 respectively). A negative correlation was found with relative humidity (r = -0.475). These findings will be used as lessons learned as well as best practices in the future to help decision makers to understand the factors controlling COVID-19′s spread in KSA.

Fusion of vectored text descriptors with auto extracted deep CNN features for improved image classification

• Transfer learning approach on pre-trained DCNN models for the WANG dataset. • Using word2cev for creating an embedding vector followed by a combination of DSSM and LSTM to reduce the size of a word vector and using these new word vectors to assign five synonyms for each label or keyword for an image to improve classification accuracy. • Fusion of auto extracted features from pre-trained models and word to vector features obtained from word2vec, DSSM, and LSTM for improved content-based image classification (CBIC). In today's age, massive image data is generated rapidly. This influx has made labeling images tedious and, in turn, made it harder to retrieve images through searching algorithms that rely only on labels, keywords, or other meta-data in the images. Modern Content-Based Image Retrieval (CBIR) techniques rely on the visual features within the image to return relevant results to a search query. Deep Convolutional Neural Network (DCNN) models made great strides in the last decade. This paper relies on these complex pre-trained models to extract visual features from images. The proposed work has used pre-trained models like VGG16, MobileNet, Inceptionv3, and Xception for this task. Some studies in the CBIR space also suggest increased accuracy when both visual and textual features are considered. This paper proposes a novel three-step process for obtaining textual features. Firstly, the proposed model receives keywords for each image using Google Cloud Vision API. Secondly, the proposed model replaces each keyword with a 300-dimensional embedding vector obtained using word2vec, trained on the Google News dataset. Finally, the proposed model trains a combination of the Deep Semantic Similarity Model (DSSM) and Long Short-Term Memory (LSTM) model to reduce the 300-dimensional vector to a 64-dimensional vector. Using these new shortened word vectors, the proposed model computes the cosine similarity to replace each keyword of an image with five of its synonyms. Here, these additional steps increased the accuracy compared to simply using a word embedding technique. Finally, the proposed model combined the visual and textual feature vectors and observed that this feature set showed maximum classification accuracy of 98.33%, which is also compared with and found relatively better than other similar model results.

Simplifying VGG-16 for Plant Species Identification

Plant species identification represents an extraordinary challenge for machine learning due to visual interspecies similarities and large intraspecies variations. Furthermore, research literature reports that plant species identification usually lacks sufficiently large datasets for training classification models. In this paper, we address this problem with a model that simplifies the VGG-16 architecture, the N-VGG model. The idea behind N-VGG is to reduce experimentally observed overfitting on VGG-16 by using as few trainable parameters as possible. To do this, we substitute the flattening layer on the VGG architecture with a global average pooling layer. This reduces the size of the feature vector. In addition, we eliminate one of the two fully-connected layers and use a new hyper-parameter, N, to indicate the number of nodes on the remaining layer. To show the robustness of the N-VGG model, we conducted extensive experimentation. We trained N-VGG on five datasets for plant species identification. Four of these datasets are publicly available and have been widely used as benchmarks for plant identification models. For all datasets, we compare the accuracy of N-VGG to that of the VGG-16, Inception-v4, and EfficienNet-B3 models. The experimental results show that the N-VGG model achieved the best classification performance for all but one datasets, whereas all the models showed a remarkable performance for the remaining dataset. This evidence supports our initial idea that, for plant species classification, some accuracy might be lost due to overfitting and that having fewer trainable parameters helps in producing a more robust model.

MAN-MADE OBJECT EXTRACTION FROM REMOTE SENSING IMAGES USING GABOR ENERGY FEATURES AND PROBABILISTIC NEURAL NETWORKS

This paper presents a novel approach for man-made object extraction in remote sensing images. This paper focuses on the design and implementation of a system that allows a user to extract multiple objects such as buildings or roads from an input image without much user intervention. The framework includes five main stages: 1) Pre-processing Stage. 2) Extraction of Local energy features using edge information and Gabor filter followed by down sampling to reduce the redundant information. 3) Further reduction of the size of feature vectors using Wavelet decomposition. 4) Classification and recognition of man-made structures using Probabilistic Neural Network (PNN) 5) NDVI based post-classification refinement. Experiments are conducted on a dataset of 200 RS images. The proposed framework yields overall accuracy of 93%. Experimental results validate the effective performance of the suggested technique for extracting man-made objects from RS images. Compared with other methods; the proposed framework exhibits significantly improved accuracy results and computationally much more efficient. Most notably, it has a much smaller input size, which makes it more feasible in practical applications.

LSTM-CNN model of drowsiness detection from multiple consciousness states acquired by EEG

This study aimed to design a deep neural network for electroencephalography (EEG)-based drowsiness detection in multiple consciousness states, i.e., “awake,” “sleep,” and “drowsiness.” Few studies have seriously considered the optimal input vector size or labeling method in classifying multiple consciousness states, which may affect classification performance. To determine the optimal input vector length, i.e., window length, three neural network models (long short-term memory [LSTM], convolutional neural network [CNN], and combined LSTM and CNN) and four feature-based models were tested with six different levels of window length. The EEG dataset was acquired from 19 participants with randomly assigned auditory stimuli and button responses. The EEG data were labeled into three classes (awake, sleep, and drowsiness) based on the defined button response pattern corresponding to the stimuli. The results demonstrated that when the input vector size exceeded 8 sec, the performance of the neural network models dropped rapidly; however, when the window size was less than 8 sec, the performance change according to the window size was small. In contrast, the performance of feature-based models increased continuously as the window size increased. The LSTM model yielded the best accuracy (86%) for a 1 sec window length, and the LSTM-CNN model yielded the best kappa index (0.77) for a 4 sec window length. In addition, the proposed model was applied to the binary classification of normal consciousness (awake) and low consciousness (drowsiness and sleep) states to determine whether this model works appropriately in actual applications such as drowsiness detection in a driving environment. For binary classification, the LSTM-CNN model resulted in 0.95 F1 scores in 4000-ms. When a short input data (500 msec) is used, the LSTM-CNN model resulted in an average accuracy of 85.6% and a kappa index of 0.77 for the three-class classification problem and 0.94 F1 scores for the binary classification problem. In conclusion, we demonstrated that the proposed model could effectively detect drowsiness. Furthermore, a significant correlation was found between reaction time and drowsiness. However, using the reaction time as an index for labeling drowsiness was challenging because of the high false-negative ratio.

Intelligent design of the chiral metasurfaces for flexible targets: combining a deep neural network with a policy proximal optimization algorithm.

Recently, deep reinforcement learning (DRL) for metasurface design has received increased attention for its excellent decision-making ability in complex problems. However, time-consuming numerical simulation has hindered the adoption of DRL-based design method. Here we apply the Deep learning-based virtual Environment Proximal Policy Optimization (DE-PPO) method to design the 3D chiral plasmonic metasurfaces for flexible targets and model the metasurface design process as a Markov decision process to help the training. A well trained DRL agent designs chiral metasurfaces that exhibit the optimal absolute circular dichroism value (typically, ∼ 0.4) at various target wavelengths such as 930 nm, 1000 nm, 1035 nm, and 1100 nm with great time efficiency. Besides, the training process of the PPO agent is exceptionally fast with the help of the deep neural network (DNN) auxiliary virtual environment. Also, this method changes all variable parameters of nanostructures simultaneously, reducing the size of the action vector and thus the output size of the DNN. Our proposed approach could find applications in efficient and intelligent design of nanophotonic devices.

Scalable spatio‐temporal smoothing via hierarchical sparse Cholesky decomposition

AbstractWe propose an approximation to the forward filter backward sampler (FFBS) algorithm for large‐scale spatio‐temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state‐space models, but it requires inverting covariance matrices which have the size of the latent state vector. The computational burden associated with this operation effectively prohibits its applications in high‐dimensional settings. We propose a scalable spatio‐temporal FFBS approach based on the hierarchical Vecchia approximation of Gaussian processes, which has been previously successfully used in spatial statistics. On simulated and real data, our approach outperformed a low‐rank FFBS approximation.

USA Policy in Sub-Saharan Africa

The article is devoted to Biden Administration Policy in Sub-Saharan Africa during the first half of 2022. This policy is carried out in accordance with a keynote speech “The United States and Africa: Building a 21st Century Partnership” made by Secretary of State Antony Blinken on November 17, 2021 in Abuja, Nigeria. The Secretary identified five spheres of common interest and cooperation – global health, the climate crisis, more stable and inclusive economy, defense of democracy, peace and security. The United States acknowledge a growing role of Africa in the world affairs and use all means at their disposal to preserve and strengthen their positions on the continent. The US “right” to be a global leader remains indisputable. The main enemies, as everywhere, are “authoritarian” China and Russia. The author reviews the US positions and activities in regard to conflict situations in Ethiopia, Mali, Somalia, Democratic Republic of Congo and South Sudan. The meetings and contacts are traced between A. Blinken, his deputies and assistants and African leaders – Chairpersons of African Union and AU Commission, presidents of Angola, Chad, Equatorial Guinea, The Gambia, Malawi, Somalia, Zambia, prime minister of Cote d’Ivoire, foreign ministers of South Africa, Kenia, Nigeria and other countries. The trips of two American delegations are described. One, led by Deputy Secretary of State W. Sherman to South Africa, Angola and Togo (May). The other – “the Department of State economic diplomacy delegation” to Nigeria, Kenia, South Africa and Namibia (February). Some statistics on US – Sub-Saharan Africa trade and investments are provided. The official position concerning the tasks facing Africom is cited. In connection with the events in Ukraine, the United States launched in Africa a frenzied slanderous campaign against Russia. Despite brutal American pressure, about half of the African states refused to vote for the anti-Russian resolution in the United Nations General Assembly (26 out of 54). The African Union Chairperson M. Sall characterized the position of Africa as “very heterogeneous” and insisted on the cancellation of sanctions. His meeting with V. Putin in Sochi on June 3 showed that the African Union is interested in cooperation with Russia and has no intention to quarrel with it. The author analyses in detail “the Congressional Budget Justification” letter which presents the State Department requests of funds for the US policy in Africa in 2023 Financial Year (1 October 2022 – 30 September 2023). Now principle changes in regard to the size of expenditures or vectors of activities are planned.

Analysis of Affective Factors and Optimization Strategies of Emotion in Online Teaching Based on Improved SVM Model

Online teaching has the advantages of not being limited by location and space but it also has some shortcomings. The lack of face-to-face real-time interaction between teachers and students will affect some students’ learning mood. The improved support vector machine (SVM) model is a simple model based on linear algebra, which can convert text data into structured data that can be processed by a computer and then calculate the similarity between two documents into the similarity between two vectors. The facial expression features of learners in the situation collected and extracted by the students of this project group are analyzed and modeled, and the time consumption, occupied space, and classification effect of the feature vectors produced by the improved model are integrated. The original feature dimension can be optimized from 100 dimensions to 60 dimensions, which not only saves the time of training feature vectors but also reduces the size of the final feature vectors. Besides, on the basis of 60-dimensional preliminary features extracted by SVM model, four classification models can also achieve the best results. Therefore, in the optimization part of feature extraction, the dimension of initial features extracted by SVM model is set to 60 dimensions. We can gradually use the improved SVM model to analyze the emotional influencing factors and optimization strategies in online teaching, so as to keep abreast of students’ lectures and let more students participate in online teaching as much as possible.

Time Is Money: Considerations for Measuring the Radiological Reading Time.

Timestamps in the Radiology Information System (RIS) are a readily available and valuable source of information with increasing significance, among others, due to the current focus on the clinical impact of artificial intelligence applications. We aimed to evaluate timestamp-based radiological dictation time, introduce timestamp modeling techniques, and compare those with prospective measured reporting. Dictation time was calculated from RIS timestamps between 05/2010 and 01/2021 at our institution (n = 108,310). We minimized contextual outliers by simulating the raw data by iteration (1000, vector size (µ/sd/λ) = 100/loop), assuming normally distributed reporting times. In addition, 329 reporting times were prospectively measured by two radiologists (1 and 4 years of experience). Altogether, 106,127 of 108,310 exams were included after simulation, with a mean dictation time of 16.62 min. Mean dictation time was 16.05 min head CT (44,743/45,596), 15.84 min for chest CT (32,797/33,381), 17.92 min for abdominal CT (n = 22,805/23,483), 10.96 min for CT foot (n = 937/958), 9.14 min for lumbar spine (881/892), 8.83 min for shoulder (409/436), 8.83 min for CT wrist (1201/1322), and 39.20 min for a polytrauma patient (2127/2242), without a significant difference to the prospective reporting times. In conclusion, timestamp analysis is useful to measure current reporting practice, whereas body-region and radiological experience are confounders. This could aid in cost–benefit assessments of workflow changes (e.g., AI implementation).

A truncated reverse transcriptase enhances prime editing by split AAV vectors

Prime editing is a new CRISPR-based, genome-editing technology that relies on the prime editor (PE), a fusion protein of Cas9-nickase and M-MLV reverse transcriptase (RT), and a prime editing guide RNA (pegRNA) that serves both to target PE to the desired genomic locus and to carry the edit to be introduced. Here, we make advancements to the RT moiety to improve prime editing efficiencies and truncations to mitigate issues with adeno-associated virus (AAV) viral vector size limitations, which currently do not support efficient delivery of the large prime editing components. These efforts include RT variant screening, codon optimization, and PE truncation by removal of the RNase H domain and further trimming. This led to a codon-optimized and size-minimized PE that has an expression advantage (1.4-fold) and size advantage (621bp shorter). In addition, we optimize the split intein PE system and identify Rma-based Cas9 split sites (573-574 and 673-674) that combined with the truncated PE delivered by dual AAVs result in superior AAV titer and prime editing efficiency. We also show that this minimized PE gives rise to superior lentiviral vector titers (46-fold) over the regular PE in an all-in-one PE lentiviral vector. We finally deliver the minimized PE to mouse liver by dual AAV8 vectors and show up to 6% precise editing of the PCSK9 gene, thereby demonstrating the value of this truncated split PE system for invivo applications.

The Accuracy Comparison Between Word2Vec and FastText On Sentiment Analysis of Hotel Reviews

Word embedding vectorization is more efficient than Bag-of-Word in word vector size. Word embedding also overcomes the loss of information related to sentence context, word order, and semantic relationships between words in sentences. Several kinds of Word Embedding are often considered for sentiment analysis, such as Word2Vec and FastText. Fast Text works on N-Gram, while Word2Vec is based on the word. This research aims to compare the accuracy of the sentiment analysis model using Word2Vec and FastText. Both models are tested in the sentiment analysis of Indonesian hotel reviews using the dataset from TripAdvisor.Word2Vec and FastText use the Skip-gram model. Both methods use the same parameters: number of features, minimum word count, number of parallel threads, and the context window size. Those vectorizers are combined by ensemble learning: Random Forest, Extra Tree, and AdaBoost. The Decision Tree is used as a baseline for measuring the performance of both models. The results showed that both FastText and Word2Vec well-to-do increase accuracy on Random Forest and Extra Tree. FastText reached higher accuracy than Word2Vec when using Extra Tree and Random Forest as classifiers. FastText leverage accuracy 8% (baseline: Decision Tree 85%), it is proofed by the accuracy of 93%, with 100 estimators.

Implementation Naïve Bayes Classification for Sentiment Analysis on Internet Movie Database

A film review is a subjective opinion of someone who has different feelings about each film. As a result, film enthusiasts will struggle to assess whether the film meets their requirements. Based on these issues, sentiment analysis is the best way to fix them. Sentiment analysis, also known as opinion mining, is the study of assigning views or emotional labels to texts in order to determine if the text contains positive or negative thoughts. The Nave Bayes method was chosen because it can classify data based on the computation of each class's probability against objects in a given data sample. The best model was created utilizing data without lemmatization, 500 vector sizes, and Nave Bayes classification, with an accuracy of 78.96 percent and a f1-score of 78.81 percent. Changes in vector size affect the system's capacity to foresee positive and negative sentiments. The difference in accuracy and recall values shows that when vector size 300 is utilized, the precision and recall outcomes are lower than when vector size 500 is used.

Forecasting of Reactive Power Consumption with the Use of Artificial Neural Networks

Many electricity customers, particularly in the area of small and medium-sized enterprises, are characterized by a system of 3-phase unbalanced current consumption and the polarization of power factor in the individual phases. Strong variation of power factor in the different phases (often with both inductive and capacitive nature) causes the inability to install classic–a 3-phase reactive power compensators. Therefore, energy consumers are exposed to higher costs for the crossing of the contractual power factor. This paper describes the problem of reactive power forecasting with the use of artificial neural networks. For calculation, the Nonlinear Autoregressive (NAR) neural network was used for different input vector sizes and different numbers of neurons in the hidden layer for foreseeing reactive power generation. Results of simulations compared to real measurements confirm that it is possible to forecast the reactive power course, useful for optimal planning of reactive power compensation strategies.

Feature selection using improved multiobjective and opposition-based competitive binary gray wolf optimizer for facial expression recognition

Facial expression recognition (FER) in computer vision is a very daunting computational task because of high-intra class variations. Researchers have developed methods for extracting features from images that apply conventional and deep learning approaches. When conventional approaches are used in FER system, the size of extracted features is very large, which may adversely affect the performance of the classifier. Therefore, in the process of FER, feature selection is an essential phase. We propose an improvement on competitive binary gray wolf optimizer in discrete search space named as Improved MOCBGWO, and it is utilized to perform feature selection within wrapper-based setup. Next, we applied the SVM and K nearest neighbors classifiers to selected features for investigating the performance of the proposed system through two publicly available standard datasets: CK+ and JAFFE. We compared the performance of the proposed improvement with binary gray wolf optimizer, binary moth flame optimizer, binary particle swarm optimizer, and competitive binary GWO for evaluating its efficacy. The experimental results reveal that our proposed improvement boosts the recognition accuracy along with reduction in the size of feature vector in a superior way as compared to other methods.

A Krylov accelerated Newton–Raphson scheme for efficient pseudo-arclength pathfollowing

The computational efficiency of an enhanced version of a pseudo-arclength pathfollowing scheme tailored for general multi-degree-of-freedom (multi-dof) nonlinear dynamical systems is discussed. The pathfollowing approach is based on the numerical computation of the Poincaré map and its Jacobian in order to tackle nonautonomous systems with discontinuous vector fields. The scheme is applied to obtain frequency response curves of multi-dof hysteretic systems with a state vector size up to 120, as well as various reduced-order models of single and multiple cantilever beams on a shuttle mass. The proposed approach is shown to drastically increase the speed of convergence in the modified Newton–Raphson scheme thanks to a Krylov sub-space iteration which makes use of the LU decomposition of a frozen Jacobian matrix, which, upon convergence, becomes the monodromy matrix. Several numerical tests performed on mechanical systems with material or geometric nonlinearities corroborate the efficiency of the numerical strategy.The C++ code implementing the proposed methodology is freely available at https://doi.org/10.5281/zenodo.6616482.