Recursive Algorithm Research Articles

Singular value decomposition based learning identification for linear time‐varying systems: From recursion to iteration

AbstractSystem identification is a critical task in various engineering applications such as motion control, signal processing and robotics. In this article, the identification of linear time‐varying (LTV) systems that perform tasks repetitively over a finite‐time interval is investigated. Traditional LTV system identification typically adopts recursive algorithms in the time domain, which are incapable of tracking drastic‐varying parameters and are subject to estimation lag and numerical instability. To address these issues, this article proposes the utilization of an iteration axis in addition to the time axis for estimating repetitive time‐varying parameters. Specifically, the proposed approach involves an estimation algorithm for the time‐varying parameters based on a recursive least squares (RLS) method along the iteration axis, as well as an update algorithm for the covariance matrix based on singular value decomposition (SVD) to enhance numerical stability. Additionally, a bias compensation method based on noise variance estimation is introduced for the sake of eliminating estimation error induced by measurement noise. Numerical comparisons with existing methods are conducted to demonstrate the effectiveness and superiority of the proposed method.

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix

SYNTACTIC ANALYSIS OF ARITHMETIC EXPRESSIONS FOR OPTIMIZING THE OPERATION OF PROGRAMS

Our algorithm combines the Reverse Polish Notation (RPN) and expression tree algorithms it is a novel method for efficiently evaluating arithmetic expressions. The algorithm combines the benefits of Reverse Polish Notation (RPN) and Expression Trees to provide a practical and efficient solution for evaluating expressions in both infix and postfix notation. The algorithm first converts the infix notation to RPN, which is then used to construct an expression tree. The expression tree is evaluated using a recursive function that traverses the tree and performs the required operations. The use of an expression tree allows for the optimization of sub-expressions, further improving the efficiency of the algorithm. The Combined RPN and Expression Tree Algorithm offers several advantages over other algorithms for evaluating arithmetic expressions. It is more efficient than some recursive algorithms while being more practical than stack-based algorithms. Furthermore, the use of an expression tree allows for the optimization of sub-expressions, further improving efficiency.

Application of hybrid robotic systems in crop harvesting: Kinematic and dynamic analysis

Harvesting of agricultural crops, especially when the ripe products have to be picked one by one, has always been a major concern of farmers and growers. Consequently, the use of robots and the mechanization of harvesting operations have been considered as the effective means of tackling such challenges. In the present research, the use of hybrid robots (which combine open-loop and closed-loop manipulators) has been proposed for this purpose; because these robots help reduce the size of the workforce and thus slash the harvesting costs, and they also boost the speed and accuracy of harvesting operations. However, using this type of robots without paying attention to some important factors (e.g., using motors of optimal power at the actuated joints of a robot and choosing appropriate lengths for robot links) can have a substantial adverse effect on the manufacturing cost, working space and the effective functioning of such robots. So the main focus of this paper is on the kinematic and dynamic analysis of hybrid robotic systems. The main advantage of this research over similar works is the generality by which it describes the mechanical behavior of these robots; so that by using the recursive algorithms presented in this paper, all kinds of robots in the hybrid class can be analyzed. However, due to the complexity in the analysis of such systems, a hybrid robot consisting of three closed loops and one open loop was considered in this paper as a sample case study, so that we could explain, visually and graphically, all the steps involved in deriving its motion equations. The simulation results for this robotic system demonstrate the efficacy of the proposed method in the kinematic and dynamic analysis of hybrid robots, as efficient and functional crop harvesting equipment.

The limited-memory recursive variational Gaussian approximation (L-RVGA)

We consider the problem of computing a Gaussian approximation to the posterior distribution of a parameter given a large number N of observations and a Gaussian prior when the dimension of the parameter d is also large. To address this problem we build on a recently introduced recursive algorithm for variational Gaussian approximation of the posterior, called recursive variational Gaussian approximation (RVGA), which is a single pass algorithm, free of parameter tuning. In this paper, we consider the case where the parameter dimension d is high, and we propose a novel version of RVGA that scales linearly in the dimension d (as well as in the number of observations N), and which only requires linear storage capacity in d. This is afforded by using a novel recursive expectation maximization (EM) algorithm applied for factor analysis introduced herein, to approximate at each step the covariance matrix of the Gaussian distribution conveying the uncertainty in the parameter. The approach is successfully illustrated on the problems of high dimensional least-squares and logistic regression, and generalized to a large class of nonlinear models.

A non markovian retrial queueing system

This paper studies a discrete-time queueing system in which a customer who enters in the system with a server occupied may choose to go to the retrial group or to begin its service displacing to the retrial group the customer that was in the server. If the server is idle the arriving customer begins its service immediately.Retrial and service times are general, and the only repeated customer that can go directly to the server is the one situated at the first place of the retrial group.A complete study of the model has been curried out noting specially the analysis of a recursive algorithm implemented by Theorems 2 and 3 and the study of the waiting time of a customer in the queue and in the system. Finally numerical examples are given.

Bone Biomarkers and Subsequent Survival in Men with Hormone-sensitive Prostate Cancer: Results from the SWOG S1216 Phase 3 Trial of Androgen Deprivation Therapy with or Without Orteronel

BackgroundBone biomarkers are strongly prognostic for overall survival (OS) in men with castration-resistant prostate cancer but not fully established for hormone-sensitive prostate cancer (HSPC). ObjectiveBone biomarkers in HSPC were prospectively evaluated as part of a phase 3 study of androgen deprivation therapy ± the CYP17 inhibitor orteronel. Design, setting, and participantsPatients were randomly divided into training (n = 316) and validation (n = 633) sets. Recursive partitioning and Cox proportional hazard models were employed. Outcome measurements and statistical analysisBone resorption (C-telopeptide and pyridinoline) and bone formation markers (C-terminal collagen propeptide and bone alkaline phosphatase) were assessed from patient sera. Results and limitationsOf 1279 men, 949 had evaluable baseline bone biomarkers. Optimal cutoffs were identified to define elevated levels of each of the four biomarkers (all p < 0.05) that were associated with worse OS. After adjusting for clinical risk factors in the validation set, elevated bone biomarkers were statistically significantly associated with an increased risk of death (hazard ratios ranging from 1.37 to 1.92). Recursive partitioning algorithms applied to the training set identified three risk groups (low, intermediate, and poor) with differential OS outcomes (median OS: 8.2, 5.1, and 2.1 yr, respectively) based on combinations of bone biomarkers. These results were confirmed in the validation set. ConclusionsIn men with HSPC initiating androgen deprivation therapy, bone biomarkers are strongly and independently prognostic for OS. Bone biomarker levels alone or in combination with clinical covariates identify unique subsets of men with differential OS outcomes. These results validate the clinical value of bone biomarker assessment in the HSPC state, extending bone biomarker utility beyond the castration-resistant state. Patient summaryIn men with newly diagnosed metastatic prostate cancer, high levels of bone turnover biomarkers are associated with a shorter lifespan.

Recursive Algorithm for Forming Structured Sets of Information Blocks that Increase the Speed of Performing Procedures for Determining Their Source

Purpose of research. The article examines the features of the synthesis of specialized devices that control the integrity and authenticity of individual information blocks based on CBC codes. Approaches aimed at reducing computational and resource costs when performing such procedures are considered. The dependencies between the performance indicators and the requirements for the volume of internal memory of specialized computers processing data in CBC mode are formulated..Methods. The implementation of data source authentication procedures using encoding in the mode of concatenation of individual data blocks is an effective method of increasing reliability in conditions of a limited size of verified authentication sequences. At the same time, its implementation in receivers requires the creation of specialized calculators that process tree-like structures that arise during data decoding, consisting of separate data blocks. To reduce resource and computational costs when processing such structures, indirect addressing is used, in which block data is stored in RAM, and their addresses are stored in the high-speed register memory of the computer itself.Results. A model of indirect addressing of data blocks in RAM has been created. Pointers to blocks are stored in a separate register memory and each pointer is placed according to the decoded sequence number of the block in the sequence. Each block address in RAM is supplemented by a set of pointers to subsequent blocks in the branches of the tree structure. The created mathematical model made it possible to estimate the size in bits of all the pointers involved and their number, which made it possible to determine the need for a computer processing a tree structure in register memory.Conclusion. The paper shows that using a combination of matrix and list organization of block address storage reduces the need for register memory of the calculator by 50-60%. At the same time, the computer can process the tree-like structure of information blocks using high-performance iterative algorithms, which would be impossible if only the list organization of address storage was used.

Filtering-based maximum likelihood hierarchical recursive identification algorithms for bilinear stochastic systems

Filtering-based maximum likelihood hierarchical recursive identification algorithms for bilinear stochastic systems

Identification of Tree Species in Forest Communities at Different Altitudes Based on Multi-Source Aerial Remote Sensing Data

The accurate identification of forest tree species is important for forest resource management and investigation. Using single remote sensing data for tree species identification cannot quantify both vertical and horizontal structural characteristics of tree species, so the classification accuracy is limited. Therefore, this study explores the application value of combining airborne high-resolution multispectral imagery and LiDAR data to classify tree species in study areas of different altitudes. Three study areas with different altitudes in Muyu Town, Shennongjia Forest Area were selected. Based on the object-oriented method for image segmentation, multi-source remote sensing feature extraction was performed. The recursive feature elimination algorithm was used to filter out the feature variables that were optimal for classifying tree species in each altitude study area. Four machine learning algorithms, SVM, KNN, RF, and XGBoost, were combined to classify tree species at each altitude and evaluate the accuracy. The results show that the diversity of tree layers decreased with the altitude in the different study areas. The texture features and height features extracted from LiDAR data responded better to the forest community structure in the different study areas. Coniferous species showed better classification than broad-leaved species within the same study areas. The XGBoost classification algorithm showed the highest accuracy of 87.63% (kappa coefficient of 0.85), 88.24% (kappa coefficient of 0.86), and 84.03% (kappa coefficient of 0.81) for the three altitude study areas, respectively. The combination of multi-source remote sensing numbers with the feature filtering algorithm and the XGBoost algorithm enabled accurate forest tree species classification.

Association of Body Mass Index with Insulin-like Growth Factor-1 Levels among 3227 Chinese Children Aged 2–18 Years

Insulin-like growth factor-1 (IGF-1) levels are affected by nutritional status, yet there is limited research exploring the association between body mass index (BMI) and IGF-1 levels among children. This cross-sectional study included 3227 children aged 2-18 years without specific diseases, whose height, weight, and pubertal stages were measured and assessed by pediatricians. BMI standard deviation scores (BMISDS) were used to categorize children as underweight (BMISDS < -2); normal-weight (-2 ≤ BMISDS ≤ 1); overweight (1 < BMISDS ≤ 2); and obese (BMISDS > 2). Children were divided into low-level (<-0.67 SD) and nonlow-level (≥-0.67 SD) groups based on IGF-1 standard deviation scores (IGF-1SDS). The association between IGF-1 and BMI as categorical and continuous variables was explored by Binary logistic regression, the restrictive cubic spline model, and the generalized additive model. Models were adjusted by height and pubertal development. Recursive algorithm and multivariate piecewise linear regression were further utilized to assess the threshold of the smooth curve. IGF-1 levels varied by BMI categories, with the highest levels observed in the overweight group. The proportion of low IGF-1 levels in underweight, normal-weight, overweight, and obese groups was 32.1%, 14.2%, 8.4%, and 6.5%, respectively. The risk odds of low IGF-1 levels in underweight children were 2.86-, 2.20-, and 2.25-fold higher than in children with normal weight before adjustment, after adjustment for height, and after adjustment for height and puberty, respectively. When analyzing the association between BMI and low IGF-1 levels, dose-response analysis demonstrated an inverted J-shaped relationship between BMISDS and low IGF-1 levels. Lower or higher BMISDS increased the odds of low IGF-1 levels, and significance was retained in underweight children but not in obese children. When BMI and IGF-1 levels were used as continuous variables, the relationship between the BMISDS and IGF-1SDS followed a nonlinear inverted U shape. IGF-1SDS increased with the increase of BMISDS (β = 0.174, 95% CI: 0.141 to 0.208, p < 0.01) when BMISDS was less than 1.71 standard deviation (SD) and decreased with the increase of BMISDS (β = -0.358, 95% CI: -0.474 to -0.241, p < 0.01) when BMISDS was greater than 1.71 SD. The relationship between BMI and IGF-1 levels was found to depend on the type of variable, and extremely low or high BMI values could result in a tendency toward low IGF-1 levels, emphasizing the importance of maintaining a normal BMI range for normal IGF-1 levels.

A nomogram model based on pre-treatment and post-treatment MR imaging radiomics signatures: application to predict progression-free survival for nasopharyngeal carcinoma

BackgroundTo establish a novel model using radiomics analysis of pre-treatment and post-treatment magnetic resonance (MR) images for prediction of progression-free survival in the patients with stage II–IVA nasopharyngeal carcinoma (NPC) in South China.MethodsOne hundred and twenty NPC patients who underwent chemoradiotherapy were enrolled (80 in the training cohort and 40 in the validation cohort). Acquiring data and screening features were performed successively. Totally 1133 radiomics features were extracted from the T2-weight images before and after treatment. Least absolute shrinkage and selection operator regression, recursive feature elimination algorithm, random forest, and minimum-redundancy maximum-relevancy (mRMR) method were used for feature selection. Nomogram discrimination and calibration were evaluated. Harrell’s concordance index (C-index) and receiver operating characteristic (ROC) analyses were applied to appraise the prognostic performance of nomograms. Survival curves were plotted using Kaplan–Meier method.ResultsIntegrating independent clinical predictors with pre-treatment and post-treatment radiomics signatures which were calculated in conformity with radiomics features, we established a clinical-and-radiomics nomogram by multivariable Cox regression. Nomogram consisting of 14 pre-treatment and 7 post-treatment selected features has been proved to yield a reliable predictive performance in both training and validation groups. The C-index of clinical-and-radiomics nomogram was 0.953 (all P < 0.05), which was higher than that of clinical (0.861) or radiomics nomograms alone (based on pre-treatment statistics: 0.942; based on post-treatment statistics: 0.944). Moreover, we received Rad-score of pre-treatment named RS1 and post-treatment named RS2 and all were used as independent predictors to divide patients into high-risk and low-risk groups. Kaplan–Meier analysis showed that lower RS1 (less than cutoff value, − 1.488) and RS2 (less than cutoff value, − 0.180) were easier to avoid disease progression (all P < 0.01). It showed clinical benefit with decision curve analysis.ConclusionsMR-based radiomics measured the burden on primary tumor before treatment and the tumor regression after chemoradiotherapy, and was used to build a model to predict progression-free survival (PFS) in the stage II–IVA NPC patients. It can also help to distinguish high-risk patients from low-risk patients, thus guiding personalized treatment decisions effectively.

A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification

A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.

The Recursive Algorithm for Filling Areas of Recognized Objects

Purpose of research. The recursive algorithm for painting recognized areas on a binarized image and extracting the contours of a color mark, in order to find the minimum time for counting the number of filled pixels in a recognized mark, was developed in the article.Methods. The region filling algorithm in the image is based on the recursive method. The algorithm begins the work from the central point of the image and analyzes the presence of unshaded pixels in adjacent cells. In the article is considered the definition of the shortest time for filling the recognized area in eight directions: east-south-west-north, east-north-west-south, southeast-northwest, southwest-northeast, west-south-east-north, west-north-east-south, north-east-south-west, north west south east. The algorithm contains several stages: checking the exit from the recursion provided that all areas are filled, filling the initial cell, filling the elements in four directions from the starting point, counting the number of filled elements.Results. A recursive algorithm for filling recognized areas on a binarized image with the possibility of highlighting the contours of a recognized mark has been developed. The direction of the optimal bypass, which has the shortest time in relation to other considered directions, is determined. The testing was carried out for cycles with 10, 50 and 100 iterations. According to the presented algorithm, a specialized software model was created. The number of the certificate of state registration of the computer program "Program for filling a recognized mark" is 2023612631.Conclusion. The results of experimental studies showed that for a cycle value of 10 iterations, the best time to fill the area is 12762 msec, for a cycle value of 50 iterations, the best time is 76008 msec, for a cycle value of 100 iterations, the best time is 160568 msec. The minimum average time to complete the filling operation was 84357 msec, therefore, the best of the eight pass combinations turned out to be the direction - north-east-south-west.

Joint two‐stage multi‐innovation recursive least squares parameter and fractional‐order estimation algorithm for the fractional‐order input nonlinear output‐error autoregressive model

SummaryThis paper mainly investigates the issue of parameter identification for the fractional‐order input nonlinear output error autoregressive (IN‐OEAR) model. In order to avoid the problem of large computation of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the key term separation. Through employing the hierarchial identification principle, the fractional‐order IN‐OEAR model is decomposed into two sub‐models with a smaller number of parameters. On the basis of the recursive identification methods, a recursive least squares sub‐algorithm and a gradient stochastic sub‐algorithm are proposed to estimate the parameters and the fractional‐order, respectively. With the aim of achieving more accurate parameter estimates, a two‐stage multi‐innovation least recursive algorithm is proposed by means of the multi‐innovation identification theory. The numerical simulation results test the effectiveness of the proposed methods.

A Recursive Algorithm for the Generative Study of Seljuk Muqarnas in Kayseri and Sivas

A Recursive Algorithm for the Generative Study of Seljuk Muqarnas in Kayseri and Sivas

Monitoring the health status of the population by age groups

A multi-criteria method for selecting informative sets of different features for a quantitative assessment of the population’s health status in 14 age groups is considered. To compare samples from two classes (groups), it is proposed to form a unified description of objects according to two gradations of nominal features. The unified description is used to synthesize latent features and calculate the values of the compactness measure of class objects on the numerical axis. The transformation of quantitative features into nominal gradations is implemented according to the search criterion for the minimum coverage of their values by non-overlapping intervals. The values of the boundaries of the intervals and their number are determined by a recursive algorithm considering the objects belonging to classes. An important property of the transformation is the invariance to measurement scales. A formula is proposed for calculating the membership function of class objects for each feature gradation. Function values are used to unify object descriptions and calculate the stability index of a feature, regardless of its measurement scale. The unification of descriptions by two gradations does not change the stability index but increases the contribution of each gradation to the separation of class objects. The ranking of features about their stability was used both for individual samples and for a set of defined samples. The results of ranking over a set of samples were used to search for patterns in individual features and to form sets from them to calculate the values of latent features of objects. A set of thirteen data samples from representatives of two classes was formed as follows. The first class was represented by objects of the younger age group, and the second class — by objects of different age groups. A set of seven different types of features has been identified. For each of 13 samples, the values of latent features on this set and measures of compactness of class objects on the numerical axis were calculated. A monotonically non-decreasing sequence of values of measures of compactness of data samples that are invariant to the order of precedence of age groups is obtained. The property of monotonicity of sequence values is consistent with empirical estimates of the health state in the process of population aging.

Recursive Decoding of Reed-Muller Codes Starting With the Higher-Rate Constituent Code

Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\leq 256)$ </tex-math></inline-formula> RM codes. Recursive decoding employs the Plotkin construction to split the original code into two shorter RM codes with different rates. In contrast to the standard approach which decodes the lower-rate code first, the method in this paper decodes the higher-rate code first. This modification enables an efficient permutation-based decoding technique, with permutations being selected on the fly from the automorphism group of the code using soft information from a channel. Simulation results show that the error-rate performance of the proposed algorithms, enhanced by a permutation selection technique, is close to that of the automorphism-based recursive decoding algorithm with similar complexity for short RM codes, while our decoders perform better for longer RM codes. In particular, it is demonstrated that the proposed algorithms achieve near-ML performance for short RM codes and for RM codes of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m}$ </tex-math></inline-formula> and order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m-3$ </tex-math></inline-formula> with reasonable complexity.

Robust Adaptive Control of Hypersonic Flight Vehicle With Aero-Servo-Elastic Effect

This paper investigates the notch filter based robust adaptive control for the longitudinal dynamics of flexible hyper- sonic flight vehicle using finite-time design and online estimation. Considering the aero-servo-elastic effect caused by the elastic vibration at sensor position, the recursive least-square algorithm is employed to track the natural frequencies of the flexible modes, which then be used as the center frequencies for the cascade-type notch filter. Based on the filtered signal, the robust adaptive control is studied where the neural network is used to handle aerodynamics uncertainty and the disturbance observer is employed to compensate flexible coupling. The prediction error is constructed for the update laws while the nonlinear function is further developed to achieve the finite-time tracking. The uniformly ultimately bounded stability is guaranteed under the proposed approach. The effectiveness of the design is illustrated through the simulation study.

Boundedness of the Optimal State Estimator Rejecting Unknown Inputs

The Kitanidis filter is a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs or disturbances. Though the optimality of the Kitanidis filter was founded for general time varying systems more than 30 years ago, its boundedness and stability analysis is still limited to time invariant systems, up to the authors' knowledge. In the framework of general time varying systems, this paper establishes upper and lower bounds of the error covariance of the Kitanidis filter, as well as upper bounds of all the auxiliary variables involved in the filter. By preventing data overflow, upper bounds are crucial for all recursive algorithms in real time applications. The upper and lower bounds of the error covariance will also serve as the basis of the Kitanidis filter stability analysis, like in the case of time varying system Kalman filter.