A Lightweight Learning Method for Stochastic Configuration Networks Using Non-Inverse Solution

Stochastic configuration networks (SCNs) face time-consuming issues when dealing with complex modeling tasks that usually require a mass of hidden nodes to build an enormous network. An important reason behind this issue is that SCNs always employ the Moore–Penrose generalized inverse method with high complexity to update the output weights in each increment. To tackle this problem, this paper proposes a lightweight SCNs, called L-SCNs. First, to avoid using the Moore–Penrose generalized inverse method, a positive definite equation is proposed to replace the over-determined equation, and the consistency of their solution is proved. Then, to reduce the complexity of calculating the output weight, a low complexity method based on Cholesky decomposition is proposed. The experimental results based on both the benchmark function approximation and real-world problems including regression and classification applications show that L-SCNs are sufficiently lightweight.

Form-Finding of Tensegrity Model with Triangular Cells

Tensegrity structures is a light-weight structure compared to concrete structures that are heavy and rigid in shape. The studies on form-finding for tensegrity configuration are still ongoing and have been extensively conducted. Additionally, many proposed tensegrity structures have not been built for real applications. This study aims to determine potential self-equilibrated configurations of three-stage Class I tensegrity model assemblage with triangular cells, which may be applied as deployable towers. The form-finding methodology involves phases in establishment of desired form and formulation for the self-equilibrated state. The system of equilibrium equations was solved by Moore-Penrose generalized inverse method. A range of twist angles 10o – 50o for triangular cells was investigated in the form-finding process. It was found that the form-finding method via changing of twist angles has successfully search self-equilibrated tensegrity models.

Reanalysis of Modified Structures by Adding or Removing Substructures

This study considers structural reanalysis owing to the modification of structural elements including (1) addition of substructures, (2) removal of substructures, and (3) changes in design variables. Coupling and decoupling reanalysis methods proposed in the study are performed by using the concept of compatibility conditions at interface nodes between the substructures or between the original structure and the substructures. Subsequently, a generalized inverse method to describe constrained responses is modified to obtain the reanalysis responses. In this study, constrained equilibrium equations are modified to consider a reanalysis of a structure with the addition and removal of statically stable or unstable substructures. The proposed reanalysis method is examined by using five examples of handling coupling and decoupling reanalysis of a truss structure.

Estimación de varianzas genéticas en maíz a partir de líneas S1 y S2

The analysis of lines S-l and S-2 and the regression of the measurements of the S-2 on their corresponding S-l were used to estimate the existing genetic variability in a Nebraska Stiff Stalk Synthetic (NSS) corn population at two localities, Mead and Lincoln, Nebraska-USA. A significant genetic variability was found in NSS for grain yield, days to blooming, ear and plant height, grain humidity and lodging percentage. The S-2 lines showed more frequent interaction of genotypes x environment than their S-l. In the wide sense, the heritability for the yield calculated by the analysis of variance of S-2 lines was larger than the one based on the regression of the S-2 on S-l (60 and 42%, respectively). Eight models, originated from Cockerham (1983), were used to identify the existing types of genetic variabilities. The inverse matrix method was used to estimate the parameters of genetic variability when the used co-variances gave a non-singular square matrix. The generalized inverse method o Moore-Penrose was used when the models showed a rectangular matrix. Usually, the best model was the one which estimated the additive variance only. Often times, no consistent covariance estimates were obtained among additive and dominant homocygotic (D-1) effects. For it, we could not infer to what the S-l family selection effect could be on the behavior of the resulting line crosses. The expected genetic gain per selection cycle for yield of S-2 families was 11.4%.

Structural reanalysis for a modified structure

Structural reanalysis aims to determine the variations in the displacement of a structure due to the addition or deletion of elements without solving the full degrees of freedom. The iterations change the design parameters at each step and utilize the factorization of the stiffness matrix of the initial design. This study develops a new reanalysis method to determine the additional forces that act on the initial structure and the displacements of the modified structure. It utilizes the compatibility conditions at the interfaces between the initial structure and the added or deleted members as static constraints, and applies the generalized inverse method to describe the static behavior of the constrained structure. The structural elements that are added may be statically stable substructures or floating members that possess rigid-body freedom. Examples are included to show the effectiveness of the proposed method.

Experimental and Numerical Investigation of Structural Damage Detection Using Changes in Natural Frequencies

A robust iterative algorithm is used to identify the locations and extent of damage in beams using only the changes in their first several natural frequencies. The algorithm, which combines a first-order, multiple-parameter perturbation method and the generalized inverse method, is tested extensively through experimental and numerical means on cantilever beams with different damage scenarios. If the damage is located at a position within 0–35% or 50–95% of the length of the beam from the cantilevered end, while the resulting system equations are severely underdetermined, the minimum norm solution from the generalized inverse method can lead to a solution that closely represents the desired solution at the end of iterations when the stiffness parameters of the undamaged structure are used as the initial stiffness parameters. If the damage is located at a position within 35–50% of the length of the beam from the cantilevered end, the resulting solution by using the stiffness parameters of the undamaged structure as the initial stiffness parameters deviates significantly from the desired solution. In this case, a new method is developed to enrich the measurement information by modifying the structure in a controlled manner and using the first several measured natural frequencies of the modified structure. A new method using singular value decomposition is also developed to handle the ill-conditioned system equations that occur in the experimental investigation by using the measured natural frequencies of the modified structure.