New Optimization Algorithms for Structural Reliability Analysis

Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.

The influence of interdental spacing on the detection of proximal caries lesions in primary teeth

The aim of this study was to investigate the influence of interdental spacing on the performance of proximal caries detection methods in primary molars. In addition, aspects related to temporary tooth separation with orthodontic separators were evaluated. The proximal spaces between the posterior primary teeth (n = 344) of 76 children (4-12 years old) were evaluated before and after temporary separation. Stainless steel strips with different standardized thicknesses were used to measure the presence of biological spacing and the spacing obtained after temporary separation with orthodontic rubber rings. First, the presence of proximal caries lesions was assessed by visual inspection, bitewing radiographs and a pen-type laser fluorescence device (DIAGNOdent pen). Visual inspection after temporary separation with separators was the reference standard method in checking the actual presence of caries. Multilevel analyses were performed considering different outcomes: the performance of the methods in detecting caries lesions and the spacing after temporary separation. The spacing did not influence the performance of the caries detection methods. The maximum spacing obtained with temporary tooth separation was 0.80 mm (mean +/- standard deviation = 0.46 +/- 0.13 mm). The temporary separation was more effective in the upper arch and less effective when an initial biological interdental spacing was present. The biological interdental spacing does not influence the performance of proximal caries detection methods in primary molars, and temporary tooth separation provides spacing narrower than 1.0 mm.

Isokinetic Strength and Endurance in Proximal and Distal Muscles in Patients With Peripheral Artery Disease

Background: The objective of this study was to analyze the muscle strength and endurance of the proximal and distal lower-extremity muscles in peripheral artery disease (PAD) patients. Methods: Twenty patients with bilateral PAD with symptoms of intermittent claudication and nine control subjects without PAD were included in the study, comprising 40 and 18 legs, respectively. All subjects performed an isokinetic muscle test to evaluate the muscle strength and endurance of the proximal (knee extension and knee flexion movements) and distal (plantar flexion and dorsiflexion movements) muscle groups in the lower extremity. Results: Compared with the control group, the PAD group presented lower muscle strength in knee flexion (-14.0%), dorsiflexion (-26.0%), and plantar flexion (-21.2%) movements (P < 0.05) but similar strength in knee extension movements (P > 0.05). The PAD patients presented a 13.5% lower knee flexion/extension strength ratio compared with the control subjects (P < 0.05), as well as lower muscle endurance in dorsiflexion (-28.1%) and plantar flexion (-17.0%) movements (P < 0.05). The muscle endurance in knee flexion and knee extension movements was similar between PAD patients and the control subjects (P > 0.05). Conclusion: PAD patients present lower proximal and distal muscle strength and lower distal muscle endurance than control patients. Therefore, interventions to improve muscle strength and endurance should be prescribed for PAD patients.