Quasi-Newton algorithm for optimal approximate linear regression design: Optimization in matrix space

Gaffke, Norbert; Schwabe, Rainer

doi:10.1016/j.jspi.2018.03.005

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…Correctness of estimates at the network testing stage amounted to 100% in both tested heavy metal cases. The method of learning that was aimed at minimizing the neural network error values following modification of values of the weight coefficients of neuron input signals was the Quasi-Newton (BFGS) algorithm [41].…”

Section: Numerical Analysismentioning

confidence: 99%

Immobilization of Zn and Cu in Conditions of Reduced C/N Ratio during Sewage Sludge Composting Process

2022

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In this paper we present results of research on the transformation of chemical forms of two elements (Cu, Zn) that occurred at the highest concentration in sewage sludge being processed in a composting process. The factor that had impact on the direction of the observed transformation was the amount of straw added to the mix with sewage sludge at the batch preparation stage including elimination of an additional source of organic carbon (straw). The analysis of contents of Cu and Zn chemical forms was performed applying Tessiere’s methodology. It was ascertained that reduction of supplementation has positive impact on the allocation of tested elements in organic (IV) and residual (V) fractions with a simultaneous decrease of heavy metals mobile forms share in bioavailable fractions, mostly ion exchangeable (I) and carbonate (II). Using an artificial neural network (ANN), a tool was developed to classify composts based on Austrian standards taking into account only I ÷ IV fractions treated as a labile, potentially bioavailable, part of heavy metals bound in various chemical forms in compost. The independent variables that were predictors in the ANN model were the composting time, C/N, and total content of the given element (total Cu, Zn). The sensitivity coefficients for three applied predictors varied around 1, which proves their significant impact on the final result. Correctness of the predictions of the generated network featuring an MLP 3-5-3 structure for the test set was 100%.

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Section: Numerical Analysismentioning

confidence: 99%

Immobilization of Zn and Cu in Conditions of Reduced C/N Ratio during Sewage Sludge Composting Process

2022

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“…Considering that these data are discrete and inconvenient to directly apply, curve fitting is conducted by using optimization software 1stOpt 51 with quasi-Newton algorithm. 52 The selection of curve-fitting algorithm is determined by the overall consideration of fitting accuracy and conciseness. Then, the yield strength and moduli of elasticity of ordinary and prestressed steel bars at elevated temperatures can be approximated, in the form of ratio of high temperature (T) to room temperature (20 C), by the following equations.…”

Section: Yield Strength and Modulus Of Elasticitymentioning

confidence: 99%

A hybrid steel–shape memory alloy prestressed concrete beam for improved fire resistance

Jia

et al. 2020

Struct Control Health Monit

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Summary Prestressed concrete beams are widely used in structures and infrastructures for their superior control effects on cross‐sectional area, cracking, and deformation. However, the fire resistance of ordinary prestressed beams is unsatisfactory due to the serious material degradation of concrete and steel, as well as the prestress loss at elevated temperatures. To achieve an acceptable fire resistance for prestressed concrete beams, the introduction of shape memory alloy (SMA) is proposed via the hybrid usage of prestressed steel and SMA bars. When the hybrid steel–SMA prestressed beam is exposed to fire, both the strength and modulus of elasticity of prestressed SMA bars will increase, which can compensate for the material degradation of prestressed steel bars. In addition, a desirable recovery stress can be generated in SMA bars at elevated temperatures and further compensate for the prestress loss of prestressed steel bars. To study the fire resistance of the proposed beam, the fitting formulae of material properties of concrete, steel, and SMA at elevated temperatures are given firstly. Then, the analytical model and working mechanism of the hybrid beam are also presented. Further, the methodology for the prediction of fire resistance, and the formulae for the calculation of beam's flexural bearing capacity and deflection, are also presented. A parametric study is further conducted to investigate the relationships between fire resistance and the area and location of prestressed SMA bars. Moreover, an optimal analysis is also established to obtain the most economical material cost of SMA bars. As a result, the proposed prestressed beam can achieve a better fire resistance in terms of both flexural bearing capacity and deflection control.

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“…The Fedorov–Wynn algorithm (Fedorov, 1972; Wynn, 1972) does so by iteratively replacing part of the existing design with the singular design point showing the largest derivative, while the class of multiplicative algorithms (with convergence proven by Yu, 2010a) multiplies every weight in the existing design simultaneously by a factor depending on the derivatives. Both algorithms in their basic form tend to propose a larger than necessary numbers of support points, but there are several adaptions to account for this problem (Gaffke & Schwabe, 2019; Martin & Camacha Gutierrez, 2015; Pronzato, 2013; Yang et al., 2013; Yu, 2011). In this paper, we will focus on the multiplicative algorithm, but our results do not depend on how an optimal design was obtained.…”

Section: Optimal Design Problems and Design Algorithmsmentioning

confidence: 99%

The design heatmap: A simple visualization of ‐optimality design problems

Holland‐Letz

Kopp‐Schneider

2020

Biometrical J

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Quasi-Newton algorithm for optimal approximate linear regression design: Optimization in matrix space

Cited by 5 publications

References 39 publications

Immobilization of Zn and Cu in Conditions of Reduced C/N Ratio during Sewage Sludge Composting Process

Immobilization of Zn and Cu in Conditions of Reduced C/N Ratio during Sewage Sludge Composting Process

A hybrid steel–shape memory alloy prestressed concrete beam for improved fire resistance

The design heatmap: A simple visualization of ‐optimality design problems

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