Least-squares bilinear clustering of three-way data

A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, .

Numerical and analytical study on the mechanical properties of a connector with long-fiber and metal laminated bolts for prefabricated construction

To improve the mechanical performances of joints in prefabricated construction, a type of connection structure with long-fiber and metal laminated bolts (referred to as a fiber-metal connector) is proposed and investigated by simulation and theoretical methods. The results include the following: (1) The fiber layer in bolts can form a second stiffness during rotation. This mechanical characteristic improves the bearing capacities and energy dissipation ability of the connector relative to the conventional metal connector, which are expected to effectively limit the elastoplastic rotational displacement of a structure. (2) For the reason, the fiber layer can bear load in the plastic phase due to its high-strength characteristic in the length direction. (3) A bilinear model for the bearing curve of the fiber-metal connector is proposed, and equations for optimization of fiber layer thickness are obtained with a target on bearing capacity and energy dissipation ability which are approximately higher 30% and 13% than that of the conventional metal connector, respectively. This research is expected to provide a theoretical basis for the application of this fiber-metal connector in engineering and improve the safety of prefabricated structures.

Predicting Polysomnography Parameters from Anthropometric Features and Breathing Sounds Recorded during Wakefulness

Background: The apnea/hypopnea index (AHI) is the primary outcome of a polysomnography assessment (PSG) for determining obstructive sleep apnea (OSA) severity. However, other OSA severity parameters (i.e., total arousal index, mean oxygen saturation (SpO2%), etc.) are crucial for a full diagnosis of OSA and deciding on a treatment option. PSG assessments and home sleep tests measure these parameters, but there is no screening tool to estimate or predict the OSA severity parameters other than the AHI. In this study, we investigated whether a combination of breathing sounds recorded during wakefulness and anthropometric features could be predictive of PSG parameters. Methods: Anthropometric information and five tracheal breathing sound cycles were recorded during wakefulness from 145 individuals referred to an overnight PSG study. The dataset was divided into training, validation, and blind testing datasets. Spectral and bispectral features of the sounds were evaluated to run correlation and classification analyses with the PSG parameters collected from the PSG sleep reports. Results: Many sound and anthropometric features had significant correlations (up to 0.56) with PSG parameters. Using combinations of sound and anthropometric features in a bilinear model for each PSG parameter resulted in correlation coefficients up to 0.84. Using the evaluated models for classification with a two-class random-forest classifier resulted in a blind testing classification accuracy up to 88.8% for predicting the key PSG parameters such as arousal index. Conclusions: These results add new value to the current OSA screening tools and provide a new promising possibility for predicting PSG parameters using only a few seconds of breathing sounds recorded during wakefulness without conducting an overnight PSG study.

Experimental and estimated determination of mechanical characteristics of 3D printed ABS plastic samples under tension

The paper introduces the results of an experimental study of the mechanical characteristics of 3D printed ABS plastic ABSplus-P430 samples under tension. These 3D printed samples differ in the orientation of the material layers, formed by the position of the samples when printed, and the print raster pattern. During the tests, the material showed isotropic properties in terms of Young’s modulus and anisotropic properties for elongation at break, yield strength, and ultimate strength. We revealed that the print orientation relative to the direction of the applied load significantly affects the strength of the tested samples. Using the obtained test results, the specified parameters of the bilinear model of the material were identified by performing a series of computational studies using computer finite element models of material samples. The found parameters of the bilinear model of the material can be used to carry out computational estimation of the strength and bearing capacity of ABS plastic products manufactured by 3D printing. The results obtained also make it possible to develop recommendations for the orientation of products in the printing area according to the criterion of ensuring the greatest strength, taking into account the loading mode of the product.

Numerical investigation of stability multi-storey buildings on weak ground based on their non-linearity

The problems of loss of stability and collapse of high-rise buildings located on weak soils are studied numerically. The problem is solved in a nonlinear formulation using a bilinear model of the soil base. From the point of view of construction mechanics, the critical state of the «ground base – structure» system is considered as an indifferent state. To solve this problem, the perturbation theory is used in combination with the method of successive loadings. Based on the results obtained, a variant of strengthening the foundation is proposed.

A Multi-Timescale Bilinear Model for Optimization and Control of HVAC Systems with Consistency

Reducing the energy consumption of the heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is of both academic and practical significance. However, the-state-of-the-art of the optimization model of the HVAC system is that either the thermal dynamic model is simplified as a linear model, or the optimization model of the HVAC system is single-timescale, which leads to heavy computation burden. To balance the practicality and the overhead of computation, in this paper, a multi-timescale bilinear model of HVAC systems is proposed. To guarantee the consistency of models in different timescales, the fast timescale model is built first with a bilinear form, and then the slow timescale model is induced from the fast one, specifically, with a bilinear-like form. After a simplified replacement made for the bilinear-like part, this problem can be solved by a convexification method. Extensive numerical experiments have been conducted to validate the effectiveness of this model.