Measuring Opportunity Cost in Statistics Using Evaluative Space Grid Items

Challenges to measuring students’ attitudes toward statistics remain despite decades of focused research. Measuring the expectancy-value theory (EVT) Cost construct has been especially challenging owing in part to the historical lack of research about it. To measure the EVT Cost construct better, this study asked university students to respond to items using both a Likert-type response and an Evaluative Space Grid (ESG)-type response. ESG items enable bivariate responses in a single item and permit distinguishing among two different types of neutral attitudes: indifferent and ambivalent. This pilot study evaluates the appropriateness of ESG-type items for measuring the EVT Cost construct by analyzing student response patterns to ESG-type items and comparing them with Likert-type items. Validity evidence is documented using descriptive statistics and graphs, correlations among items, and a trinomial hypothesis test. Internal consistency reliability indices are also reported. Friedman’s Test is used to compare the average response times for items of different types. Results indicate that students can meaningfully respond to ESG-type items in ways that are similar to their Likert-type responses, that students respond to ESG-type items quicker with more practice, and that distinguishing among indifferent and ambivalent attitudes seems appropriate for the EVT Cost construct. These findings suggest that ESG-type items may provide new insights not possible with Likert-type items but also that more research should be conducted to better understand their advantages and disadvantages within statistics education.

Model-Free Method for Damage Localization of Grid Structure

A model-free damage identification method for grid structures based on displacement difference is proposed. The inherent relationship between the displacement difference and the position of structural damage was deduced in detail by the Sherman–Morrison–Woodbury formula, and the basic principle of damage localization of the grid structure was obtained. That is, except for the tensile and compressive deformations of the damaged elements, the deformations of other elements were small, and only rigid body displacements occurred before and after the structural damage. According to this rule, a method for identifying the position of the damage was proposed for the space grid structure by using the rate of change of length for each element. Taking a space grid structure with a large number of elements as an example, the elastic modulus reduction method was used to simulate the damage to the elements, and the static and dynamic test parameters were simulated respectively to obtain the difference in displacement before and after the structural damage. The rate of change of length of each element was calculated based on the obtained displacement difference, and data noise was added to the simulation. The results indicated that the element with the larger length change rate in the structure was the most likely to be damaged, and the damaged element can be accurately evaluated even in the presence of noise in data.

Looseness Monitoring of Bolted Spherical Joint Connection Using Electro-Mechanical Impedance Technique and BP Neural Networks

The bolted spherical joint (BSJ) has wide applications in various space grid structures. The bar and the bolted sphere are connected by the high-strength bolt inside the joint. High-strength bolt is invisible outside the joint, which causes the difficulty in monitoring the bolt looseness. Moreover, the bolt looseness leads to the reduction of the local stiffness and bearing capacity for the structure. In this regard, this study used the electro-mechanical impedance (EMI) technique and back propagation neural networks (BPNNs) to monitor the bolt looseness inside the BSJ. Therefore, a space grid specimen having bolted spherical joints and tubular bars was considered for experimental evaluation. Different torques levels were applied on the sleeve to represent different looseness degrees of joint connection. As the torque levels increased, the looseness degrees of joint connection increased correspondingly. The lead zirconate titanate (PZT) patch was used and integrated with the tubular bar due to its strong piezoelectric effect. The root-mean-square deviation (RMSD) of the conductance signatures for the PZT patch were used as the looseness-monitoring indexes. Taking RMSD values of sub-frequency bands and the looseness degrees as inputs and outputs respectively, the BPNNs were trained and tested in twenty repeated experiments. The experimental results show that the formation of the bolt looseness can be detected according to the changes of looseness-monitoring indexes, and the degree of bolt looseness by the trained BPNNs. Overall, this research demonstrates that the proposed structural health monitoring (SHM) technique is feasible for monitoring the looseness of bolted spherical connection in space grid structures.