<p>Commonly used basis functions.</p>

In engineering structures, uncertain interval analysis is a study hotspot. However, how to obtain the accurate and efficient upper and lower solution bounds of uncertainty in the uncertain interval analysis is one of the key problems at present. To address this issue, the paper proposes a new adaptive extended radial basis function based interval analysis method to obtain accurate and efficient structural bound solutions. Instead of the pre-selecting the width of the basis functions, an Extended Radial Basis Function (E-RBF) and the adjusted widths are combined to confirm each width of the Gaussian basis function. In order to obtain the widths of the Gaussian basis function, the adaptive scaling technique is introduced in the E-RBF model. Then six numerical functions are selected to evaluate the accuracy of the E-RBF method with adjusted widths. On the basis of ensuring the accuracy of the widths of the Gaussian basis function, the adaptive E-RBF based interval analysis method is constructed by using the E-RBF with adjusted widths, catching the critical points and establishing the adaptive procedure for solving the extreme certain interval bounds of complex structural engineering problems. Next, three structural numerical examples and one composite shell are produced to verify the validity and effectiveness of this adaptive E-RBF based interval analysis method.