{'fraction_non_alphanumeric': 0.04369414101290963, 'fraction_numerical': 0.012578616352201259, 'mean_word_length': 4.8565891472868215, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
High‐dimensional model representation for structural reliability analysis: Authors' reply to comments by S. Rahman and H. Xu

The purpose of the present communication is to provide response to the comments made by Rahman and Xu (RX) [1] in relation to our paper on high-dimensional model representation (HDMR) for structural reliability analysis [2]. It is our belief that this response will have the role of correctly informing the readers about the real origin of HDMR concepts adopted in the manuscript [2] and erroneous claims of RX on the development of decomposition methods based on HDMR concepts without giving appropriate credit to the original development of HDMR. Below we provide response to the points raised in RX’s letter. Nowhere in the manuscript [2], we claimed inventing HDMR as our original contribution to the literature. Hence, the comment, ‘. . .convey the impression that they are presenting a new methodology and original contribution to the literature. . .’ under section 1 of RX’s letter [1] is incorrect. In fact, at the beginning of the last paragraph of introduction section we clearly mentioned that the manuscript explores the potential of a new class of computational methods, referred to as HDMR [3–10], for predicting reliability of structural/mechanical systems subject to random loads, material properties, and geometry. All the papers related to the original development of HDMR have been appropriately cited in the manuscript [2]. Hence the comment ‘. . .therefore the original development of the decomposition predates the timeline specified in the authors’ response’ under section 2 of RX’s letter [1] is a misleading statement intended to snow the reader with erroneous arguments. We leave to the original developers of HDMR concepts, to judge the truth in RX’s comments [1] such as ‘. . .Hickernell (1996) developed a reproducing kernel Hilbert space version. This decomposition has been lately examined by Rabitz and Alis (1999) for HDMR . . .’. The concept of HDMR was originally developed by Rabitz’s group [3–9] for multivariate function approximation. Later after 4 years, Sobol [10] suggested to use the mean value of the variables as reference points for HDMR approximation. Much later, it was Xu and Rahman [11] who reinvented the wheel without giving appropriate credit to the original development of HDMR by coining new terms such as ‘Decomposition methods’, ‘Univariate approximation’, ‘Bivariate approximation’, ‘S-variate approximation’, in place of HDMR, first-, second-, and S-order HDMR approximation, respectively. Regarding the selection of the reference point as the mean point, again RX [1] are making erroneous arguments and misleading statements. The selection of reference points as mean point suggested by Sobol [10] was also reinvented by Xu and Rahman [11] without giving appropriate credit to Sobol [10]. In our manuscript [2], citing [10] reference we stated that ‘. . .it is shown that it is optimal to choose reference point c as mean values of the