A machine learning approach to nonlinear modal analysis

Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw–Pierre approach is rather demanding technically, depending as it does on the construction of a polynomial mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach to the Shaw–Pierre method which exploits the idea of independence to optimise the parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD)

EQ-5D in skin conditions: an assessment of validity and responsiveness

Aims and objectives This systematic literature review aims to assess the reliability, validity and responsiveness of three widely used generic preference-based measures of health-related quality of life (HRQL), i.e., EQ-5D, Health Utility Index 3 (HUI3) and SF-6D in patients with skin conditions. Methods A systematic search was conducted to identify studies reporting health state utility values obtained using EQ-5D, SF-6D, or HUI3 alongside other HRQL measures or clinical indices for patients with skin conditions. Data on test-retest analysis for reliability, known group differences or correlation and regression analyses for validity, and change over time or responsiveness indices analysis were extracted and reviewed. Results A total of 16 papers reporting EQ-5D utilities in people with skin conditions were included in the final review. No papers for SF-6D and HUI3 were found. Evidence of reliability was not found for any of these measures. The majority of studies included in the review (12 out of 16) examined patients with plaque psoriasis or psoriatic arthritis and the remaining four studies examined patients with either acne, hidradenitis suppurativa, hand eczema, or venous leg ulcers. The findings were generally positive in terms of performance of EQ-5D. Six studies showed that EQ-5D was able to reflect differences between severity groups and only one reported differences that were not statistically significant. Four studies found that EQ-5D detected differences between patients and the general population, and differences were statistically different for three of them. Further, moderate-to-strong correlation coefficients were found between EQ-5D and other skin-specific HRQL measures in four studies. Eight studies showed that EQ-5D was able to detect change in HRQL appropriately over time and the changes were statistically significant in seven studies. Conclusions Overall, the validity and responsiveness of the EQ-5D was found to be good in people with skin diseases, especially plaque psoriasis or psoriatic arthritis. No evidence on SF-6D and HUI3 was available to enable any judgments to be made on their performance