Meta-models for structural reliability and uncertainty quantification

A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g. a finite element model in mechanics) while being inexpensive to evaluate, in contrast to the original model which may take hours or even days of computer processing time. In this paper various types of meta-models that have been used in the last decade in the context of structural reliability are reviewed. More specifically classical polynomial response surfaces, polynomial chaos expansions and kriging are addressed. It is shown how the need for error estimates and adaptivity in their construction has brought this type of approaches to a high level of efficiency. A new technique that solves the problem of the potential biasedness in the estimation of a probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural Reliability and its Applications (5th APSSRA) May 2012, Singapor

Pembangunan modul pembelajaran autocad dan kajian penerimaan pelajar. Satu kajian kes di Politeknik Kota Bharu

Modul Pengajaran dan Pembelajaran AutoCAD (MPP) merupakan satu media pengajaran yang mengandungi asas-asas mengenai komputer, perisian AutoCAD 2000 dan langkah-langkah berperingkat membuat lukisan teknikal menggunakan AutoCAD 2000. Kajian ini adalah bertujuan untuk menilai sejauh mana MPP ini boleh digunakan dalam proses pengajaran dan pembelajaran dalam aspek kesesuaian isi kandungan, sifat mesra pengguna dan kebolehlaksanaannya. Respondan untuk kajian ini ialah seramai 42 orang pelajar Diploma Kejuruteraan Elektrik Politeknik Kota Bharu. Untuk kajian ini instrumen yang digunakan ialah borang soal selidik di mana penilaian dilakukan berdasarkan persepsi responden terhadap MPP. Data-data yang dikumpulkan dianalisis menggunakan SPSS VI1.0 yang melibatkan skor min. Hasil kajian melaporkan dapatan yang diperolehi berkenaan penerimaan terhadap MPP. Hasil dapatan kajian menunjukkan penerimaan yang positif terhadap MPP oleh pelajar dan ianya mempimyai kebolehlaksanaan yang tinggi (skor min = 3.96) untuk diaplikasikan dalam proses pengajaran dan pembelajaran. Walaubagaimanapun pengkaji percaya MPP ini mempunyai ruang untuk penambahbaikan seperti saranan oleh penilai yang mengesahkan MPP ini agar ia lebih menarik dan sesuai digunakan pada masa depan

Issues of scale for environmental indicators

The value of environmental indicators largely depends upon the spatial and temporal scale that they represent. Environmental indicators are dependent upon data availability and also upon the scale for which statements are required. As these may not match, changes in scales may be necessary. In this paper a geostatistical approach to analyse quantitative environmental indicators has been used. Scales, defined in terms of resolution and procedures, are presented to translate data from one scale to another: upscaling to change from high resolution data towards a low resolution, and downscaling for the inverse process. The study is illustrated with three environmental indicators. The first concerns heavy metals in the environment, where the zinc content is used as the indicator. Initially, data were present at a 1km2 resolution, and were downscaled to 1m2 resolution. High resolution data collected later showed a reasonable correspondence with the downscaled data. Available covariates were also used. The second example is from the Rothamsted’s long-term experiments. Changes in scale are illustrated by simulating reduced data sets from the full data set on grass cuts. A simple regression model related the yield from these condcut to that of the first cut in the cropping season. Reducing data availability (upscaling) resulted in poor estimates of the regression coefficients. The final example is on nitrate surpluses on Danish farms. Data at the field level are upscaled to the farm level, and the dispersion variance indicates differences between different farms. Geostatistical methods were useful to define, change and determine the most appropriate scales for environmental variables in space and in time