Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.]
Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values fo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Research Management Institute (RMI)
2014
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| Subjects: | |
| Online Access: | https://ir.uitm.edu.my/id/eprint/12793/1/AJ_NG%20SET%20FOONG%20SRJ%2014%201.pdf |
| _version_ | 1825734060878594048 |
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| author | Ng, Set Foong Ch’ng, Pei Eng Chew, Yee Ming Ng, Kok Shien |
| author_facet | Ng, Set Foong Ch’ng, Pei Eng Chew, Yee Ming Ng, Kok Shien |
| author_sort | Ng, Set Foong |
| collection | UITM |
| description | Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimized. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained. |
| first_indexed | 2024-03-06T01:26:10Z |
| format | Article |
| id | oai:ir.uitm.edu.my:12793 |
| institution | Universiti Teknologi MARA |
| language | English |
| last_indexed | 2024-03-06T01:26:10Z |
| publishDate | 2014 |
| publisher | Research Management Institute (RMI) |
| record_format | dspace |
| spelling | oai:ir.uitm.edu.my:127932016-05-26T03:12:10Z https://ir.uitm.edu.my/id/eprint/12793/ Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] srj Ng, Set Foong Ch’ng, Pei Eng Chew, Yee Ming Ng, Kok Shien Soils. Soil science. Including soil surveys, soil chemistry, soil structure, soil-plant relationships Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimized. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained. Research Management Institute (RMI) 2014 Article PeerReviewed text en https://ir.uitm.edu.my/id/eprint/12793/1/AJ_NG%20SET%20FOONG%20SRJ%2014%201.pdf Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.]. (2014) Scientific Research Journal <https://ir.uitm.edu.my/view/publication/Scientific_Research_Journal/>, 11 (1). pp. 16-28. ISSN 1675-7009 https://srj.uitm.edu.my/ |
| spellingShingle | Soils. Soil science. Including soil surveys, soil chemistry, soil structure, soil-plant relationships Ng, Set Foong Ch’ng, Pei Eng Chew, Yee Ming Ng, Kok Shien Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title | Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title_full | Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title_fullStr | Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title_full_unstemmed | Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title_short | Applying the method of Lagrange Multipliers to derive an estimator for unsampled soil properties / Ng Set Foong ... [et al.] |
| title_sort | applying the method of lagrange multipliers to derive an estimator for unsampled soil properties ng set foong et al |
| topic | Soils. Soil science. Including soil surveys, soil chemistry, soil structure, soil-plant relationships |
| url | https://ir.uitm.edu.my/id/eprint/12793/1/AJ_NG%20SET%20FOONG%20SRJ%2014%201.pdf |
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