Abstract: Environmental factors are taken into account for low-carbon design in product life cycle, which is a multiple backs design process in balancing conventional performance and low-carbon performance. Efficiency and effectiveness of low-carbon design are promoted with knowledge reuse technique; however, the premise is similar cases retrieval. A retrieval method based on the dependent function is proposed. Firstly, previous construction method of multi-dimensional dependent function and mathematical principle of side distance are combined, the one-dimensional dependent function is expanded to the multi-dimensional dependent function, and application condition is also improved by setting the optimal point only in geometric center to arbitrary point. Rule of dimensionality reduction for multi-dimensional dependent function is derived, and similarity function is constructed. In final, the proposed method is applied to attributes retrieval for screw compressor cases, and the computational result is consistent with the spatial position of each case. Comparisons are analyzed with Euclidean geometry distance method and the KNN classification method; it reveals that the weakness of unreasonable retrieval due to the neglected natural property of each attribute is overcome by proposed method, and the retrieval result is similar to that of the Euclidean geometry distance method; the classification result is equal to that of KNN method, and each one-dimensional dependent function value can be taken as the criteria for adaptation of attributes.

Key words: cases retrieval, dependent function, dimensionality reduction, knowledge reuse, multiple attributes