A two-step method for cusp catastrophe model construction based on the selection of important variables

ZHANG Ming; FU Dong-mei; CHENG Xue-qun; YANG Bing-kun; HAO Wen-kui; CHEN Yun; SHAO Li-zhen

doi:10.13374/j.issn2095-9389.2021.07.19.006

Volume 45 Issue 1

Jan. 2023

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Article Navigation > Chinese Journal of Engineering > 2023 > 45(1): 128-136

ZHANG Ming, FU Dong-mei, CHENG Xue-qun, YANG Bing-kun, HAO Wen-kui, CHEN Yun, SHAO Li-zhen. A two-step method for cusp catastrophe model construction based on the selection of important variables[J]. Chinese Journal of Engineering, 2023, 45(1): 128-136. doi: 10.13374/j.issn2095-9389.2021.07.19.006

Citation:

ZHANG Ming, FU Dong-mei, CHENG Xue-qun, YANG Bing-kun, HAO Wen-kui, CHEN Yun, SHAO Li-zhen. A two-step method for cusp catastrophe model construction based on the selection of important variables[J]. Chinese Journal of Engineering, 2023, 45(1): 128-136. doi: 10.13374/j.issn2095-9389.2021.07.19.006

Citation:

ZHANG Ming, FU Dong-mei, CHENG Xue-qun, YANG Bing-kun, HAO Wen-kui, CHEN Yun, SHAO Li-zhen. A two-step method for cusp catastrophe model construction based on the selection of important variables[J]. Chinese Journal of Engineering, 2023, 45(1): 128-136. doi: 10.13374/j.issn2095-9389.2021.07.19.006

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A two-step method for cusp catastrophe model construction based on the selection of important variables

doi: 10.13374/j.issn2095-9389.2021.07.19.006

ZHANG Ming¹,
FU Dong-mei^{1, 2, 3
,
,},
CHENG Xue-qun^{4, 5
,
,},
YANG Bing-kun⁶,
HAO Wen-kui⁶,
CHEN Yun⁶,
SHAO Li-zhen^{1, 2}

1.
Shunde Graduate School, University of Science and Technology Beijing, Foshan 528399, China
2.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
3.
Beijing Engineering Research Center of Industrial Spectrum Imaging, University of Science and Technology Beijing, Beijing 100083, China
4.
Institution for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China
5.
National Materials Corrosion and Protection Scientific Data Center, University of Science and Technology Beijing, Beijing 100083, China
6.
State Key Laboratory of Advanced Transmission Technology, Global Energy Interconnection Research Institute Limited Company, Beijing 102209, China

More Information

Corresponding author: FU Dong-mei, E-mail: fdm_ustb@ustb.edu.cn; CHENG Xue-qun, chengxuequn@ustb.edu.cn
Received Date: 2021-07-19
Available Online: 2021-11-01
Publish Date: 2023-01-01

Abstract

Abstract

Sudden transition is a widely existing phenomenon in engineering practice. When the state of the system experiences sudden abrupt transition, calculus-based traditional mathematical modeling methods has low accuracy. Although theoretically, machine learning algorithms, such as artificial neural networks, can approximate any nonlinear function, this type of black-box method makes no reasonable explanation for the sudden transition phenomenon. The cusp catastrophe model based on the catastrophe theory can be applied to explain the discontinuous changes in the system’s state. However, the construction of traditional cusp catastrophe models is often based on large amounts of prior knowledge to select the input variables for modeling. On the condition that there is a lack of prior knowledge and comparatively large dimensions of input variables, the model has high complexity and poor accuracy. In this paper we have put forward a two-step method for constructing a cusp catastrophe model based on the selection of variables to solve the abovementioned problems. The first step was to apply multimodel ensemble important variable selection (MEIVS) to quantify the importance of the variables to be selected and extract important variables. The second step was to use the extracted important variables to construct a cusp catastrophe model based on the framework of maximum likelihood estimation (MLE). Results indicate that on a dataset with characteristics of catastrophe, the cusp catastrophe model is simple in form using the MEIVS dimensionality reduction algorithm and outperforms the unreduced cusp catastrophe model and reduced cusp catastrophe model using other dimensionality reduction algorithms in terms of evaluation indicators. This shows that the algorithm proposed in this paper have improved the accuracy and reduced the complexity of the cusp catastrophe model. At the same time, the cusp catastrophe model exhibits higher accuracy compared with the linear and logistic models. Thus, it can be used to explain the discontinuous changes of the research object, and it has a practical engineering significance.
- catastrophe theory,
- catastrophe flag,
- cusp catastrophe model,
- variable selection,
- model integration

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References(29)

References

[1]	Qiao C, Guo Y H, Li C H. Study on rock burst prediction of deep buried tunnel based on cusp catastrophe theory. Geotech Geol Eng, 2021, 39(2): 1101 doi: 10.1007/s10706-020-01547-4
[2]	Zhi Y J, Yang T, Fu D M. An improved deep forest model for forecast the outdoor atmospheric corrosion rate of low-alloy steels. J Mater Sci Technol, 2020, 49: 202 doi: 10.1016/j.jmst.2020.01.044
[3]	裴甲坤, 王飛躍, 郭換換, 等. 基于改進尖點突變模型的化工事故致因分析. 中國安全科學學報, 2019, 29(7):20 doi: 10.16265/j.cnki.issn1003-3033.2019.07.004 Pei J K, Wang F Y, Guo H H, et al. Cause analysis of chemical accidents based on improved cusp catastrophe model. China Saf Sci J, 2019, 29(7): 20 doi: 10.16265/j.cnki.issn1003-3033.2019.07.004
[4]	林黎. 中國股票市場的隨機尖點突變模型. 系統工程學報, 2016, 31(1):55 doi: 10.13383/j.cnki.jse.2016.01.006 Lin L. Stochastic cusp catastrophe model for Chinese stock market. J Syst Eng, 2016, 31(1): 55 doi: 10.13383/j.cnki.jse.2016.01.006
[5]	Barunik J, Kukacka J. Realizing stock market crashes: Stochastic cusp catastrophe model of returns under time-varying volatility. Quant Finance, 2015, 15(6): 959 doi: 10.1080/14697688.2014.950319
[6]	馬躍如, 易丹, 胡斌. 養老護理員工作幸福感的隨機突變機理. 系統管理學報, 2021, 30(3):526 Ma Y R, Yi D, Hu B. Analysis of stochastic catastrophe mechanism of occupational well-being of nursing practitioner servicing for the elderly. J Syst Manag, 2021, 30(3): 526
[7]	Eladany M M, Eldesouky A A, Sallam A A. Power system transient stability: An algorithm for assessment and enhancement based on catastrophe theory and FACTS devices. IEEE Access, 2018, 6: 26424 doi: 10.1109/ACCESS.2018.2834906
[8]	Xiao X P, Duan H M. A new grey model for traffic flow mechanics. Eng Appl Artif Intell, 2020, 88: 103350 doi: 10.1016/j.engappai.2019.103350
[9]	Wei X, Fu D M, Chen M D, et al. Data mining to effect of key alloying elements on corrosion resistance of low alloy steels in Sanya seawater environmentAlloying Elements. J Mater Sci Technol, 2021, 64: 222 doi: 10.1016/j.jmst.2020.01.040
[10]	Pei Z B, Zhang D W, Zhi Y J, et al. Towards understanding and prediction of atmospheric corrosion of an Fe/Cu corrosion sensor via machine learning. Corros Sci, 2020, 170: 108697 doi: 10.1016/j.corsci.2020.108697
[11]	Thom R. Structural Stability and Morphogenesis: An Outline of a General Theory of Models. London: Benjamin W A, 1975
[12]	Cobb L. Stochastic catastrophe models and multimodal distributions. Syst Res, 1978, 23(4): 360 doi: 10.1002/bs.3830230407
[13]	Cobb L, Zacks S. Applications of catastrophe theory for statistical modeling in the biosciences. J Am Stat Assoc, 1985, 80(392): 793 doi: 10.1080/01621459.1985.10478184
[14]	Zeeman E C. Catastrophe theory. Sci Am, 1976, 234(4): 65 doi: 10.1038/scientificamerican0476-65
[15]	Niu D X, Wang K K, Sun L J, et al. Short-term photovoltaic power generation forecasting based on random forest feature selection and CEEMD: A case study. Appl Soft Comput, 2020, 93: 106389 doi: 10.1016/j.asoc.2020.106389
[16]	Al-Fugara A, Ahmadlou M, Shatnawi R, et al. Novel hybrid models combining meta-heuristic algorithms with support vector regression (SVR) for groundwater potential mapping. Geocarto Int, 2020: 1
[17]	Zhang J L, da Xu, Hao K J, et al. FS-GBDT: Identification multicancer-risk module via a feature selection algorithm by integrating Fisher score and GBDT. Brief Bioinform, 2020, 22(3): bbaa189
[18]	Tsai C F, Sung Y T. Ensemble feature selection in high dimension, low sample size datasets: Parallel and serial combination approaches. Knowl Based Syst, 2020, 203: 106097 doi: 10.1016/j.knosys.2020.106097
[19]	Bolón-Canedo V, Alonso-Betanzos A. Ensembles for feature selection: A review and future trends. Inf Fusion, 2019, 52: 1 doi: 10.1016/j.inffus.2018.11.008
[20]	Pes B. Ensemble feature selection for high-dimensional data: A stability analysis across multiple domains. Neural Comput Appl, 2020, 32(10): 5951 doi: 10.1007/s00521-019-04082-3
[21]	Hartelman P A I, Maas H L J, Molenaar P C M. Detecting and modelling developmental transitions. Br J Dev Psychol, 1998, 16(1): 97 doi: 10.1111/j.2044-835X.1998.tb00751.x
[22]	Grasman R P P P, van der Maas H L J, Wagenmakers E J. Fitting the cusp catastrophe inR: AcuspPackage primer. J Stat Soft, 2009, 32(8): 1
[23]	Aaron F, Cynthia R, Francesca D. All models are wrong, but many are useful: learning a variable's importance by studying an entire class of prediction models simultaneously. J Machine Learning Research, 2019, 20(177): 1
[24]	Breiman L. Random forests. Machine Learning, 2001, 45(1): 5 doi: 10.1023/A:1010933404324
[25]	Buscema M. Back propagation neural networks. Subst Use Misuse, 1998, 33(2): 233 doi: 10.3109/10826089809115863
[26]	Karatzoglou A, Smola A, Hornik K, et al. Kernlab- AnS4Package for kernel methods inR. J Stat Soft, 2004, 11(9): 1
[27]	Amar Aladžuz. Hotels accommodation prices dataset [DB/OL]. Kaggle (2020-12-24) [2021-07-16].https://www.kaggle.com/aladzuzamar/hotels-accommodation-prices-dataset
[28]	Biecek P. DALEX: explainers for complex predictive models in R. J Mach Learn Res, 2018, 19(1): 3245
[29]	Pei Z B, Cheng X Q, Yang X J, et al. Understanding environmental impacts on initial atmospheric corrosion based on corrosion monitoring sensors. J Mater Sci Technol, 2021, 64: 214 doi: 10.1016/j.jmst.2020.01.023