The Multidimensional Algorithm of Cumulative Sums for Detecting Changes in Time Series Characteristics
DOI:
https://doi.org/10.24160/1993-6982-2021-1-86-94Keywords:
multidimensional algorithm of cumulative sums, detection of simultaneous changes in the vector of means and covariance matrix entries, linear transformation of covariance matrices, simultaneous change in mean and variance, synthesis of a monitoring algorithmAbstract
The article presents a cumulative sum algorithm intended to detect a sudden step-like change in the probabilistic characteristics of a monitored time series when such a change (“disorder”) is associated with a simultaneous change in both the location characteristics and the dispersion characteristics of the corresponding distribution functions. In the general case of a multidimensional time series, the disorder is associated with a jump in the values of the mathematical expectation vector (the vector of means) and covariance matrix entries. To solve this problem, it is proposed to use a preliminary linear transformation of the time series values, as a result of which the covariance matrix is transformed to the unity form before disordering and to the diagonal form after disordering. The change in the vector of means is analyzed, and the main relations describing the considered detection algorithm are derived. It is noted that by using the above-mentioned linear transformation it is possible to simplify the obtaining of the reference data necessary for synthesizing the monitoring algorithm with the predetermined properties.
As an example, a particular case of a one-dimensional time series and a disorder in the form of a simultaneous change in the mean and variance is considered. For this case, reference data obtained by applying the simulation method are given, using which it is possible to find the monitoring algorithm triggering threshold and estimate the average delay time of detecting the specified disorder from the given interval between false alarms.
This study is a logical continuation and further development of the approach to construction of multidimensional algorithms for detecting disorders [1].
References
2. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes // ITEE J. 2018. V. 7. Iss. 2. Pp. 1—11.
3. Page E.S. Continuous Inspection Schemes // Biometrika. 1954. V. 41. No. 1. Pp. 100—115.
4. Никифоров И.В. Последовательное обнаружения изменения свойств временных рядов. М.: Наука, 1983.
5. Ширяев А.Н. Задача скорейшего обнаружения нарушения стационарного режима // Доклады АН СCСР. 1961. Т. 138. № 5. С. 1039—1042.
6. Maman A., Djauhari A. Multivariate Process Variability Monitoring Based on Individual Observations // Modern Appl. Sci. 2010. V. 4. No. 10. Pp. 91—96.
7. Носкова А.И., Токранова М.В. Обзор автоматизированных систем мониторинга // Интеллектуальные технологии на транспорте. 2017. № 1. С. 42—47.
8. Еремин Н.А. и др. Информационная автоматизированная система мониторинга и анализа технологических данных объектов нефтегазодобычи // Автоматизация, телемеханизация и связь в нефтяной промышленности. 2020. № 2. С. 11—20.
9. Funk P., Xiong N. Why We Need to Move to Intelligent and Experience Based Monitoring and Diagnostic Systems // Proc. 23th Int. Conf. Condition Monitoring and Diagnostic Eng. Management. 2010. Pp. 111—115.
10. Kopáčik A., Kyrinovič P., Erdélyi J., Lipták I. New Trends of Automated Bridge Monitoring // Reportson Geodesy. 2011. No. 1. Pp. 173—181.
11. Сивова Д.Г., Филаретов Г.Ф. Последовательный алгоритм обнаружения момента изменения характеристик векторных временных рядов // Вестник МЭИ. 2014. № 2. С. 63—69.
12. Филаретов Г.Ф., Червова А.А. Последовательный алгоритм обнаружения момента изменения дисперсии временного ряда // Заводская лаборатория. Диагностика материалов. 2019. Т. 85. № 3. С. 75—82.
---
Для цитирования: Филаретов Г.Ф., Симоненков П.С. Многомерный алгоритм кумулятивных сумм для обнаружения изменений характеристик временных рядов // Вестник МЭИ. 2021. № 1. С. 86—94.
#
1. Filaretov G.F., Simonenkov P.S. Algoritm Kumulyativnykh Summ dlya Obnaruzheniya Izmeneniy Kovariatsionnoy Matritsy Mnogomernykh Vremennykh Ryadov. Vestnik MEI. 2020;3:92—101. (in Russian).
2. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes. ITEE J. 2018;7;2:1—11.
3. Page E.S. Continuous Inspection Schemes. Biometrika. 1954;41;1:100—115. (in Russian).
4. Nikiforov I.V. Posledovatel'noe Obnaruzheniya Izmeneniya Svoystv Vremennykh Ryadov. M.: Nauka, 1983. (in Russian).
5. Shiryaev A.N. Zadacha Skoreyshego Obnaruzheniya Narusheniya Statsionarnogo Rezhima. Doklady AN SCSR. 1961;138;5:1039—1042. (in Russian).
6. Maman A., Djauhari A. Multivariate Process Variability Monitoring Based on Individual Observations. Modern Appl. Sci. 2010;4;10:91—96.
7. Noskova A.I., Tokranova M.V. Obzor Avtomatizirovannykh Sistem Monitoringa. Intellektual'nye Tekhnologii na Transporte. 2017;1:42—47. (in Russian).
8. Eremin N.A. i dr. Informatsionnaya Avtomatizirovannaya Sistema Monitoringa i Analiza Tekhnologicheskikh Dannykh Ob′ektov Neftegazodobychi. Avtomatizatsiya, Telemekhanizatsiya i Svyaz' v Neftyanoy Promyshlennosti. 2020;2:11—20. (in Russian).
9. Funk P., Xiong N. Why We Need to Move to Intelligent and Experience Based Monitoring and Diagnostic Systems. Proc. 23th Int. Conf. Condition Monitoring and Diagnostic Eng. Management. 2010:111—115.
10. Kopáčik A., Kyrinovič P., Erdélyi J., Lipták I. New Trends of Automated Bridge Monitoring. Reportson Geodesy. 2011;1:173—181.
11. Sivova D.G., Filaretov G.F. Posledovatel'nyy Algoritm Obnaruzheniya Momenta Izmeneniya Kharakteristik Vektornykh Vremennykh Ryadov. Vestnik MEI. 2014;2:63—69. (in Russian).
12. Filaretov G.F., Chervova A.A. Posledovatel'nyy Algoritm Obnaruzheniya Momenta Izmeneniya Dispersii Vremennogo Ryada // Zavodskaya Laboratoriya. Diagnostika Materialov. 2019;85;3:75—82. (in Russian).
---
For citation: Filaretov G.F., Simonenkov P.S. The Multidimensional Algorithm of Cumulative Sums for Detecting Changes in Time Series Characteristics. Bulletin of MPEI. 2021;1:86—94. (in Russian).
