# PSI - Issue 50

I. Shardakov et al. / Procedia Structural Integrity 50 (2023) 257–265 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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a

b

2014 2015 2016 2017 2018 2019 2020 -50 -40 -30 -20 -10 0 Date δUz, mm Real_data Line_interp Line_extrap ARIMA(1,1,1)(0,1,0) ARIMA(1,1,1)(0,1,1)

2014 2015 2016 2017 2018 2019 2020 -50 -40 -30 -20 -10 0 Date δUz, mm Real_data Line_interp Line_extrap ARIMA(1,1,1)(0,1,0) ARIMA(1,1,1)(0,1,1)

Fig. 5. Foundation settlements at a increasing rate: ARIMA model forecast for 1-year (a) and 2-year (b).

3.3. Settlement at decreasing rate Figure 6 shows the prediction of foundation settlement at a decelerating rate. It can be seen from the figure that the ARIMA model corresponds quite well to the observed development of the process. On the forecasting interval of 1 and 2 years, the forecast according to the ARIMA model is more accurate than the forecast in accordance with the linear trend. By the end of the first year, Option 1 gives a discrepancy EE = 0.1 mm, RMSE = 0.15 mm, Option 2 gives a discrepancy EE = 0.51 mm, RMSE = 0.27 mm. By the end of the second year, Option 1 gives a discrepancy EE = 1.30 mm, RMSE = 0.56 mm, Option 2 gives a discrepancy EE = 1.46 mm, RMSE = 0.57 mm. a b

Real_data Line_interp Line_extrap

2014 2015 2016 2017 2018 2019 2020 -25 -20 -15 -10 -5 0 Date δUz, mm Real_data Line_interp Line_extrap ARIMA(1,1,1)(0,1,0) ARIMA(1,1,1)(0,1,1)

-20 -15 -10 -5 0

ARIMA(1,1,1)(0,1,0) ARIMA(1,1,1)(0,1,1)

δUz, mm

2014 2015 2016 2017 2018 2019 2020

Date

Fig. 6. Foundation settlements at a decreasing rate: ARIMA model forecast for 1-year (a) and 2-year (b ).

3.4. Periodic seasonal processes Figure 7 shows foundation settlement curves that have a distinct seasonal periodicity. Such graphs have been obtained from monitoring data in several buildings and may reflect processes associated, for example, with seasonal changes in soil properties. In general, forecasting based on the ARIMA model quite well reflects the nature of seasonal changes in the observed value. As in the previous examples, Option 1 (green line) gives a better fit to the observed data. By the end of the first year, Option 1 yields a discrepancy EE = 1.1 mm and RMSE = 0.62 mm. By the end of the second year, the discrepancy according to the same model is EE = 1.4 mm and RMSE = 0.50 mm.

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