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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3. Results and Discussions A statistical time series model with parameters adjusted according to data obtained on individual object can then be used to predict the behavior of other similar objects. Let's demonstrate this on the examples of several buildings that were under the supervision of the monitoring system for a long period. As before, based on the 5-year history of observations, we will build a forecast for 1-year and 2-year periods and compare these results with real observational data. We will evaluate the quality of the forecast by the difference EE between the observed and predicted values at the end of the forecast interval, as well as by the root-mean-square difference RMSE of these values for the entire forecast interval. The following series of figures illustrates the result of predicting the settlement of the foundation of several buildings located in different parts of the observed area. The graphs show observational data for 5 years and forecasting results obtained using the ARIMA model. The observed settlement values are shown on the graphs with a black line. Predicted values are indicated by colored lines. They are obtained using a model with two sets of parameters: Option 1 – ARIMA (1,1,1)(0,1,0), and Option 2 – ARIMA (1,1,1)(0,1,1). The dotted line shows the trend line. Based on the observational data, a 1-year (left) and 2-year (right) forecast was constructed. 3.1. Settlement at constant rate Figure 4 shows the result of predicting the settlement of the foundation, changing at a constant rate. It can be seen from the figure that the forecasts by the ARIMA model with both sets of parameters are in good agreement with the observational data. The deviation of the predicted values from the observed one was as follows: when Option 1 is used on a forecast horizon of 1 year, the maximum discrepancy is EE = 0.22 mm, and the standard deviation is RSME = – 0.160 mm. For a 2-year forecast, these values are EE = 0.65 mm and RSME = 0.127 mm. Options 2 gave the following results: for a 1-year forecast, these values are EE = 0.06 mm and RSME = 0.173 mm. For a 2-year forecast, EE = 0.56 mm and RSME = 0.150. a b

Real_data Line_interp Line_extrap

Real_data Line_interp Line_extrap

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

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

δUz, mm

δUz, mm

2014 2015 2016 2017 2018 2019 2020 -12 -10 -8 -6 -4 -2 0 Date

2014 2015 2016 2017 2018 2019 2020 -12 -10 -8 -6 -4 -2 0 Date

Fig. 4. Foundation settlements at a constant rate: ARIMA model forecast for 1-year (a) and 2-year (b).

3.2. Settlement at increasing rate Figure 5 shows the prediction data for a building that has accelerated foundation settlement. As in the previous example, the forecast was obtained using the ARIMA model with two sets of parameters. The forecasting interval was 1 and 2 years. It can be seen from the figure that the ARIMA model forecast is significantly more realistic than the linear trend forecast (dashed line in the graph), but it gives lower values compared to the observed data. By the end of one year, the best of the ARIMA models (1,1,1)(0,1,0) gives discrepancy EE = 3 mm and RMSE = 0.92 mm. By the end of the second year, these values are EE =6.4 mm and RMSE = 1.7 mm.