# Robust Simulation of Cyber-Physical Systems for Environmental Monitoring on Construction Sites
## 5 Uncertainty Detection and Processing
### Abnormality Detection and Processing of Monitoring Data  
The spatio-temporal correlation method can more accurately identify the anomalous data in the E-CPS system. An anomalous-data-identification model is then developed  
Figure 6: Identification of uncertainty factors and scenarios. based on the principle of spatio-temporal correlation. During the uncertainty detection, the probability of abnormal data is a crucial indicator for identifying abnormal data [53]. \[P_{j}(t_{i})=P_{j}(t_{i-1})+c \tag{1}\]  
where \(P_{j}(t_{i})\) is an accumulated value that represents the probability of an abnormality at sampling time \(t_{i}\), and \(c\) is a variable representing the increase in the probability of anomalies at the sampling moment \(t_{i}\) over the sampling moment \(t_{i-1}\). If sensor reading \(r_{j}(t_{i})\) is continuously judged as the abnormal data at several sampling moments, \(P_{j}(t_{i})\) is accumulated. If sensor reading \(r_{j}(t_{i})\) fails to meet the judgment condition, it is cleared until it meets the standard. When \(P_{j}(t_{i})\) reaches threshold \(R\), the anomaly is detected in the node and fed back to the platform in order to prevent the abnormal data from entering the E-CPS [54]. Considering the differences of several sensors and the method robustness, \(R\) can be determined according to the sampling period of each sensor and the statistical characteristics of the dataset [55]. According to the definition of anomalous data provided by [PERSON] [56] and the construction practice, this study considers PM10 as an example in order to detect and process the anomalous data regarding the environmental monitoring in Uncertain Scenario 1. This can be categorized into the following: the monitoring data are less than the detected value; constant value; the measured data inside the field is much less than that outside the field; the monitoring value of PM10 is less than the value of PM2.5; and the PM10 monitoring value is abnormal on rainy and snowy days. (1) The monitoring data are less than the detected value  
This category of conflict data is a monitored data value that is not within the set range of the detected value. The monitoring data are manifested as 0 or lower than the detection limit (the detection limit of the PM10 and PM2.5 monitoring data is 5 ug/m\({}^{3}\)), which fails to conform to the laws of nature. In this study, the monitoring data are less than the detected value. If \(r_{j}(t_{i})<5\), the monitoring data are judged as abnormal data. If \(r_{j}(t_{i})\geq 5\), the monitoring data are maintained. (2) Constant value  
Since PM10 is continuously monitored in the E-CPS, a fluctuation in the monitoring data exists within a certain range. When encountering circumstances such as equipment failure, poor network transmission environment, data acquisition and processing device crash, energy exhaustion, or damage, the same data can be continuously produced at different sampling moments. Hence, the constant-value detection is defined as follows. If \(r_{j}(t_{i})=r_{j}(t_{i-1})\) and the monitored value remains unchanged for a long time, they should be judged as abnormal data. (3) The measured data inside the field is much less than that outside the field  
According to the law of dust propagation, the value of the dust within the boundary of the construction site should be greater than that of the dust outside the boundary of the site. The actual measurement data within the field boundary is much smaller than the abnormal event detection concept outside the field boundary. There is no processing when the absorbable particulate matter concentration \(r_{j}(t_{i})\) within the construction site's boundary is not lower than the surrounding absorbable particulate matter concentration \(r_{nearby}(t_{i})\) far away from the construction site. If \(r_{j}(t_{i})<r_{nearby}(t_{i})\), the probability value of abnormal data is accumulated.