SANY Sensors Anywhere

Spatial data fusion services provide spatial trends of environmental parameters using observation data which are collated from a network of in situ sensors. This leads to the prediction of environmental parameters in areas where sensing is not available. The computation and analysis of spatial data uncertainties can also lead to identifying the areas where new sensor observations are required. Three types of spatial fusion algorithms have been developed and tested in SANY:

Krigingi

Kriging is a method of spatial interpolation, which predicts values of an environmental parameter following observations of the same parameter at a finite number of sensors locations. The spatial predictions are simply weighted averages of the observed parameter values, according to the respective distances between the sensor points respective locations. The weights in Kriging are computed so that the variance is minimised. In this sense, Kriging is often called Optimal Interpolation.

The dependency of the interpolation weights on the distances between sensors is manifested in a variogram. The Kriging variogram essentially describes the variance of the difference between two distinct spatial observations. Furthermore, a realistic modelling of the variogram, should be based on reasonably accurate observations and a good understanding of the most dominant environmental processes that influence the spatial and temporal trends of the environmental parameter under study. This is of paramount importance for good Kriging results.

The numerical procedures in Kriging additionally involve the determination of measures of uncertainty when estimating environmental parameters in a spatial domain of interest. The approach leads to a good assessment of how observation sensors should be spatially distributed for achieving minimum uncertainty in spatial fusion.

To support Kriging we have added elevation correction, periodic variable support (e.g. wind direction), automated variogram selection and multi-region variogram support.

Bayesian Maximum Entropy

Data fusion methods based upon Bayesian Maximum Entropy (BME) are able to consider soft sensor data, e.g. the sensor value lies in an interval, and additional phenomenological knowledge in the form of models. The results are statistics encompassing the uncertainty of the spatial/temporal interpolation given the uncertainty of the available information.

The overall BME fusion method is structured in three stages:

1. prior stage: consideration of general physical and scientific knowledge G about the spatio-temporal properties of the phenomenon of interest. This knowledge may, for example, be expressed in the form of spatiotemporal
   differential equations derived from physical laws or as covariance models. It is what is known before experience with the specific situation is applied. The prior probability distribution of the so-called random field of the phenomenon is determined using the maximum entropy (ME) principle, i.e. it is the most uninformative (unbiased) probability distribution given only G.

2. meta-prior stage: consideration of case-specific hard and soft data of the phenomenon of interest. This information is denoted by S (for specific knowledge) and is based on observations and measurements. Hard data refers to values believed to be accurate. Soft data is accompanied by uncertainty information such as a probability distribution for the value range.
   
3. posterior stage: processing (fusion) of the available knowledge G and S ofthe prior and meta-prior stages respectively to make a probabilistic map of the phenomenon for a given set of spatio-temporal points (typically a grid). The map is a statement of the general knowledge G relative to the case specific knowledge S and is derived using Bayesian conditional probabilities.

If the general knowledge G comprises the mean and covariance, and if S includes only hard data, then the BME estimate coincides with the simple Kriging estimate. Similarly, if G is limited to the variogram and if S includes only hard data, then the BME estimate coincides with the ordinary Kriging estimate.

When applying the BME method in the SensorSAi, the knowledge S is represented as an observation collection described with the O&M model and including uncertainty information in uncertML. The map resulting from the posterior stage
is represented as coverage with associated uncertainty information.

Socio-economic spatial correlation

This spatial correlation algorithm fuses information from an economic impact database about buildings, cracking and the potential economic impact of this cracking with ground displacement sensor data in the Barcelona region. Correlation is between each identified building and the nearest ground displacement measurement. A displacement threshold limit, determined via temporal analysis of the regions historical correlation between displacements and eventual cracking, is used to flag buildings at different likelihoods of cracking. The output is a list of buildings, spatially correlated displacement values for each building, economic information such as tax and rental income and a 'likely cracking' warning flag based on the ground displacement threshold limit.