BRIEF DESCRIPTION OF THE FIGURES
A full understanding of the invention can be gained from the following detailed description of the invention when read in conjunction with the accompanying figures in which:
FIG. 1 is a block diagram of a preferred embodiment of an apparatus according to the present invention.
FIG. 2 is a flow chart showing Phase I of neural network modeling, that is, the generation of the model. More specifically, it shows how the procured data is preprocessed, how the neural network is modeled, how the neural network iteratively trains itself to find the optimal weights, how it verifies the model, and finally, how it stores the appropriate problem-specific neural network.
FIG. 3 is a flow chart showing Phase II of neural network modeling, that is, the application of the model. This phase takes the saved neural network from the previous phase and uses procured data that is validated to detect and predict water quality conditions. Data validation encompasses checking the data for insufficiency, checking the data for abnormality, checking whether the data is historically justified and filtering random sensor noise.
FIG. 4 is a table showing the correlation coefficients calculated between various water quality parameters in an example of nitrification prediction.
FIG. 5 are two graphs, the first of which is the actual water quality data plot for pH of a water sample over a period of time (top) and the second of which is the standardized water quality data plot for pH of the water sample over the same period of time (bottom).
FIG. 6 includes two graphs, the first of which is the actual water quality data plot for temperature of a water sample over a period of time (top) and the second of which is the standardized water quality data plot for temperature of the water sample over the same period of time (bottom).
FIG. 7 is a graph of the mean squared errors (MSE) that were calculated with two neurons and ten trials for five different time delay periods in the nitrification example.
FIG. 8 is a graph of the squared correlation coefficients (R2) that were calculated with two neurons and ten trials for five different time delay periods in the nitrification example.
FIG. 9 is a graph of the MSE calculations with three neurons and ten trials for five different time delay periods in the nitrification example.
FIG. 10 is a graph of the R2 calculations with three neurons and ten trials for five different time delay periods in the nitrification example.
FIG. 11 is a schematic diagram of the architecture of the neural network model.
FIG. 12 is a graph showing the error function minimization. The blue line represents the training set, the green line represents the cross validation set, and the black line represents the ideal value for MSE that the model wants to achieve.
FIG. 13 is a graph showing how the neural network model is generated by separating the data into three data sets: training, cross validation, and testing sets.
FIG. 14 is a graph showing plots of actual data and filtered data.