Calibration by artificial neural networks

By means of these variances the limits of detection XkLD of the k analytes tmder investigation can be estimated in analogy to the univariate case (see Sect. 7.5), namely on the basis of the critical values ynetkyC of the net signals their vector is denoted yk,c in the last term of Eq. (6.116b)  

A detailed derivation can be found in Bauer et al. [1991b]. The limit of detection according to Eq. (6.116a) corresponds to Kaiser s so-called 3a criterion see Sect. 7.5., Lorber and Kowalski [1988] as well as Faber and Kowalski [1997b] take into account errors of the first and second kind. The multivariate detection limits are estimated then in analogy to the univariate limits being twice the 3a-limit (with ua = up) see Sect. 7.5 and Ehrlich and Danzer [2006]). 

In general, there is no connection between neurons within the same layer, but each neuron is connected with each neuron of the next layer. The structure of an ANN can be seen from Fig. 6.18. 

Neural networks are characterized by their weights, wXp and their respective sums are given by the weight matrixes, between the diverse layers. The weights represent the strength of the directed connection between neurons i and j see Fig. 6.19. 

Neurons have one or more inputs, an output, oiy an activation state, Aiy an activation function, facU and an output function, fout. The propagation function (net function) 

---

Additionally, a variety of analytical equipment and techniques that allow the examination of small- (and micro-) scale microbial cultures and their products have become available. Examples include near infrared and Fourier transform infrared spectroscopy, which offer the ability for in situ detection of specific compounds in fermentation broth [22]. However, sensitivity and the required sample volumes pose serious obstacles that still have to be overcome. Another alternative is offered by sensitive pyrolysis mass spectroscopy, which was demonstrated to be suitable for quantitative analysis of antibiotics in 5-pl aUquots of fermentation broth when combined with multivariate calibration and artificial neural networks [91]. The authors concluded that a throughput of about 12,000 isolates per month could be expected. Furthermore, standard chromatographic methods such as gas chromatography or high-performance liquid chromatography, possibly in combination with mass spectroscopy (MS) for detection, can provide simultaneous quantitative detection of many metabolic products. 

Ni Y, Chen S, and Kokot S (2002) Spectrophotometric determination of metal ions in electroplating solution in the presence of ethylenediaminetetraacetic acid by multivariate calibration and artificial neural networks. Analytica Chimica Acta 463 305-316. 

Analgin Powder Non-destructive drug determination by means of artificial neural network. Different calibration strategies compared. Relative predictive error lower than 2.5% 149... 

M. Blanco, J. Coello, H. Iturriaga, S. Maspoch and J. Pages, NIR calibration in non-linear systems by different PLS approaches and artificial neural networks, Chemom. Intell. Lab. Syst., 50, 2000, 75-82. 

No chapter on modern chemometric methods would be complete without a mention of artificial neural networks (ANN). In a simple form these attempt to imitate the operation of neurons in the brain. Such networks have a number of linked layers of artificial neurons, including an input and an output layer (see Figure 8.13). The measured variables are presented to the input layer and are processed, by one or more intermediate ( hidden ) layers, to produce one or more outputs. For example, in inverse calibration, the inputs could be the absorbances at a number of wavelengths and the output could be the concentration of an analyte. The network is trained by an interactive procedure using a training set. Considering the example above, for each member of the training set the neural network predicts the concentration of the analyte. The discrepancy between the observed and predicted values... 

Using artificial neural networks (ANN) Ivanduc et al. compared those results with multi-linear regression (MLR or MRA) results and found that, in this case, the neural network approach offers only slightly better results, both for calibration and cross validation. Apparently the same conclusion concerning prediction of C NMR chemical shifts of alkanes was reached by Svozil et al. [88] indicating, according to Ivanciuc, that the relationship between the path counts and CSS has a small non-linear character and the ANN model could not provide much better result than the MLR model ... 

Since the 1970s, NIR spectroscopy has provided the means to test wheat at delivery to handlers, merchants, or direct to the mill. For ground wheat, protein may be determined with three or four fixed filters 2180, 2100 (1940 required for corrected moisture basis), and either 1680 or 2230 nm. In countries with wheat grading systems, such as Australia, Canada, and the US, segregation is carried out on the basis of load-by-load NIR testing of growers deliveries at country silos. Nowadays, this is almost exclusively by whole grain instruments, the most popular of which is the FOSS Infratec. This type of instrument is calibrated with tens of thousands of samples and development of a model based on artificial neural networks (8, 9). 

Electronic tongue systems for remote environmental monitoring applications have been presented in several applications. A new approach in the chemical sensor field consists in the use of an array of nonspecific sensors coupled with a multivariate calibration tool which may form a node of a sensor network. The proposed arrays were made up of potentiometric sensors based on polymeric membranes, and the subsequent cross-response processing was based on a multilayer artificial neural network model as proposed by Mimendia et al. who described environmental monitoring of ammonium as a pollutant plus alkaline ions at different measuring sites in the states of Mexico and Hidalgo (Mexico), and monitoring of heavy metals (Cu ", Pb ", Zn ", and Cd " ) in open-air waste streams and rivers. 

Systems such as the one illustrated in figure 23.2 will also incorporate artificial intelligence. The information from the sensors will be used with fuzzy logic and neural networking to enable decisions by individual controllers based on the input from multiple sensors. Such systems will also incorporate sensor self-testing, self-calibration, and fault correction, resulting in reliable, automated systems applicable to any process or production line. These systems will significantly affect the productivity and profitability of food, chemical, and pharmaceutical production. 

---