**5.1. Effect of A:I intensity ratio on predictive ability of ANNs and PLS for different Δ***λ*

The predictive performance of ANNs and PLS was found to be inter-dependent on two key variables, specifically **A:I** ratio and Δ*λ*. Experimental results summarizing absolute |Error| are shown in **Figure 10**.

It can be concluded that ANNs (with an average prediction error of the concentration of an Analyte (**A**) of ~4.1%) performed equally as well as PLS (with an average prediction error of ~4.4%).

### **5.2. Effect of added white (random) noise on prediction of A:I ratios**

the scanning plate is stopped and a measurement of the intensity is made at the wavelength where the plate was stopped. Then, the wavelength is incremented (typically by about 0.01 nm) by rotating the plate and another measurement of the intensity is made and so on until the desired spectral range has been covered (typically ~0.100 nm). In other words, a scan is accomplished using a step-measure-and-repeat process. The dots in the "example spectral scan" (**Figure 8**) indicate intensity measurements at each step, the presentation software simply *"connects-the-dots"*. Such experimentally obtained spectral scans were used for both

**Figure 9.** Wavelength shift (misalignment) due to scanning plate (**Figure 8**) reset-errors. (a) Experimentally obtained signal response from Zn (Analyte) + Cu (Interferent) plus V (added to generate a marker peak). And (b) same as (a) but

**Wavelength shift (misalignment):** When repeatedly scanning the same spectral window, it was discovered that scans were offset from each other. An example is shown in **Figure 9a**. To address the effect of this spectrometer limitation, a fixed amount of a reference element was added to the **A** and **I** mixtures. The reference element was selected so that (where possible) its spectral line was separated from the analyte and from the interfering peaks. Subsequently, the spectral scans were corrected by manually aligning them with respect to the marker peak

**The intensity ratio** of **A**:**I** ranged between 1:1, 1:0.01, and 1:0.01, for both simulations and experimental spectral scans. **A**:**I** ratios higher than 1:1 were not tested because they were deemed too unrealistic for practical analytical applications. If **A**:**I** is higher than 1:1, an alternative spectral line (if possible) should be used or, the sample may have to undergo some

From the large number of experiments that were run (**Tables 2** and **3**), for brevity, only a few

ANNs and PLS.

(**Figure 9a**). An example is shown in **Figure 9b**.

after manual alignment of spectral scans. See text for discussion.

238 Advanced Applications for Artificial Neural Networks

form of chemical separation (per Section 1).

results will be included here (and are briefly discussed below).

**5. Results and discussion**

To avoid the effect of 1/f noise, only simulated spectral scans were used for noise-studies. Noise levels tested were as high as an (unrealistic for practical applicability) 18%. Results are shown in **Figure 11**.

**Figure 10.** Predictive ability of ANNs and PLS using only four pairs (selected for clarity) of overlapping spectral lines (scans obtained experimentally) with their Δ*λ* ranging between 0 and 15 pm.

**Figure 11.** Predictive ability of ANNs and PLS for six pairs of simulated spectral lines with their Δλ ranging from 0 to 15 pm and with % added random level noise added ranging from 0 to 18% (with two traces overlapping).

The predictive ability of ANNs (on the average) was 5.0%, and of PLS was (on the average) 5.1%. As expected, prediction errors increased as noise levels increased. A key difference between ANNs and PLS is that PLS did poorly when Δ*λ* was 0 pm (even at very low noise levels). Interestingly, from the simulated spectral scans when 0% noise was added (**Figure 11**) both ANNs and PLS had a prediction errors (on the average) of less than 1%, essentially the predictions were error free. Thus, it can be concluded that (likely) predictive ability was noisedepended (or noise-limited).
