**4. Experimental**

For both ANNs and PLS, MatLab (www.mathworks.com) with the neural network and the PLS toolbox were used. To eliminate the effects of instrument-drift (often referred to as 1/f noise) and (potentially) eliminate any other instrument-induced errors, initially both ANNs and PLS were tested using in-house developed spectral simulation software. An example output of this software has been shown in **Figure 1**. The variables tested and the ranges used are listed in **Table 1** and will be briefly discussed next.

**Random noise level:** Spectral simulations were used to study the effect of random (white) noise, because simulations do not suffer from drift (or 1/f noise) and because a pre-determined amount of noise can be easily added to a simulated spectral scan.

**Wavelength separation:** What is meant by wavelength separation Δλ (typically in a few pm) is shown in **Figure 6**. Spectral overlaps can be distinguished as *"direct overlaps"* (**Figure 6a**), intermediate overlaps (**Figure 6b**), and *"wing type"* overlaps (**Figure 6c**). The question


**Table 1.** Variables potentially affecting predictive ability of ANNs and PLS.

**4. Experimental**

234 Advanced Applications for Artificial Neural Networks

those used for ANNs.

listed in **Table 1** and will be briefly discussed next.

For both ANNs and PLS, MatLab (www.mathworks.com) with the neural network and the PLS toolbox were used. To eliminate the effects of instrument-drift (often referred to as 1/f noise) and (potentially) eliminate any other instrument-induced errors, initially both ANNs and PLS were tested using in-house developed spectral simulation software. An example output of this software has been shown in **Figure 1**. The variables tested and the ranges used are

**Figure 5. PLS**-top frame: Example spectral scans. Bottom frame: Simplified diagram of the PLS algorithm. To facilitate meaningful comparisons, simulations and experimentally obtained spectral scans (where possible) were the same as

**Random noise level:** Spectral simulations were used to study the effect of random (white) noise, because simulations do not suffer from drift (or 1/f noise) and because a pre-deter-

**Wavelength separation:** What is meant by wavelength separation Δλ (typically in a few pm) is shown in **Figure 6**. Spectral overlaps can be distinguished as *"direct overlaps"* (**Figure 6a**), intermediate overlaps (**Figure 6b**), and *"wing type"* overlaps (**Figure 6c**). The question

mined amount of noise can be easily added to a simulated spectral scan.

addressed was *"how far does an interfering spectral line have to be (in units of Δλ) before its effect on the analyte spectral line is negligible?"* As listed in **Table 1**, the effect of Δλ on predictive ability was as large as 15 pico-meter (pm).

**Intensity ratio A:I** affects the measured (or combined) response. For practical reasons, different ratios were used for simulations (**Table 2**) and for spectral scans (**Table 3**). An example is shown in **Figure 7**.

The spectral lines used for the spectral simulations are listed in **Table 2** and those used for the experimentally obtained spectral scans in **Table 3**.

**Figure 6.** Wavelength separation (Δλ). (a) *"direct spectral overlap"*, small Δλ, (b) intermediate case, (c) *"wing spectral overlap"*, large Δλ. Depending on Δλ, the max measured response in the spectral axis visually "appears" to have shifted (but actually it has not), the visual effect is due to the presence of the interferent. The intensity was scaled to a max of 100% (for **A**) with **I** scaled appropriately. Intensities >100% are due to combined contributions of **A** and **I**.


**Table 2.** Analyte (**A**) and Interferent (**I**) line pairs used in spectral simulations.


**Table 3.** Analyte and Interferent line pairs used for the experimentally obtained spectral scans.

**Figure 7.** Effect of **A:I** intensity ratio. The intensity axis was scaled to a max of 100% (for **A**) with **I** scaled appropriately. Intensities >100% are due to combined contributions of **A** and **I**.

For the experimentally measured scans, a sequential, optical emission spectrometer (OES, a Czerny-Turner scanning monochromator) with a focal length of 0.75 m, an 1800 grooves/ mm holographic grating, a photo multiplier tube (PMT) detector, and an ICP were used (Varian Liberty 100). The total weight of this instrument was 300 kg. This ICP-OES system was selected due to its spectral resolution and its ability to scan user-defined spectral windows. A diagram is shown in **Figure 8** and it included here to facilitate explanations of some experimental observations made during the course of this research.

A liquid sample is introduced into a 1–2 kW plasma (**Figure 8**). For simplicity, assume that the plasma generates only two spectral lines (at wavelengths **λ**<sup>1</sup> for Analyte **A** and **λ**<sup>2</sup> for Interferent **I**) from a sample introduced into it. Scanning a wavelength-window (dotted line, bottom of **Figure 8**) is accomplished using two mechanisms, one, by initially rotating the computer-controlled grating. Once the beginning of the desired wavelength range has been reached, further scanning is obtained by rotating the computer-controlled scanning plate. To complete a scan,

**No. Elements Spectral line pairs, wavelength (nm) Wavelength separation (pm)**

**Figure 7.** Effect of **A:I** intensity ratio. The intensity axis was scaled to a max of 100% (for **A**) with **I** scaled appropriately.

Intensities >100% are due to combined contributions of **A** and **I**.

**No. Elements Spectral line pairs, wavelength (nm) Wavelength separation (pm)**

 Zn and Ni 213.856 and 213.856 0 Cr and Pt 267.716 and 267.715 1 Zn and Cu 213.856 and 213.853 3 Ni and Cr 232.003 and 232.008 5 B and Mo 208.959 and 208.952 7 Be and V 313.042 and 313.027 15

**Table 2.** Analyte (**A**) and Interferent (**I**) line pairs used in spectral simulations.

 Zn and Ni 213.856 and 213.856 0 Cr and Pt 267.716 and 267.715 1 Zn and Cu 213.856 and 213.853 3 Ni and Cr 232.003 and 232.008 5 B and Mo 208.959 and 208.952 7 Ca and Co 315.887 and 315.878 9 Be and V 315.042 and 313.027 15

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**Table 3.** Analyte and Interferent line pairs used for the experimentally obtained spectral scans.

**Figure 8.** Illustration of the 75 cm focal length (f) scanning spectrometer, scans were 60–160 points.

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

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 ANNs and PLS.

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

**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 form of chemical separation (per Section 1).
