**6. Conclusions**

16 Will-be-set-by-IN-TECH

0

5

10

water content [%] (predicted)

• Thirdly, the parts described by these linear models are subtracted from the measured values and the variables of interest and the algorithm is restarted using this new data in

• and finally, the procedure is repeated iteratively until a specified number *H* of hidden path

All determined regression coefficients and weighting factors are used finally for the calculation of the regression equation. This means for the validation (and later application) that only a linear combination of the input values need to be calculated. Hence the calculation effort is much smaller in comparison to the ANN. The only degree of freedom is *H*, the number of factors to be used (number of iterations). When H is too high the *RMSEc* is significantly smaller than the *RMSEv*. This means that overfitting occurs. However, as shown in Figure 12 *H* should be selected where *RMSEv* has a minimum. Furthermore *RMSEc* should not be much smaller (factor 1/2) than *RMSEv*, otherwise the PLSR calibration could not handle

The performance of the PLSR is shown in Figure 13. For test series 1 *RERc* = 52 (*excellent*) and *RERv* = 28.1 (*good*). This is a further improvement in comparison to the ANN. For test series

Principal component analysis and regression lead to acceptable results but the best calibrations were obtained with ANN and PLSR. However the computation effort is much higher with ANN and in general more samples are necessary for a successful training. PLSR is a linear operation and can be performed fast in real time. For this reason PLSR is the best choice for calibration of the application discussed here. In Table 2 the results of both test series are compared with similar experiments presented in several other publications. As can be seen, the performance obtained here is in the upper range. However one has to take into account the further advantages of the system discussed here: it is non-contacting, the objects

2 the results stay similar to those of ANN: *RERc* = 26.5 (*good*) and *RERv* = 17.1 (*fair*).

15

20

PLSR : RMSEc

0 5 10 15 20

(b) Test series 2: ethanol-water mixtures.

water content [%]

=0.68%, RMSEv

=1.05%

cal. val.

0 5 10 15 20 25

moisture [%]

**Figure 13.** Results obtained with PLSR for both test series.

(a) Test series 1: clay granules.

order to calculate the next factor,

variables is calculated.

unknown samples.

**5.4. Best calibration method**

can be rotated, and can have irregular shapes and sizes.

=0.375%, RMSEv

=0.693%

cal. val.

moisture [%] (predicted)

PLSR : RMSEc

Many industrial and scientific applications require extensive on-line process monitoring and quality control. Often the composition of goods (e.g. moisture content) is of great interest but also abstract parameters, for example quality or freshness, play an important role. The microwave sensor described is able to penetrate the investigated materials and by using UWB-techniques it is possible to gain information at various frequencies. The applied time domain techniques operate with low hardware effort and fast measurement speed while having a high accuracy. Using commercial MMICs signals exceeding a bandwidth of 10GHz can be generated and sampled with cheap and compact dedicated hardware. Today it is possible to employ multivariate calibration methods like artificial neural networks, which have a high computational effort, in real time. These methods are well established in, for example, NIR or image processing and are successfully adopted. The feasibility of the method has been successfully proven with accuracy even greater than in many previous publications using contacting methods. It has a great potential for many kinds of future applications in microwave sensing.
