# Non-Destructive Infrared Evaluation of Thermo-Physical Parameters in Bamboo Specimens
## 6 Estimation of Thermo-Physical Properties of Bamboo Using Experimental Data  
Estimating thermo-physical properties of bamboo can be complicated, particularly when done in a non-destructive way. Bamboo's tissue is inhomogeneous; it varies along and across the culm. Most of the studies [10; 28; 29] that estimate thermal properties of bamboo both along and across the culm take small pieces of bamboo culms since the analysis equipment imposes such specific geometries on the specimens to be analyzed. Even though these works provide insight into the thermal properties of bamboo, they lack practical use when inspecting numerous samples whose geometries are mostly cylindrical. Here, we address the problem of estimating thermal conductivity, volumetric heat capacity, and convective heat transfer coefficient of bamboo samples, which are approximately half a cylinder, from data obtained as explained in Section 5. The direct model assumes no interactions in z and \(\phi\) directions and constant properties radially to reduce complexity in the inverse procedure. Therefore, our experiments yield average values of \(k\), \(\rho c_{p}\), and \(h\). As mentioned in Section 4, estimating \(k\), \(\rho c_{p}\), and \(h\) is challenging not only for the nonlinearity of the IHCP, but for the correlation among the three parameters. As a result, we optimized over the parameter space defined by \(k\) and \(\rho c_{p}\) while \(h\) is assumed known. Removing \(h\) from the optimization parameters diminishes the correlation between \(k\) and \(\rho c_{p}\) from 1 to \(0.6\pm 0.15\). This allows the LM algorithm to have more consistent results in the sense that variations of 5% around an initial guess produce variations of 0.1% around the convergence point of the initial guess, which is a desirable behavior according to [26]. Figure 7: Examples of temperature curves in (**a**) the electrical resistence \(T_{res}\) and (**b**) \(T_{cum}\) the external side of the bamboo sample. Table 2 shows the average estimates of ten bamboo samples subjected to preservation and another ten left untreated (as exposed in Section 5). Although on average we find the estimates to be consistent with the measurements performed by [9; 10; 29], bamboo itself poses a big challenge because its properties depend on its species, porosity, density, vessel distribution among others. In addition, it is worth noting that in general it is difficult to make a fair comparison since most of the works in this area use different techniques and assumptions to measure the thermal properties of bamboo. Table 2 also shows that, although the variation of \(h\) causes great changes in the estimated parameters (\(k\) and \(\rho c_{p}\)), the standard errors are small in magnitude; the least standard error is reached when \(h\) equals 25, however. Figure 8 shows the curves of the estimates against the bamboo sample number. These curves permit us to visualize that, for values of \(h\) less than 25, the estimation of \(k\) tends to the lower bound in the optimization parameter space (OPS). By contrast, when \(h\) is greater than 25, some values \(\rho c_{p}\) tend to the upper bounds in the OPS. This effect is undesirable since it implies that the optimization action of the LM algorithm is being saturated, thus converging to a optimal value that is unnatural within the defined bounds. As a result, we consider that values of the parameters that converge within the bounds are better than those that lie over the lower and upper bounds; in this case, the best results are achieved when \(h=25\). Here, as done in Section 4, we also remove the scaling effect of \(h\) by dividing the curves in Figure 8 to obtain the thermal diffusivity of the bamboo samples as shown in Figure 9. In this figure, we can see that, for every value of \(h\), the thermal diffusivity of the samples tend to be the same except for the points that converge to lower limits of the thermal conductivity boundaries. Figure 10a accounts for the goodness of fit of the proposed approach for a chosen experimental temperature curve.