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A D V A N C E D M A T E R I A L S & P R O C E S S E S | O C T O B E R 2 0 1 8 2 3 agent, crosslinking agent, and carbon black. Process variables include extru- sion, cooling, and the oven, as well as line and screw speed. Dimensional vari- ables include extruded sheet (matrix) width and thickness. Nonlinear models of cross-linked foams can be developed for product and material properties (e.g., tensile strength, density, cell size, and tear strength) and for economic variables such as production rate, raw material cost per kg and m 3 of product, and total production cost. MODELING RESULTS As mentioned previously, nonlin- ear modeling requires either produc- tion or experimental data. In this case, the authors carried out experiments on the production line. Flow rate of poly- mer (LDPE), foaming and cross-linking agents, carbon black, and matrix width and thickness were varied in 38 exper- iments and several material properties were measured from each experiment. Thermal conductivity was measured at eight different temperatures from each experiment. Nonlinear modeling re- sults of only a few material properties are presented here. Measurement data from these ex- periments are high quality, which made model development easier. Using NLS 020 software, nonlinear models in the form of feed-forward neural networks with sigmoidal activation functions were developed for six material proper- ties and slab thicknesses, the statistical characteristics of which are included in the sidebar on the next page. Figure 4 shows a comparison of measured values of tensile strength in the extrusion direction on the horizon- tal axis with values predicted by the nonlinear model on the vertical axis. The RMS error (roughly speaking, the standard deviation of the error) of pre- diction is 0.0175 MPa. The correlation coefficient is 99.77%, which is excel- lent considering that the model covers a wide range of products with densities varying from about 26 to 210 kg/m 3 and strengths from 0.2 to 2.1 MPa. Models were combined and aug- mented with equations for production Fig. 4 — Comparison of measured values of tensile strength in extrusion direction with values predicted using nonlinear model. Fig. 5 — Effect of foaming agent on tensile strength for different amounts of cross-linking agent. Fig. 6 — Determining recipes to produce material with a given combination of properties.