Material selection processes and exchange of material information in concurrent engineering environment using neural network and web technology

Abstract

Selection of the proper materials for a structural component is critical in engineering design. Existing design procedures may currently be sufficient, especially where experience exists, but fierce industrial competition is spurring the search for improved methods and tools. The main drivers are quality, life-cycle cost, time-to-market and material selection. Improved design efficiency and accuracy may depend on specific material selection. This paper discusses the one of the Concurrent Engineering integration strategies i.e., “selection of material” using neural networks that can be adapted for successful integration within industry and beyond using XML and web services. The introduction of computerized design and analysis systems offered the promise of selecting the right material for an optimized design early in the product development cycle. This requires consistent and high-quality material information throughout the design to manufacturing process.

Appendix A

1.1 A-I summary of back propagation algorithm

• 1. Apply the input vector X(n) to the input units

• 2. Initialize the weights randomly

• 3. Calculate the net-input values to the hidden layer units

  $$\begin{aligned}&\hbox {net}\_{\mathrm{hidden}} = \sum _{i=1}^{N} {w_{ji}^{h}} x_{pi} +\theta _{j}^{h} \\&\hbox {Input}^{*}\hbox {wt}\_{\mathrm{hidden}} + \hbox {bias}\_{\mathrm{hidden}}\nonumber \end{aligned}$$

  (6)

• 4. Calculate the outputs from the hidden layer

  $$\begin{aligned} \hbox {op}\_{\mathrm{hiddenlayer}} = \hbox {I}_{\mathrm{pj}}=f_{j}^{h}(\hbox {net}\_{\mathrm{hidden}}) \end{aligned}$$

  (7)

• 5. Calculate the net input values to each unit of the output layer

  $$\begin{aligned} \hbox {net}\_{\mathrm{op}}&= (\hbox {op}\_\mathrm{hidden~layer}^{*} \hbox {wt}\_{\mathrm{op}}) + \hbox {bias}\_{\mathrm{op}} \nonumber \\ \hbox {net}_{pk}^{o}&= \sum _{j=1}^L {w_{kj}^{o} i_{pj} +\theta _{k}^{o}} \end{aligned}$$

  (8)

• 6. Calculate the outputs of the output layer

  $$\begin{aligned} \hbox {op}\_{\mathrm{outputlayer}} = \hbox {O}_{\mathrm{pk}}=f_k^o (net\_op) \end{aligned}$$

  (9)

• 7. Calculate the error terms for the output units

  $$\begin{aligned} \hbox {Error}\_{\mathrm{op}}&= (\hbox {desired}\_{\mathrm{op}} -{\mathrm{op}}\_{\mathrm{outputlayer}})~f_{k}^{o^{{\prime }}}(\hbox {net}\_{\mathrm{op}})\nonumber \\ \delta _{pk}^{o}&= (y_{pk}-o_{pk})~f_{k}^{{o}^{{\prime }}}(net_{pk}^{o}) \end{aligned}$$

  (10)

• 8. Calculate the error terms for the hidden layer units

  $$\begin{aligned} \hbox {error}\_{\mathrm{hidden}}&= f_j^{h^{{\prime }}} (net\_hidden){*}(error\_op{*}wt\_op) \nonumber \\&= f_{j}^{h^{{\prime }}} (net\_hidden)\sum _{k} {\delta _{pk}^{o} w_{kj}^{o}} \end{aligned}$$

  (11)

• 9. Update the weights on the output layer

  $$\begin{aligned}&\!\!\!\!\hbox {wt}\_{\mathrm{op}} = \hbox {wt}\_{\mathrm{op}} + \hbox {learn}\_{\mathrm{para}}^{*}\nonumber \\&\qquad (\hbox {error}\_{\mathrm{op}}^{*} \hbox {op}\_\mathrm{hidden~layer}) \!+\!\hbox {momentum}^{*}\nonumber \\&\qquad \hbox {learn}\_{\mathrm{para}}^{*} \hbox {error}\_{\mathrm{op}}^{*} \hbox {op}\_{\mathrm{hidden~layer}} \nonumber \\&\!\!\!\!\!w_{kj}^{o} (t+1)=w_{kj}^{o}(t)+\eta \delta _{pk}^{o} i_{pj} +\alpha \delta _{pk}^{o} i_{pj} \eta \end{aligned}$$

  (12)

• 10. Update weights on the hidden layer

  $$\begin{aligned} \hbox {wt}\_{\mathrm{hidden}}&= \hbox {wt}\_{\mathrm{hidden}} + \hbox {learn}\_{\mathrm{para}}^{*} \hbox {error}\_{\mathrm{hidden}}^{*}\nonumber \\&\quad \hbox {input} +\hbox {momentum}^{*} \hbox {learn}\_{\mathrm{para}}^{*}\nonumber \\&\quad \hbox {error}\_{\mathrm{hidden}}^{*}\hbox {input} \nonumber \\ w_{ji}^{h} (t\!+\!1)\!&= \! w_{ji}^{h} (t)\!+\!w_{ji}^{h} (t)\!+\!\eta \delta _{pj}^{h} x_{i} \!+\!\alpha \Delta _{p} w_{ji}^{h}(t-1) \nonumber \\&= w_{ji}^{h} (t)+\eta \delta _{pj}^{h} x_{i} +\alpha \eta \delta _{pj}^{h} x_{i} \end{aligned}$$

  (13)

$$\begin{aligned} 11.\, \,\,\hbox {Error term}= \frac{1}{2}(error-op)^{2}=\frac{1}{2}\sum _{k=1}^{M} {\delta _{pk}^{2}} \end{aligned}$$

(14)