## 7 Case Validation and Analysis
### Deviation Transfer Model for MAP
above frame structure is completed and the state space equation for the multi-level assembly deviation transfer of the frame structure is obtained according to Equations (43)-(45):  
\[X(k)=X(k-1)+D^{P}(k)+D^{Q}(k)+R(k) \tag{43}\]  
\[D^{P}(k)=B(k)\cdot U(k)=L(k)\cdot E(k)\cdot F(k)\cdot G(k)\cdot U(k) \tag{44}\]  
\[D^{Q}(k)=S(k)\cdot C(k)\cdot T(k) \tag{45}\]  
In Equations (43)-(45), \(k=1,2,3,4,5\). The specific values of the system matrices \(E\), \(F\), \(G\) and \(L\) in this mathematical model are:  
\[E(1)= \begin{bmatrix}E_{A_{1}P_{1}}&0^{5\times 15}\\ 0^{5\times 5}&E_{A_{2}P_{3}}&0^{5\times 5}&0\\ 0^{5\times 5}&0^{5\times 5}&E_{A_{3}P_{5}}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&E_{A_{4}P_{5}}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&0^{5\times 5}&E_{A_{4}P_{5}}\end{bmatrix} ,\ E(5)= \begin{bmatrix}E_{A_{1}P_{1}}&0^{5\times 5}&0^{5\times 5}&0\\ 0^{5\times 5}&E_{A_{2}P_{3}}&0^{5\times 5}&\vdots\\ 0^{5\times 5}&0^{5\times 5}&E_{A_{3}P_{5}}&0^{5\times 5}\\ 0&\cdots&0^{5\times 5}\end{bmatrix}  \tag{46}\]  
\[E_{A_{1}P_{1}}= \begin{bmatrix}1&0&0&1753&0\\ 0&1&0&-149&0\\ 0&0&1&0&1753\\ 0&0&0&1&0\\ 0&0&0&0&1\end{bmatrix} ,\ E_{A_{2}P_{3}}= \begin{bmatrix}1&0&0&589&0\\ 0&1&0&-97&0\\ 0&0&1&0&589\\ 0&0&0&1&0\\ 0&0&0&0&1\end{bmatrix}  \tag{47}\]  
\[F(1)= \begin{bmatrix}F_{A_{1}P_{1}}&0^{5\times 5}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&F_{A_{3}P_{5}}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&0^{5\times 5}&F_{A_{4}P_{5}}\end{bmatrix} ,\ E(5)= \begin{bmatrix}F_{A_{1}P_{1}}&0^{5\times 5}&0^{5\times 5}&0\\ 0^{5\times 5}&0^{5\times 5}&0^{5\times 5}&\vdots\\ 0&\cdots&0^{5\times 5}\end{bmatrix}  \tag{48}\]  
\[F_{A_{1}P_{1}}= \begin{bmatrix}1&0&0&0&0\\ 0&1&0&0&0\\ 0&0&1&0&0\\ 0&0&0&1&0\\ 0&0&0&0&-11\end{bmatrix} ,\ F_{A_{2}P_{3}}= \begin{bmatrix}1&0&0&0&0\\ 0&1&0&0&0\\ 0&0&1&0&0\\ 0&0&0&1&0\\ 0&0&0&0&NaN\end{bmatrix}  \tag{49}\]\[G(1)= \begin{bmatrix}G_{P_{1},P_{2}}&0^{5\times 18}\\ 0^{15\times 6}&0^{15\times 18}\end{bmatrix} ,\ G(2)= \begin{bmatrix}G_{P_{1},P_{2}}&0^{5 \times 6}&0\\ 0^{5\times 6}&G_{P_{3},P_{4}}&\vdots\\ 0&\cdots&0^{10\times 12}\end{bmatrix} ,\ G(3)= \begin{bmatrix}G_{P_{1},P_{2}}&0^{5 \times 6}&0^{5\times 6}&0\\ 0^{5\times 6}&G_{P_{3},P_{4}}&\vdots\\ 0^{5\times 6}&0^{5\times 5}&G_{P_{3},P_{6}}&\\ 0&\cdots&0&0^{5\times 6}\end{bmatrix}  \tag{50}\] \[G(4)= \begin{bmatrix}G_{P_{1},P_{2}}&0^{5\times 6}&0^{5\times 6}&0^{5 \times 6}\\ 0^{5\times 6}&G_{P_{3},P_{4}}&0^{5\times 6}&0^{5\times 6}\\ 0^{5\times 6}&0^{5\times 5}&G_{P_{5},P_{6}}&0^{5\times 6}\\ 0^{5\times 6}&0^{5\times 6}&G_{P_{3},P_{6}}&0^{5\times 6}\\ 0&0^{5\times 6}&0^{5\times 6}&G_{P_{3},P_{6}}\end{bmatrix} ,\ G(5)= \begin{bmatrix}F_{A_{1},P_{ 1}}&0^{5\times 5}&0^{5\times 5}&0^{5\times 5}\\ 0^{5\times 5}&F_{A_{2},P_{3}}&0^{5\times 5}&0^{5\times 5}\\ 0^{5\times 5}&0^{5\times 5}&F_{A_{3},P_{5}}&0^{5\times 5}\\ 0&0^{5\times 5}&0^{5\times 5}&F_{A_{4},P_{5}}\end{bmatrix} \]  
\[G_{P_{1},P_{2}}= \begin{bmatrix}1&0&0&0&0\\ 0&1&0&0&0\\ 0&0&1&0&0&0\\ -0.0076&0&0.0076&0&0\\ 0&0&-0.0076&0&0&0.0076\end{bmatrix} ,G_{P_{3},P_{4}}= \begin{bmatrix}1&0&0&0&0 &0\\ 0&1&0&0&0\\ 0&0&1&0&0&0\\ -0.0030&0&0&0.0030&0&0\\ 0&0&-0.0030&0&0&0.0030\\ 0&0&-0.0030&0&0&0.0030\\ 0&0&1&0&0&0\\ -0.0067&0&0&0.0067&0&0\\ 0&0&-0.0067&0&0&0.0067\end{bmatrix} ,G_{P_{5},P_{6}}= \begin{bmatrix}1&0&0&0&0 &0\\ 0&1&0&0&0&0\\ 0&0&1&0&0&0\\ -0.0022&0&0&0.0022&0&0\\ 0&0&-0.0022&0&0&0.0022\end{bmatrix}  \tag{51}\]  
\[L(1)= \begin{bmatrix}0^{20\times 20}\end{bmatrix} ,\ L(2)= \begin{bmatrix}\Pi_{1}&0^{5 \times 5}&0^{5\times 5}\\ 0^{15\times 5}&0^{15\times 5}\end{bmatrix} ,\ L(3)= \begin{bmatrix}\Pi_{1}&0^{5 \times 5}&0\\ 0^{5\times 5}&\Pi_{2}&\vdots\\ 0&\cdots&0^{5\times 5}\end{bmatrix}  \tag{52}\]  
\[\Pi_{1}= \begin{bmatrix}0&0&1\\ 1&0&0\\ 0&1&0\end{bmatrix} ,\ \Pi_{2}= \begin{bmatrix}0&1&0\\ 1&0&0\\ 0&0&-1\end{bmatrix} ,\ \Pi_{3}= \begin{bmatrix}0&0&-1\\ 1&0&0\\ 0&-1&0\end{bmatrix} ,\ \Pi_{4}= \begin{bmatrix}0&-1&0\\ 1&0&0\\ 1&0&0\\ 0&0&1\end{bmatrix}