I would recommend avoiding using subscript variable in evaluations. Just use simple notation like g3. Also avoid Greek and special notation when you can. All this makes code huge and unstable and hard to read.

As an experiment, I tried minimizing just the first term of your expression and got a useful error message

In[51]:= NMinimize[{(E1[6.5] - tsd1[[1]])^2, a > 10 && b > 20}, {a, b}]

During evaluation of In[51]:= NMinimize::nnum: The function value (96.4742 +Sqrt[86916. -Sqrt[7.55438*10^9+Times[<<2>>]]]/(2 Sqrt[2])+Sqrt[86916. +Sqrt[7.55438*10^9-3.97633*10^6 Plus[<<2>>]]]/(2 Sqrt[2]))^2 is not a number at {a,b} = {11.9186,21.6635}.

During evaluation of In[51]:= NMinimize::nnum: The function value (96.4742 +Sqrt[86916. -Sqrt[7.55438*10^9+Times[<<2>>]]]/(2 Sqrt[2])+Sqrt[86916. +Sqrt[7.55438*10^9-3.97633*10^6 Plus[<<2>>]]]/(2 Sqrt[2]))^2 is not a number at {a,b} = {11.9186,21.6635}.

During evaluation of In[51]:= NMinimize::nnum: The function value (96.4742 +Sqrt[86916. -Sqrt[7.55438*10^9+Times[<<2>>]]]/(2 Sqrt[2])+Sqrt[86916. +Sqrt[7.55438*10^9-3.97633*10^6 Plus[<<2>>]]]/(2 Sqrt[2]))^2 is not a number at {a,b} = {11.9186,21.6635}.

During evaluation of In[51]:= General::stop: Further output of NMinimize::nnum will be suppressed during this calculation.

Out[51]= NMinimize[{(-1739.3 + 
    a (179.376 - 8/5 b Cos[(43 \[Pi])/180]) + 
    1/(2 Sqrt[
      2]) (\[Sqrt](a^2 (222.029 + (7.51018 + 
               32/65 Sqrt[3] b Sin[(17 \[Pi])/180]) (12.1941 + 
               16/65 Sqrt[3]
                 b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                  Sin[(17 \[Pi])/
                   180]))) - \[Sqrt](a^4 (222.029 + (7.51018 + 
                  32/65 Sqrt[3] b Sin[(17 \[Pi])/180]) (12.1941 + 
                  16/65 Sqrt[3]
                    b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                    Sin[(17 \[Pi])/180])))^2 - 
            4 a^4 (-47.7013 + 
               7.51018 (7.51018 + 
                  32/65 Sqrt[3]
                    b Sin[(17 \[Pi])/180])) (-89.1844 + (12.1941 + 
                  16/65 Sqrt[3]
                    b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                    Sin[(17 \[Pi])/180])) (6.00082 + 13/(2 
\!\(\*SubscriptBox[\(17\), \(\[AliasDelimiter]\)]\))))))) + 
    1/(2 Sqrt[
      2]) (\[Sqrt](a^2 (222.029 + (7.51018 + 
               32/65 Sqrt[3] b Sin[(17 \[Pi])/180]) (12.1941 + 
               16/65 Sqrt[3]
                 b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                  Sin[(17 \[Pi])/
                   180]))) + \[Sqrt](a^4 (222.029 + (7.51018 + 
                  32/65 Sqrt[3] b Sin[(17 \[Pi])/180]) (12.1941 + 
                  16/65 Sqrt[3]

                    b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                    Sin[(17 \[Pi])/180])))^2 - 
            4 a^4 (-47.7013 + 
               7.51018 (7.51018 + 
                  32/65 Sqrt[3]
                    b Sin[(17 \[Pi])/180])) (-89.1844 + (12.1941 + 
                  16/65 Sqrt[3]
                    b (Sqrt[3] Cos[(17 \[Pi])/180] + 
                    Sin[(17 \[Pi])/180])) (6.00082 + 13/(2 
\!\(\*SubscriptBox[\(17\), \(\[AliasDelimiter]\)]\))))))))^2, 
  a > 10 && b > 20}, {a, b}]