Error message with multiple equations: ! Missing } inserted. <inserted text> } l.231 \end{align}

Question

I am working on an equation set with some long equations. I use split to divide the long equations into multiple lines. However, I keep getting the error. ! Missing } inserted. } l.231 \end{align}

I expect to create an equation set like this:

Below is my code:

\begin{align} \label{eq:3.22}
  \begin{split}
  \left({PC}_i,{SV}_i\right) = &f_{PCA}(\bar{\frac{ds}{dt}},\sigma_\frac{dx_v}{dt},{CF}_\frac{dx_v}{dt},{\frac{ds}{dt}}_{max},\\
  &{\frac{ds}{dt}}_{rms},{IF}_\frac{ds}{dt},{SF}_\frac{ds}{dt},{ED}_\frac{ds}{dt},{CLF}_\frac{ds}{dt})
  \end{split}   \\
  \begin{split}
  d_{j,m}(k) = &\sqrt{(\frac{{SV}_1({PC}_1(k)-{{PC}_{1,m}}^j)}{{SV}_1+{SV}_2+\ldots+{SV}_n})^2\\
  &+(\frac{{SV}_2({PC}_2(k)-{{PC}_{2,m}}^j)}{{SV}_1+{SV}_2+\ldots+{SV}_n})^2+\ldots\\
  &+(\frac{{SV}_n({PC}_n(k)-{{PC}_{n,m}}^j)}{{SV}_1+{SV}_2+\ldots+{SV}_n})^2}
  \end{split}   \\
  P_{det,j}\left(k\right) = f_{det}(d_{j,m}\left(k\right),d_{j,m_1,m_2}\left(k\right))  \\
  \begin{split}
  s\left(k\right) = &s\left(k-1\right)+(m_3n_3\Delta T_j\left(k-1\right)^{n_3-1}\left(\Delta T_j\left(k\right)-\Delta T_j\left(k-1\right)\right)\\
  &+m_1n_1\Delta K\left(k-1\right)^{n_1-1}(\Delta K\left(k\right)-\Delta K\left(k-1\right)))e^{\omega\left(k\right)}
  \end{split}   \\
  l\left(k\right) = m_2{I_{load}}^{n_2}+m_3\Delta T_j\left(k\right)^{n_3}   \\
  y\left(k\right) = s\left(k\right)+v_1(k)  \\
  \Delta T_y\left(k\right) = \Delta T_j\left(k\right)+v_2\left(k\right) \\
  \left[s(0)  \Delta T_j(0)  I_{load}\right] = \left[s_0  \Delta T_{j0}  I_{load}\right]
\end{align}

I am particularly frustrated that trying some possible solutions in the other threads didn't help. Can anybody take a look? Thank you so much!

Answer 1

I did some minimal damage repair to your equation. The error was due to the fact that you wrapped a \sqrt{...} around some split that runs over several lines and has & characters in it. One way to go is to work with [...]^{1/2} instead.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align} \label{eq:3.22}
  \begin{split}
  \left({PC}_i,{SV}_i\right) = &
  f_{PCA}\left(\bar{\frac{ds}{dt}},\sigma_\frac{dx_v}{dt},{CF}_\frac{dx_v}{dt},{\frac{ds}{dt}}_{max},
  \right.\\
  &\hphantom{f_{PCA}\left(\right.}\left.{\frac{ds}{dt}}_{rms},{IF}_\frac{ds}{dt},{SF}_\frac{ds}{dt},{ED}_\frac{ds}{dt},{CLF}_\frac{ds}{dt}
  \right)
  \end{split}   \\
  \begin{split}
  d_{j,m}(k) =
  &\left[\left(\frac{{SV}_1\left({PC}_1\left(k\right)-{{PC}_{1,m}}^j\right)}{{SV}_1+{SV}_2+\ldots+{SV}_n}\right)^2\right.\\
  &+\left(\frac{{SV}_2\left({PC}_2\left(k\right)-{{PC}_{2,m}}^j\right)}{{SV}_1+{SV}_2+\ldots+{SV}_n}\right)^2+\ldots\\
  &\left.+\left(\frac{{SV}_n\left({PC}_n\left(k\right)-{{PC}_{n,m}}^j\right)}{{SV}_1+{SV}_2+\ldots+{SV}_n}\right)^2\right]^{1/2}
  \end{split}   \\
  P_{det,j}\left(k\right) = & f_{det}(d_{j,m}\left(k\right),d_{j,m_1,m_2}\left(k\right))  \\
  \begin{split}
  s\left(k\right) = &s\left(k-1\right)+(m_3n_3\Delta T_j\left(k-1\right)^{n_3-1}\left(\Delta T_j\left(k\right)-\Delta T_j\left(k-1\right)\right)\\
  &+m_1n_1\Delta K\left(k-1\right)^{n_1-1}(\Delta K\left(k\right)-\Delta K\left(k-1\right)))e^{\omega\left(k\right)}
  \end{split}   \\
  l\left(k\right) = &m_2{I_\mathrm{load}}^{n_2}+m_3\Delta T_j\left(k\right)^{n_3}   \\
  y\left(k\right) = &s\left(k\right)+v_1(k)  \\
  \Delta T_y\left(k\right) = &\Delta T_j\left(k\right)+v_2\left(k\right) \\
  \left[s(0)  \Delta T_j(0)  I_\mathrm{load}\right] = & \left[s_0  \Delta T_{j0}  I_{load}\right]
\end{align}
\end{document}

I guess that, even though I made some more cosmetic corrections such as the introduction of \left and \right and \mathrm, both of us will agree that there is still considerable room for improvement. In particular, I am wondering about the following questions:

1. Are you sure you want to use labels like eq:3.22? What if this equation ends up as 4.12? Wouldn't this potentially drive you crazy. (Technically, however, this is a valid label.)
2. Are you sure that you want to lump these equations together in that way? How many readers will really benefit from this? Wouldn't it be better to group these things in related objects, each of which comes in a smaller set of equations, and to add explanation in between?
3. I would replace the differential d by upright d's. E.g. the physics package has \dd for that.

Answer 2

Some suggestions:

• You can't have an alignment point (&) inside a \sqrt{...} object. Use [...]^{1/2} notation instead.

• Don't overuse \left and \right. Use explicit sizing instructions only where needed.

• Use \overline if the bar needs to span the full width of the associated fractional expression.

• Use \mathit{...} to denote multi-letter variable names. Use \mathrm for whole words and acronyms such as "load", "PCA", "det", "rms", and "max".

• In most places where you use \ldots, \cdots would be more appropriate. However, it's even better to just write \dots and let LaTeX figure out which type of (typographic) ellipsis to employ.

• Use less space between the variable names and some of their fraction-style subscript terms.

\documentclass{article}
\usepackage{amsmath} % for 'align' environment
\usepackage{geometry} % set page size parameters suitably
% some macros to ease the inputting burden:
\newcommand\SVitem[2]{\mathit{SV}_{\!#1}(\mathit{PC}_{\!#1}(k)-{\mathit{PC}_{\!#1,m}}^j)}
\newcommand\sumSV{\mathit{SV}_{\!1}+\mathit{SV}_{\!2}+\dots+\mathit{SV}_{\!n}}

\begin{document}
\begin{align} \label{eq:3.22} % why just 1 \label for 8 equations?
  (\mathit{PC}_{\!i},\mathit{SV}_{\!i}) 
  &= f_{\mathrm{PCA}} \biggl(\,
      \overline{\frac{ds}{dt}},
      \sigma_\frac{dx_v}{dt},
      \mathit{CF}_{\!\frac{dx_v}{dt}},
      \frac{ds}{dt}_{\max},
      \frac{ds}{dt}_{\mathrm{rms}},
      \mathit{IF}_{\!\frac{ds}{dt}},
      \mathit{SF}_{\!\frac{ds}{dt}}, 
      \mathit{ED}_{\!\frac{ds}{dt}},
      \mathit{CLF}_{\!\frac{ds}{dt}} \biggr) \\
\begin{split}
  d_{j,m}(k) &= \biggl\{ 
      \biggl(\frac{\SVitem{1}}{\sumSV}\biggr)^{\!\!2}
     +\biggl(\frac{\SVitem{2}}{\sumSV}\biggr)^{\!\!2}\\
    &\qquad +\dots+
      \biggl(\frac{\SVitem{n}}{\sumSV}\biggr)^{\!\!2} 
   \,\biggr\}^{\!1/2}
\end{split}   \\
  P_{\textrm{det},j}(k) 
      &= f_{\textrm{det}}\bigl(d_{j,m}(k),
           d_{j,m_1,m_2}(k)\bigr)  \\
\begin{split}
  s(k) &= s(k-1)+\bigl\{ m_3n_3\Delta T_j(k-1)^{n_3-1}
          \bigl(\Delta T_j(k)-\Delta T_j(k-1)\bigr)\\
  &\qquad +m_1n_1\Delta K(k-1)^{n_1-1}
         \bigl(\Delta K(k)-\Delta K(k-1)\bigr)
         \bigr\} e^{\omega(k)}
\end{split}   \\
  l(k) &= m_2{I_{\textrm{load}}}^{n_2}+m_3 \Delta T_j(k)^{n_3}   \\
  y(k) &= s(k)+v_1(k)  \\
  \Delta T_y(k) &= \Delta T_j(k)+v_2(k) \\
  [s(0)\Delta T_j(0)I_{\textrm{load}}] 
       &= [s_0\Delta T_{j0}I_{\textrm{load}}]
\end{align}
\end{document}