This　paper　proposed　a　single-piston　free　piston　expander-linear　generator　(SFPE-LG)　prototype　applied　to　organic　Rankine　cycle　systems.　Two　valve　timing　control　strategies,　namely,　time　control　strategy　(TCS)　and　position　control　strategy　(PCS),　were　developed.　Based　on　the　experimental　data,　a　back　propagation　neural　network　(BPNN)　prediction　model　was　established.　The　effects　of　structural　parameters　such　as　neural　network　layers,　transfer　function,　training　function,　hidden　layer　nodes,　and　learning　rate　on　the　prediction　accuracy　of　this　BPNN　model　were　discussed.　The　training　and　prediction　accuracy　of　the　BPNN　model　was　verified　using　5-fold　cross-validation　and　Wilcoxon　signed-rank　test.　Moreover,　the　BPNN　model　was　integrated　with　a　genetic　algorithm　to　predict　and　optimize　the　maximum　output　power　of　the　SFPE-LG.　The　results　showed　that　the　BPNN　model　used　to　predict　the　motion　characteristics　and　output　performance　of　the　SFPE-LG　exhibits　strong　learning　ability　and　high　prediction　accuracy.　Notably,　the　prediction　accuracy　of　the　BPNN　model　is　significantly　higher　under　the　PCS　compared　to　TCS.　The　effect　of　hidden　layer　nodes　on　mean　square　error　(MSE)　and　correlation　coefficient　(R)　is　greater　than　that　of　the　learning　rate.　When　the　number　of　hidden　layer　nodes　exceeds　30,　the　BPNN　model　consistently　achieves　low　MSE　and　high　R.　The　optimization　results　showed　that　the　SFPE-LG　can　obtain　a　maximum　output　power　of　141.69　W　under　the　TCS,　when　the　working　parameters　are　inlet　pressure　of　0.7　MPa,　intake　duration　of　35　ms,　load　resistance　of　67　omega,　and　expansion　duration　of　104　ms,　respectively.