does you router not have a security or system log, available from the admin page? Chances are your router is being pinged, but it doesn't mean that someone is trying to attack you What router are you using?
t looks like a standard model with the usual features. As long as you keep the DMZ feature turned off people can not ping past the router into your computers. There are sites available that will check the security of your network from the internet to verify the router is doing it's job. Google ping checks.