Resolution:
There are two ways to separate BWSE component logs for the Stdout log:
1-    Use Classical Logging:

- Upload your Service Assembly (SA) into the AMX Admin.
- Map it to a node.
- Go to Service Unit/BW Loggings tab and change the value of "Engine.Log.Type" to "classic".
- Deploy and start the SA.
- Check folder "\tibco-home\amx\data\< environment >\&ltnode>\bin\logs". Under this folder, a file gets created for BWSE logs.
The file name format is "&ltenvironment>-&ltnode>-httpwww.example.com< AMX SOA project >-BusinessWorks.log
Check this file for all BWSE related logs.

2-    Use Log4j Logging:

- Upload your Service Assembly (SA) into the AMX Admin.
- Map it to a node.
- Go to Logging Configurations and select your Object.
- Edit and select File for Appender and All for Severity; enter the location of the File (i.e. c:/BWSE.log),
specify the Max File Size, Max Index and then save.
- Go to Service Unit/BW Loggings tab and change the value of "Engine.Log.Type" to "log4j".
- Deploy and start the SA.
- Check “c:/BWSE.log ".  The file name format is in xml. ( Refer the AMSG Documentation Chapter 10. Managing Logging – Log files – View Logging in Business Studio) or can user Log Viewer in Administrator to view the log files.

How to separate the BWSE component logs for the Stdout log?