Advanced Log Correlation and Anomaly Detection System

Construct a sophisticated Bash-based log aggregation and analysis pipeline that can ingest logs from multiple distributed systems, perform real-time pattern matching, and detect potential security incidents or performance anomalies. The script should support parsing various log formats (JSON, syslog, custom), implement machine learning-inspired anomaly detection algorithms, and generate both immediate alerts and long-term trend analysis reports. Include elasticsearch/Splunk export capabilities and support for multiple log sources.