The following error occurs during a MySQL database backup:

InnoDB: Operating system error number 24 in a file operation.
InnoDB: Error number 24 means ‘Too many open files’ 
InnoDB: Some operating system error numbers are described at http://dev.mysql.com/doc/refman/5.7/en/operating-system-error-codes.html 

It is found that there are too many data files:

a total of 90811 data files.

View number of open files:

[root@localhost ~]# ulimit -Sn
1024
[root@localhost ~]# ulimit -Hn
4096

Description of this check command:

ulimit [-HSTabcdefilmnpqrstuvx [limit]]
              Provides  control over the resources available to the shell and to processes started by it, on systems that allow such control.  The -H and -S options specify that the hard or soft
              limit is set for the given resource.  A hard limit cannot be increased by a non-root user once it is set; a soft limit may be increased up to the value of the hard limit. 
  -n     The maximum number of open file descriptors (most systems do not allow this value to be set)

Query the maximum number of files opened by the operating system:

# cat /proc/sys/fs/nr_open
1048576

In the file/etc/security/limits Conf settings:

mysql hard nofile 65535
mysql soft nofile 65535

mysql hard nproc 65535
mysql soft nproc 65535

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the problem of re backup is solved.