On Windows machines, you may often have problems with your updates, either on downloading or applying them to the machines. In my troubleshooting days, I therefore created a little function to retrieve all important logs and event information: 

<#
 .Synopsis
 Gathers all Windows Update relevant logs from the local computer and open the file path.
 .DESCRIPTION
 Gathers all Windows Update relevant logs from the local computer - Get-Hotfix, Get-WindowsUpdateLog and all log in C:Windowslogs
 .EXAMPLE
 Get-WULogs
 .EXAMPLE
 Get-WULogs -LogFilePath 'D:Logs'
#>
function Get-WULogs
{
 [CmdletBinding()]
 Param
 ( 
 # LogFilePath
 [Parameter(Mandatory = $false, 
 Position = 0)]
 $LogFilePath = 'c:TempWindowsUpdateLogs'
 )
 Begin
 {
 if (-not (Test-Path $LogFilePath))
 {
     New-Item -Path $LogFilePath -ItemType Directory
 }
 }
 Process
 { 

 #region variables
 $WUDOFilePathCsv = [System.IO.Path]::Combine($LogFilePath, 'WUDOLog.Clixml')
 $WUDOFilePathCli = [System.IO.Path]::Combine($LogFilePath, 'WUDOLog.Clixml')
 $HotFixFilePathCsv = [System.IO.Path]::Combine($LogFilePath, 'Hotfix.csv')
 $HotFixFilePathCli = [System.IO.Path]::Combine($LogFilePath, 'Hotfix.Clixml')
 $WUFilePath = [System.IO.Path]::Combine($LogFilePath, 'WindowsUpdateEvents.csv')
 $WUFilePathCli = [System.IO.Path]::Combine($LogFilePath, 'WindowsUpdateEvents.Clixml')
 $GetWindowsUpdateLogOutFile = Join-Path -Path (Join-Path -Path ($Env:tmp) -ChildPath 'WindowsUpdateLog') -ChildPath "WindowsUpdateLog.log"
 #endregion

 #region Delivery Optimization logs
 #Get WUDO log
 $WUDOlog = Get-DeliveryOptimizationLog 
 $WUDOlog | Export-Csv $WUDOFilePathCsv
 $WUDOlog | Export-Clixml $WUDOFilePathCli
 #endregion

 #region WinEvents
 $WinEvents = Get-WinEvent -ProviderName Microsoft-Windows-WindowsUpdateClient 
 $WinEvents | Export-Clixml $WUFilePathCli
 $WinEvents | Export-Csv $WUFilePath -Delimiter ';'
 #endregion

 #region HotFixes
 $Hotfixes = Get-HotFix 
 $Hotfixes | Export-Clixml $HotFixFilePathCli
 $Hotfixes | Export-Csv $HotFixFilePathCsv -Delimiter ';'
 #endregion

 #region WindowsUpdateLogs
 #Get-WindowsUpdateLog -SymbolServer https://msdl.microsoft.com/download/symbols
 Get-WindowsUpdateLog -LogPath $GetWindowsUpdateLogOutFile 
 
Copy-Item -Path ($GetWindowsUpdateLogOutFile) -Destination (Join-Path -Path $LogFilePath -ChildPath 'WindowsUpdateLog.log')
Robocopy.exe 'c:Windowslogs' $([System.IO.Path]::Combine($LogFilePath, 'WindowsLogs')) /mir /MT:8 /R:0 /W:0
#endregion

#Open FilePath 
Invoke-Item $LogFilePath
}
End
{}
}

You can easily make changes to this script and use it for your environment to retrieve consolidated troubleshooting information easily from the machines.