{"id":699,"date":"2024-12-30T23:43:59","date_gmt":"2024-12-30T22:43:59","guid":{"rendered":"https:\/\/alma-consulting.eu\/?p=699"},"modified":"2025-01-12T23:47:43","modified_gmt":"2025-01-12T22:47:43","slug":"working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification","status":"publish","type":"post","link":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/","title":{"rendered":"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification"},"content":{"rendered":"\n

What are we doing here?<\/h2>\n\n\n\n

This second post comes as more in-depth and practical answer to the very simple question:<\/p>\n\n\n\n

What is this sensor\u2019s (instrument, setup) resolution? Or, more practically, how can I determine\/identify my sensors\u2019 instrumental noise.<\/em><\/p>\n\n\n\n

After all, forgetting the principles and keeping to the basics, rather than making theoretical estimations, we would like to directly measure the \u201cnoise\u201d added by the actual instrument itself (and not by relying on some dummy transducer as we did previously). Indeed, indirect measurements has the following downsides: i\/ it is still to prone to extrapolation error and ii\/ it is not always possible (typically, for situations with integrated electronics, i.e. when transducer and electronics cannot be separated – a very common situation nowadays). As seen in part 1, direct measurement at least in principle, can be very simply performed by either one of the following two methods:<\/p>\n\n\n\n

  1. corrected difference.<\/li>
  2. spectral correlation correlation.<\/li><\/ol>\n\n\n\n

    Sadly enough, both methods (\u2018two channels methods\u2019) suffer from the same limitations. Namely, they work under the hypothesis that the pair of particular sensors used for the characterization consists of two units with perfectly identical self-noise and frequency responses<\/em> (in other words, the sensors are not required to be perfect i.e. have no deviation but the sensor-to-sensor deviation has to be sufficiently small). More precisely, this implies that the instrumental noise to be measured is larger than the actual signal magnitude multiplied by the module of mismatch<\/em> between frequency responses. For sensors with high-sensitivity and low noise, this pre-requisite can be very difficult to achieve.<\/p>\n\n\n\n

    Hence, we will be looking for an approach not requiring such ideal conditions.<\/p>\n\n\n\n

    Three-sensors method<\/strong><\/h2>\n\n\n\n

    Using appropriate signal processing, it is possible to isolate the signal and the noise, even in the general case of sensors with different frequency reponse functions. As far as I know, the idea dates back to the old Testament, namely the book by Bendat and Piersol ([1] originally from 1971, see \u00a7 6.2.3).<\/p>\n\n\n\n

    For those that are curious, I will outline the reasoning : let\u2019s assume we have a series of co-located sensors, all measuring the same physical signal (mesurand X<\/em>)  .<\/p>\n\n\n\n

    The series of output signals ((1,..i ..n) have Fourier transform Yi<\/em> related to the signal X<\/em>, individual frequency response Hi<\/em> and instrumental noise Ni<\/em> by :<\/p>\n\n\n\n

    (1) <\/span>   <\/span>\"\begin{equation*} {Y}_{i} = {H}_{i} . X + {N} _{i} \end{equation*}\"<\/p><\/p>\n\n\n\n

    Assuming that the mesurand and the instrument noise are un-correlated, the cross PSD between the i-th and j-th sensors reads :<\/p>\n\n\n\n

    (2) <\/span>   <\/span>\"\begin{equation*} P_{ij}= H_i H^*_jP_{XX}+N_{ij}\end{equation*}\"<\/p><\/p>\n\n\n\n

    This is worth reiterating : using noisy sensors, we can still get noise-freea ( in the sense of unbiased<\/em> ) estimates of the cross spectral density between sensors. Conversely, only the direct (auto) spectral density will remain contaminated by the instrumental noise (in the sense that averaging will not eliminate its contribution). This is the central idea here : avoiding using direct PSD\u2019s.<\/p>\n\n\n\n

    Using the previous equation for three sensors (i ,j,k), the frequency response ratio <\/em>can be found :<\/p>\n\n\n\n

    (3) <\/span>   <\/span>\"\begin{equation*} \dfrac{P_{ji}}{P_{kl}} = \dfrac{H_j}{H_k} \end{equation*}\"<\/p><\/p>\n\n\n\n

    (i.e. since the cross-spectral density is unbiased, the cross-spectral density ratio is also unbiased).<\/p>\n\n\n\n

    The last step involves the estimation of the direct to cross-spectral density ratio estimation:<\/p>\n\n\n\n

    (4) <\/span>   <\/span>\"\begin{equation*} \dfrac{P_{ii}} {P_{ji}} = \dfrac{H_i}{H_j} +\dfrac{N_ii}{P_{ji}}\end{equation*}\"<\/p><\/p>\n\n\n\n

    In this expression, all quantities are known except for the self-noise Nii<\/em>, so that we finally arrive at the desired formula :<\/p>\n\n\n\n

    (5) <\/span>   <\/span>\"\begin{equation*} N_{ii} = P_{ii} -P_{ji} \dfrac{P_{ik}}{P_{jk}}\end{equation*}\"<\/p><\/p>\n\n\n\n\n\n\n\n

    Practical Method, Limitations and Results<\/strong><\/h2>\n\n\n\n

    As we know, the above formula is only valid in a mathematical -i.e. idealized- sense. Actual values will be statistical estimated of the 4 required quantities (And all of them will only converge to their final value after a number of averages which may or may not be achievable in practice). Again, we refer to [1] for details, but for now let\u2019s just remind that the relative error on obtained using n averages (i.e. averaging n<\/em> short term DFT\u2019s) can be approximated as:<\/p>\n\n\n\n

    (6) <\/span>   <\/span>\"\begin{equation*} \epsilon = \dfrac{1} {\sqrt{n}}\end{equation*}\"<\/p><\/p>\n\n\n\n

    Now, let\u2019s say that the noise PSD we are looking for accounts for 50 % of the total PSD (this, of course, we don\u2019t know beforehand. I am just making things up to clarify the discussion). And, in order to be in a position to compare various sensors and setups we wish for no more than 10 % uncertainty on the instrumental noise estimation .<\/p>\n\n\n\n

    It follows that we should be able to estimate PSD down to 5 % relative error, so that a minium of 1\/(0.05)^2= 400 averages is required. That\u2019s already a lot of data to be collected, we will come back to this point in an upcoming article.<\/p>\n\n\n\n

    Now let\u2019s make a numerical test case. We will assume 3 signals recorded for a duration of 1000s, originating from different sensors.<\/p>\n\n\n\n

    Let\u2019s say our 3 sensors have noise standard deviations within \u00b1 20 %, and sensitivities within 5 %.<\/p>\n\n\n\n

    A short Matlab\/Octave script can be written for that purpose. Let\u2019s select the numerical parameters. We select comparable amplitudes (1-sigma deviation) for both the mesurand (i.e. actual physical quantity existing at the sensors input) and the instrumental noise.<\/p>\n\n\n\n

    fSampling=256;  % sps   - sampling frequency\nduration=1000;  % s     - simulated record duration\n \n% assumed RMS amplitude for signal (i.e. mesurand)\nsigmaX=1e-4;\n \n% assumed RMS amplitude for white noise (1-standard deviation)\nsigmaN1=0.8e-4;\nsigmaN2=1.2e-4;\nsigmaN3=1.0e-4;<\/code><\/pre>\n\n\n\n
    First, we create our test signals :<\/p>\n\n\n\n
    <\/pre>\n\n\n\n
    %% create mesurand and noises realization\nnSamples=fSampling*duration;\n \nsignal=sigmaX*randn(nSamples,1);\n \nn1=sigmaN1*randn(nSamples,1);\nn2=sigmaN2*randn(nSamples,1);\nn3=sigmaN3*randn(nSamples,1);\n \n% superimpose signal and noise to get measured quantities\n% This is what we can observe in real life.\ny1=signal+n1;\ny2=signal+n2;\ny3=signal+n3;\n \n% merge 3 signal vectors into a signal matrix (nSamplesx3). \ny=cat(2,y1,y2,y3);\n<\/code><\/pre>\n\n\n\n
    Now, let\u2019s compute the observed signals cross-power spectral density matrix. Using the \u2018MIMO\u2019 option, the result is stored as a 3D matrix, with size (nFFTlinesxnChannelsxnChannels) :<\/p>\n\n\n\n
    %% Extract noise from redudant measurements\n\n% Step1: Create Cross-PSD matrice\nnFFT=fSampling;         % 1Hz frequency resolution\nnOverlap=nFFT\/2;\nnAverage=nSamples\/nFFT;\nwindow=hanning(nFFT);   % window\ndf=fSampling\/nFFT;      % frequency resolution  \n[Pyy,f]=cpsd(y,y,window,nOverlap,nFFT,fSampling,'mimo');\n<\/code><\/pre>\n\n\n\n
    Lastly, let\u2019s estimate the extraneous noise for each of the 3 channels:<\/p>\n\n\n\n
    %  Step2: Extract various noise PSD's\nN11=extractExtraneousNoise(Pyy,1,2,3);\nN22=extractExtraneousNoise(Pyy,2,3,1);\nN33=extractExtraneousNoise(Pyy,3,1,2);\n<\/code><\/pre>\n\n\n\n
    The local function extractExtraneousNoise function simply reads :<\/p>\n\n\n\n
    function Nii=extractExtraneousNoise(Pyy,i,j,k)\n    Pii=Pyy(:,i,i);\n    Pji=Pyy(:,j,i);\n    Pik=Pyy(:,i,k);\n    Pjk=Pyy(:,j,k);\n    Nii=Pii-Pji.*(Pik.\/Pjk);\nend\n<\/pre>\n\n\n\n
    Now, how good are the results? I let you decide.<\/p>\n\n\n\n
    \"\"
    Instrument’s noise PSD’s as estimated using the 3 channels method – 100 averages<\/figcaption><\/figure>\n\n\n\n
    A few comments follow :<\/p>\n\n\n\n
    -the PSDs are not quite smooth, but this was to be expected : using 100 averages, the spectral estimator has a standard deviation of 10 %, so that we have to expect individual results to be contained in +\/-30 % around the \u00ab true \u00bb value.<\/p>\n\n\n\n
    -the total variance is perfectly well estimated, the deviation to the true value being less than 1 %, whichever the channel. This is also to be expected (the deviation of the total energy being equal to the deviation of the individual components divided by the number of terms in the sum, here there are 128 of them since the analysis bandwidth is 128Hz and we have selected a 1Hz frequency resolution). Hence, the 1-sigma relative uncertainty is 0.1\/(128)^(1\/2)~0.004, i.e. a 3-sigma relative error of about 2.4 %.<\/p>\n\n\n\n
    So far, so good, now let\u2019s turn to a real life test case.<\/p>\n\n\n\n\n\n\n\n
    Real-life test case<\/strong><\/h2>\n\n\n\n
    Finally, we want to test our method on real-life signals. The setup comprises 3 high sensitivity accelerometers (model CA YD-119, 1000pC\/m\/s\u00b2), a MMF model M72B3 charge amplifier, and a DT 9837A DAQ. The entire setup is located in a low vibration environment: our lab is located in a basement with heavy masonry walls, and the setup is resting on a heavy (20mm thick), steel plate.<\/p>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    Applying the same signal processing procedure as previously, the sensors noise spectral content (expressed as Amplitude Spectral Density of acceleration, i.e. mm\/s\u00b2\/(Hz)^(1\/2)) is obtained as follows:<\/p>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    As expected, the 3 DUT\u2019s being identical, they provide very similar estimates, with an exception around 12Hz. At this frequency, the physical signal content completely dominates the measurements (it comes from a highway bridge located about 250m away, continuously excited by road traffic), so that the estimate is poor and the corresponding values should be discarded. This is of course not a problem: since the noise is known to have a smooth spectral content, it is legitimate to discard the data and fill-in by linear interpolation (in log-log units).<\/p>\n\n\n\n
    Nota: since the DAQ has 4 input channels, the last one has been fitted with a 50ohm shunt, so that digitizer\u2019s noise could be estimated. This confirms that the overall measurement noise levels are dominated by the transducer\u2019s electronics.<\/p>\n\n\n\n\n\n\n\n
    Where to we go from here?<\/strong><\/h2>\n\n\n\n
    To summarize, we have at our disposal a simple method allowing to isolate the instrumental noise of any setup, provided that we have 3 independent sensors (not necessarily identical). The convergence rate will be dependent on the Signal to Noise Ratio, but ultimately this estimator is unbiased, it will converge to the true value.<\/p>\n\n\n\n
    The ultimate objective, of course in not to perform a beauty contest among sensors. What we want to do is performing actual measurements in the field, where signal levels can not be controlled (in particular, OMA tasks, or even more specifically, the directly useful motion transmissibility functions ).<\/p>\n\n\n\n
    Knowing one\u2019s sensor noise allows of course to wisely choose among vendor\u2019s (and trust me, you can\u2019t trust them. Well, not all of them).<\/p>\n\n\n\n
    But what are we to do with the numbers. Say, we have this PSD amplitude of 10-3<\/sup>mm\/s\u00b2\/Hz1\/2 <\/sup>around 1Hz. How small or big is that number, anyway?<\/p>\n\n\n\n
    Perhaps the simplest way to decide on this is to compare with the natural earth background noise. After all, if the instrumental noise is comparable to the earth background noise or even below, this means, at least in principle that we will never need artificial excitation to characterize an actual structure. The trouble being that, background noise it is heavily dependent on the actual location being considered, even letting aside cultural (human induced) contribution.<\/p>\n\n\n\n
    To illustrate this, let\u2019s turn to another classic, the paper by Peterson [2].<\/p>\n\n\n\n
    \"\"
    New High Noise Model and New Low Noise Model according to Peterson93 [2]<\/figcaption><\/figure>\n\n\n\n
    It appears that, at least for the most seismically active regions, the background noise expressed using acceleration has PSD amplitude around 1Hz about 10-12<\/sup> (m\/s\u00b2)^2\/Hz, that is an Amplitude Spectral Density of about 10-6<\/sup> (m\/s\u00b2)^2\/Hz1\/2<\/sup>. Now, here comes the good news: that\u2019s about the same level than that of our instrument setup. And for frequencies above 1Hz, the signal-noise-ratio would become largely positive.<\/p>\n\n\n\n
    In real life, the micro-seismic noise will generally exhibit a significant -if not dominant- contribution from the cultural noise above 2Hz. The natural environment will also play a role. For example nearby buildings or trees act as \u201ctransducers\u201d, converting the wind power into ground vibrations. Rail or road traffic, obviously, will tend to contribute, with an efficiency drastically dependent on track or road condition.<\/p>\n\n\n\n
    Conclusion<\/strong><\/h2>\n\n\n\n
    As it appears, there are indeed lots of situations where a conventional vibration measurement setup, with suitable configuration and adequate shielding from external influences, can be used to characterize large structures and components, only by taking advantage of background vibrations.<\/p>\n\n\n\n
    Now, there will always be some need for de-noising of some sort, but we will save those aspects for an upcoming article. In the meantime, happy holidays to you all and see you in 2025.<\/p>\n\n\n\n
    References<\/h2>\n\n\n\n
    1. J. Bendat and A. Piersol \u2013 Random Data \u2013 Analysis and measurement procedures – 4th<\/sup> edition – Wiley.<\/li>
    2. J. Peterson \u2013 Observation and modeling of seismic background noise \u2013 USGS \u2013 Open File report 93-322<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"
      What are we doing here? This second post comes as more in-depth and practical answer to the very simple question: What is this sensor\u2019s (instrument, setup) resolution? Or, more practically, how can I determine\/identify my sensors\u2019 instrumental noise. After all, forgetting the principles and keeping to the basics, rather than making theoretical estimations, we would […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-699","post","type-post","status-publish","format-standard","hentry","category-technical-literature"],"yoast_head":"\nWorking Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\" \/>\n<link rel=\"next\" href=\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting\" \/>\n<meta property=\"og:description\" content=\"What are we doing here? This second post comes as more in-depth and practical answer to the very simple question: What is this sensor\u2019s (instrument, setup) resolution? Or, more practically, how can I determine\/identify my sensors\u2019 instrumental noise. After all, forgetting the principles and keeping to the basics, rather than making theoretical estimations, we would […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\" \/>\n<meta property=\"og:site_name\" content=\"Alma Consulting\" \/>\n<meta property=\"article:published_time\" content=\"2024-12-30T22:43:59+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-01-12T22:47:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png\" \/>\n<meta name=\"author\" content=\"admin9661\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin9661\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\"},\"author\":{\"name\":\"admin9661\",\"@id\":\"https:\/\/alma-consulting.eu\/#\/schema\/person\/67349dff7b3613d00b9310b853e1544c\"},\"headline\":\"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification\",\"datePublished\":\"2024-12-30T22:43:59+00:00\",\"dateModified\":\"2025-01-12T22:47:43+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\"},\"wordCount\":1852,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/alma-consulting.eu\/#organization\"},\"image\":{\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png\",\"articleSection\":[\"Technical Literature\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\",\"url\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\",\"name\":\"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting\",\"isPartOf\":{\"@id\":\"https:\/\/alma-consulting.eu\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png\",\"datePublished\":\"2024-12-30T22:43:59+00:00\",\"dateModified\":\"2025-01-12T22:47:43+00:00\",\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage\",\"url\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png\",\"contentUrl\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png\",\"width\":875,\"height\":656},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/alma-consulting.eu\/#website\",\"url\":\"https:\/\/alma-consulting.eu\/\",\"name\":\"Alma Consulting\",\"description\":\"No limits, except for physics\",\"publisher\":{\"@id\":\"https:\/\/alma-consulting.eu\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/alma-consulting.eu\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/alma-consulting.eu\/#organization\",\"name\":\"Alma Consulting\",\"url\":\"https:\/\/alma-consulting.eu\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/alma-consulting.eu\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2020\/06\/LOGO_V1_bis.png\",\"contentUrl\":\"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2020\/06\/LOGO_V1_bis.png\",\"width\":1579,\"height\":447,\"caption\":\"Alma Consulting\"},\"image\":{\"@id\":\"https:\/\/alma-consulting.eu\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.linkedin.com\/in\/nicolas-jobert\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/alma-consulting.eu\/#\/schema\/person\/67349dff7b3613d00b9310b853e1544c\",\"name\":\"admin9661\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/alma-consulting.eu\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/4a042c685169086f29596c15b956a482?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/4a042c685169086f29596c15b956a482?s=96&d=mm&r=g\",\"caption\":\"admin9661\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/","next":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/2\/","og_locale":"en_US","og_type":"article","og_title":"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting","og_description":"What are we doing here? This second post comes as more in-depth and practical answer to the very simple question: What is this sensor\u2019s (instrument, setup) resolution? Or, more practically, how can I determine\/identify my sensors\u2019 instrumental noise. After all, forgetting the principles and keeping to the basics, rather than making theoretical estimations, we would […]","og_url":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/","og_site_name":"Alma Consulting","article_published_time":"2024-12-30T22:43:59+00:00","article_modified_time":"2025-01-12T22:47:43+00:00","og_image":[{"url":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png","type":"","width":"","height":""}],"author":"admin9661","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin9661","Est. reading time":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#article","isPartOf":{"@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/"},"author":{"name":"admin9661","@id":"https:\/\/alma-consulting.eu\/#\/schema\/person\/67349dff7b3613d00b9310b853e1544c"},"headline":"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification","datePublished":"2024-12-30T22:43:59+00:00","dateModified":"2025-01-12T22:47:43+00:00","mainEntityOfPage":{"@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/"},"wordCount":1852,"commentCount":0,"publisher":{"@id":"https:\/\/alma-consulting.eu\/#organization"},"image":{"@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage"},"thumbnailUrl":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png","articleSection":["Technical Literature"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/","url":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/","name":"Working Wonders with Dynamic Instrumentation \u2013 Ep02: Instrumental Noise Identification - Alma Consulting","isPartOf":{"@id":"https:\/\/alma-consulting.eu\/#website"},"primaryImageOfPage":{"@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage"},"image":{"@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage"},"thumbnailUrl":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png","datePublished":"2024-12-30T22:43:59+00:00","dateModified":"2025-01-12T22:47:43+00:00","inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/alma-consulting.eu\/index.php\/2024\/12\/30\/working-wonders-with-dynamic-instrumentation-part-2-instrumental-noise-identification\/#primaryimage","url":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png","contentUrl":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2025\/01\/NoiseASD-100.png","width":875,"height":656},{"@type":"WebSite","@id":"https:\/\/alma-consulting.eu\/#website","url":"https:\/\/alma-consulting.eu\/","name":"Alma Consulting","description":"No limits, except for physics","publisher":{"@id":"https:\/\/alma-consulting.eu\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/alma-consulting.eu\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/alma-consulting.eu\/#organization","name":"Alma Consulting","url":"https:\/\/alma-consulting.eu\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/alma-consulting.eu\/#\/schema\/logo\/image\/","url":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2020\/06\/LOGO_V1_bis.png","contentUrl":"https:\/\/alma-consulting.eu\/wp-content\/uploads\/2020\/06\/LOGO_V1_bis.png","width":1579,"height":447,"caption":"Alma Consulting"},"image":{"@id":"https:\/\/alma-consulting.eu\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.linkedin.com\/in\/nicolas-jobert\/"]},{"@type":"Person","@id":"https:\/\/alma-consulting.eu\/#\/schema\/person\/67349dff7b3613d00b9310b853e1544c","name":"admin9661","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/alma-consulting.eu\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/4a042c685169086f29596c15b956a482?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/4a042c685169086f29596c15b956a482?s=96&d=mm&r=g","caption":"admin9661"}}]}},"_links":{"self":[{"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/posts\/699","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/comments?post=699"}],"version-history":[{"count":26,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/posts\/699\/revisions"}],"predecessor-version":[{"id":729,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/posts\/699\/revisions\/729"}],"wp:attachment":[{"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/media?parent=699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/categories?post=699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alma-consulting.eu\/index.php\/wp-json\/wp\/v2\/tags?post=699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}