help.html

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    <div class="page-header">
        <h1>Help</h1>
    </div>
    <div class="left-align-div">
        <h2>1. Purpose of ViroCon</h2>
        <p>
            ViroCon helps you design marine structures, which need to
            withstand load combinations based on wave, wind and current. It
            lets you identify extreme environmental conditions with a defined
            return period using the environmental contour method. ViroCon is
            built to cover the complete workflow to derive an
            environmental contour, which can be seperated
            into three steps:
        </p>
        <ol>
            <li>
                Upload data, which describes the environment (wave, wind,
                current, ...).
            </li>
            <li>
                Fit a probabilistic model to these data (or alternatively enter
                the probabilistic model directly).
            </li>
            <li>
                Compute the environmental contour.
            </li>
        </ol>
        The implemented methods to address these steps align with DNVGL's
        current recommended practices for environmental conditions and
        environmental loads [1].
        <h2>2. Measurement data</h2>
        ViroCon allows you to upload measurement data with a file size of up
        to 100 MiB. Measuremennt files are required to follow a file structure
        containing a header and values seperated by semicolons (Fig. 1).
        <div align="center">
            <img src="{% static 'images/example_csv.png' %}"
                 class="img-responsive">
        </div>
        <div class="img-caption">
            Example showing the required file structure if two
            environmental variables are used.
            The first two lines represent the header.
            The first line holds the variable names, it is
            interpreted as "variable name 1",
            "variable name 2".
            The second line holds the variable symbols, it is
            interprted as "variable symbol 1", "variable symbol 2".
            All following lines contain the
            numerical values of the variables, each line represents
            one time step.
            The first column is associated with variable 1, the second
            columne is associated with variable 2. All values must be
            seperated by semicolons.
        </div>
        You can download an example file
        <a href="{% static 'data/1yeardata_vanem2012pdf_withHeader.csv'  %}"
           class="textlink">
           here
        </a>.
        <h2>3. Fitting</h2>
        Fitting is done via maximum likelihood estimation, which is the
        most general method of estimation [2].
        <h2>4. Probabilistic model</h2>
        <p>
            In ViroCon's context a probabilistic model represents a
            probabilistic description of the environment. It describes the
            long-term statistics of the environment with a multivariate
            distribution.
        </p>
        <h3>4.1 Conditonal modeling approach (CMA)</h3>
        <p>
            ViroCon uses the conditonal modeling aproach (CMA) [3] for its
            probabilistic models. In the CMA one environmental variable has a
            marginal distribution and all other environmental variables have
            conditonal distributions.
        </p>
        <h2>5. Environmental contour</h2>
        <p>
            An environmental contour is the boundary of the mathematical region
             that makes up the environmental states that must be considered
            in a design. Along the contour, discrete extreme environmental
            design conditions (EEDCs) can be selected for ultimate load
            calculations (Fig. 2).
            Environmental contours are derived based on a probabilist model.
        </p>
        <div align="center">
            <img src="{% static 'images/coastalengineeringarticle_fig1.jpg' %}"
                 class="img-responsive">
        </div>
        <div class="img-caption">
            Fig. 2. Concept of an environmental contour. (a) The environmental
            contour encloses all variable combinations, which must be
            considered in the design process (the design region).
            (b) Flowchart describing the design process utilizing an
            environmental contour. Image and caption from Haselsteiner
            <i>et al.</i>
            [4].
        </div>
        <p>
            There exist different mathematical definitions for environmental
            contours. ViroCon supports the following two definitons for
            environmental contours:
        </p>
        <ul>
            <li>Inverse first order reliability method (IFORM) contour [5]</li>
            <li>Highest density contour (HDC) [4]</li>
        </ul>
        <p>
            Other definitions, which are currently not supported are:
        </p>
        <ul>
            <li>Huseby's approach based on hyperplanes and the Monte Carlo
            method [6]</li>
            <li>Inverse second order reliability method (ISORM) contour
                [7]</li>
        </ul>
        <h3>5.1 Inverse first order reliability method (IFORM)</h3>
        <p>
            Contours based on the inverse first order reliability method (IFORM)
            are defined by hyperplanes in the standard normal space.
            Consequently, the probabilistic model is first transformed to the
            normal space. There, the environmental contour is defined as a
            hypersphere. Then, this hypersphere is transformed back to the
            original space (Fig. 3).
        </p>
        <div align="center">
            <img src="{% static 'images/coastalengineeringarticle_fig3_iform.jpg' %}"
                 class="img-responsive">
        </div>
        <div class="img-caption">
            Fig. 3. Contour based on the inverse first order reliability method.
            Image altered from Haselsteiner <i>et al.</i> [4].
        </div>
        More information on the IFORM contour can be found
        in the publication from Winterstein <i>et al.</i> [5], which introduced the
        method.
        <h3>5.2 Highest density contour (HDC) </h3>
        <p>
            A highest density contour (HDC) is defined in the original
            variable space. The contour <i>C</i> is the boundary of the
            highest density region <i>R</i>:
            <div class="equation-at-help">
                {% latexify 'C(f_m) = \{ x:x \in \mathbb{R}^p, f(x) = f_m\}' math_inline=True %},
            </div>
            <div class="equation-at-help">
                {% latexify 'R (f_m) = \{x:x \in \mathbb{R}^p, f(x) \geq f_m \}' math_inline=True %},
            </div>
            <div class="equation-at-help">
                {% latexify '\int_{R(f_m)} f(x)dx = 1 - \alpha' math_inline=True %},
            </div>
        </p>
        <p>
            where <i>α</i> is the exceedance
            probability, which depends on the return period <i>T</i> (in years) and the
            environmental state duration <i>D</i> (in hours):
            <div class="equation-at-help">
                {% latexify '\alpha = \dfrac{1}{n} = \dfrac{1}{T \times 365.25 \times 24/D}' math_inline=True %}.
            </div>
        </p>
        <p>
            By definition a highest density contour has constant probability
            density along
            its path and encloses a region that contains 1-<i>α</i> probability
            (Fig. 4).
        </p>
        <div align="center">
            <img src="{% static 'images/coastalengineeringarticle_fig2_iform_hdc.jpg' %}"
                 class="img-responsive">
        </div>
        <div class="img-caption">
            Fig. 4. Definition of a highest density contour. Image altered from
            Haselsteiner <i>et al.</i> [4].
        </div>
        More information on the highest density contour method can be found
        in the publication from Haselsteiner <i>et al.</i> [4], which introduced the
        method.
        <h2>References</h2>
        <p>
            <a href="https://rules.dnvgl.com/docs/pdf/dnv/codes/docs/2010-10/rp-c205.pdf"
               class="textlink">
                [1] Det Norske Veritas (2010): Recommended practice - DNV-RP-
                C205 Environmental conditions and environmental loads.
                Technical report.
            </a>
            <br>
            <a href="https://doi.org/10.1002/0471667196.ess1571.pub2"
               class="textlink">
                [2] Scholz, F.W. (2006). Maximum likelihood estimation.
                In Encyclopedia of statistical sciences (eds S. Kotz,
                C.B. Read, N. Balakrishnan, B. Vidakovic and N.L. Johnson).
            </a>
            <br>
            [3] E. Bitner-Gregersen, S. Haver (1991): Joint environmental
            model for reliability calculations, in: Proceedings of the
            International Offshore and Polar Engineering Conference.
            Edinburgh, United Kingdom, 1991.
            <br>
            <a href="https://doi.org/10.1016/j.coastaleng.2017.03.002"
               class="textlink">
                [4] A.F. Haselsteiner, J.-H. Ohlendorf, W. Wosniok, K.-D.
                Thoben (2017): Deriving environmental contours
                from highest density regions, Coastal Engineering 123, 42-51.
            </a>
            <br>
            [5] S. Winterstein, T. Ude, C. Cornell, P. Bjerager, S. Haver
            (1993): Environmental parameters for extreme
            response: inverse FORM with omission factors, in: Proceedings,
            ICOSSAR-93. Innsbruck, Austria, 1993.
            <br>
            <a href="https://doi.org/10.1016/j.oceaneng.2012.12.034"
               class="textlink">
                [6] A.B. Huseby , E. Vanem, B. Natvig (2013): A new approach
                to environmental contours for ocean engineering
                applications based on direct Monte Carlo simulations,
                Ocean Engineering 60, 124-135.
            </a>
            <br>
            <a href="https://doi.org/10.1016/j.marstruc.2018.03.007"
               class="textlink">
                [7] W. Chai, B.J. Leira (2018): Environmental contours
                based on inverse SORM,
                Marine Structures 60, 34-51.
            </a>
            <br>
        </p>
        <h2>Developers</h2>
        <p>
            <strong>Repo.</strong>
            ViroCon's GitHub repository can be found
            <a href="https://github.com/virocon-organization/viroconweb"
               class="textlink">
                here.
            </a>
        </p>
        <p>
            <strong>Docs.</strong>
            ViroCon's documentation can be found
            <a href="https://virocon-organization.github.io/viroconweb"
               class="textlink">
                here.
            </a>
        </p>
        <p>
            <strong>Viroconcom.</strong>
            ViroCon uses our python package called 'viroconcom', which is purely
            dedicated to the statistical computations.
            It has its own
            <a href="https://github.com/virocon-organization/viroconcom"
               class="textlink">GitHub repository</a>
            and its own
            <a href="https://virocon-organization.github.io/viroconcom/"
               class="textlink">
                documentation
            </a>.
        </p>
        <h2>Still questions?</h2>
        <p>
            Send us an
            <a href="mailto:virocon@unibremen.de" class="textlink">
                email
            </a>
            .
        </p>
        <p>
            Or in case you spotted a bug or have a feature request, open
            an issue at our
            <a href="https://github.com/virocon-organization/viroconweb/issues"
               class="textlink">
                GitHub repository
            </a>
            .
        </p>
    </div>
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